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None( #&()+,/159<=>?}Return the error corresponding to an exit code from the Agda process11312071421 6 6*1$( "None( #&()+,/159<=>?QDecoder for bytestringsString to renderResulting builderNone( #&()+,/159<=>?.A data file path relative to the project root.Agda's embedded data files.The subdirectory in the Agda data directory containing the emacs mode.The Agda mode's Emacs Lisp files, given in the order in which they should be compiled.None) #&()+,/159<=>?D8Run an action with an exclusive lock over the given pathNone( #&()+,/159<=>?The standard semiring on s.HasZero is needed for sparse matrices, to tell which is the element that does not have to be stored. It is a cut-down version of SemiRing, which is definable without the implicit ?cutoff. Semirings. Addition.Multiplication.Zero. The one is never used in matrix multiplication , one :: a -- ^ One.The standard semiring on s.The standard semiring on s.  - -% %None( #&()+,/159<=>?y%A term with many holes (error value).,A term with one hole and the (old) contents.A constant term. $ None( #&()+,/159<=>?6Guard: return the value a only if the boolean is TrueGuard: return the action f only if the boolean is TrueBranch over a  collection of values.Branch over a 3 collection of values using the supplied action.Better name for .None( #&()+,/159<=>?Modify the contents of an atomic variable. If the continuation fails, or receives an asynchronous exception, the variable is returned to its old state.No thread, *including the calling thread*, can access the contents of the same  while this function is executing, for reading *or* writing. This means that *any* nested use of the variable, as in f var = modifyAtomic var old -> -- ... modifyAtomic var old' -> ... -- (!) readAtomic var -- (!) will result in a deadlock. The new state of the variable is evaluated (to WHNF).:Create a new atomic variable with the given initial value.Read the current state of the atomic variable, waiting if any other thread is modifying it.Like ,  is multiple-wakeup, which means that all threads waiting on a modification will be woken up when it finishes.A mutable variable which can be read from and *modified*. This provides a < combinator with atomic semantics for modification, unlike . None( #&()+,/159<=>?hBoolean algebras.Set difference, dual to .Types isomorphic to .   ' None) #&()+,/159<=>?  Conclude u2 from  funUniv u1 u2 and u1. Conclude u1 from  funUniv u1 u2 and u2.Compute the universe type of a function space from the universe types of domain and codomain.Hacky showing of standard universes, does not take actual names into account.Fibrancy of standard universes.*The successor universe type of a universe.We have IsFibrant < IsStrict.Fibrant universe.Non-fibrant universe.Flavor of standard universe (Prop < Type < SSet,).!Fibrant universe of propositions.Non-fibrant universe.Fibrant universe. kind of the funSort. kind of the domain.* kind of the codomain, if uniquely exists.Have ? kind of the funSort. kind of the codomain. kind of the domain, if unique.   ! !")+/#18& &  None( #&()+,/159<=>? Transform a  CallStack by filtering each CallSiteGet the most recent CallSite in a  CallStack, if there is one. Transform a  CallStack by transforming its list of CallSitePops n entries off a  CallStack using  popCallStack.. Note that frozen callstacks are unaffected.1The same as the un-exported internal function in %GHC.Exceptions (prettyCallStackLines) Prints like: +doFoo, called at foo.hs:190:24 in main:MainPretty-print a  CallStack". This has a few differences from GHC.Stack.prettyCallStackLines. We omit the "CallStack (from GetCallStack)" header line for brevity. If there is only one entry (which is common, due to the manual nature of the  HasCallStack constraint), shows the entry on one line. If there are multiple, then the following lines are indented. CallStack! comprising only the most recent CallSiteType of an entry in a  CallStackType of a filter for CallSite$Type of the name of a function in a CallSite | e.g. proveEverythingType of a column of a SrcLocType of a filename of a SrcLoc | e.g. `srcfullAgdaUtilsFoo.hs`Type of a line number of a SrcLocType of the module name of a SrcLoc | e.g. Type of the package name of a SrcLoc | e.g. `Agda-2.@`#2! None( #&()+,/159<=>?)Total function to convert an integer to a character. Maps surrogate code points to the replacement character U+FFFD.&Is a character a surrogate code point.?Map surrogate code points to the unicode replacement character.%The unicode replacement character  .None+ #&()+,/159<=>?l Add a value to a compact region.:Create a new compact region with given initial block size. None( #&()+,/159<=>?"Expand a telescope of environment variables (each value may refer to variables earlier in the list).&List of environment variable bindings.~. $VARIABLE or  ${VARIABLE}.Ordinary characters.3Tokenization for environment variable substitution.Tokenize a string. The ~ is recognized as $HOME% only at the beginning of the string.Home directory.&Environment variable substitution map.Input.Output with variables and ~ (home) substituted.. ...None( #&()+,/159<=>?            None( #&()+,/159<=>?! #(  None) #&()+,/0159<=>? $Left-associative strict application.applyUnless b f a applies f to a unless b.applyUnlessIts p f a applies f to a unless p a.Monadic version of  applyUnlessapplyWhen b f a applies f to a when b.applyWhenIts p f a applies f to a when p a. version of .Monadic version of  applyWhen version of .Repeat a state transition f :: a -> (b, a) with output b while condition cond on the output is true. Return all intermediate results and the final result where cond is False.(Postconditions (when it terminates): (fst (last (iterWhile cond f a)) == False. $all fst (init (interWhile cond f a)). n f x applies f to x n times and returns the result.)The applications are calculated strictly.Iteration to fixed-point.iterateUntil r f a0 iterates endofunction f, starting with a0 , until r( relates its result to its input, i.e., f a r a.9This is the generic pattern behind saturation algorithms.If f is monotone with regard to r , meaning a r b implies f a r f b , and f-chains starting with a09 are finite then iteration is guaranteed to terminate.*A typical instance will work on sets, and r could be set inclusion, and a0 the empty set, and f- the step function of a saturation algorithm.Monadic version of .Repeat something while a condition on some state is true. Return the last state (including the changes of the last transition, even if the condition became false then).Monadic version of .More general trampoline, which allows some final computation from iteration state a into result type b.Monadic version of .%A version of the trampoline function.The usual function iterates f :: a -> Maybe a as long as Just{}, is returned, and returns the last value of a upon Nothing.usualTrampoline f = trampolineWhile $ a -> maybe (False,a) (True,) (f a).trampolineWhile is very similar to  repeatWhile, only that it discards the state on which the condition went False;, and returns the last state on which the condition was True.Monadic version of .** None( #&()+,/159<=>? ?Composition: pure function after functorial (monadic) function.Any decoration is a lens. set is a special case of dmap.#Any decoration is traversable with traverse = traverseF. Just like any 6 is a functor, so is any decoration, given by just  traverseF , a functor.The true pure for loop.  is a misnomer, it should be forA.?A decoration is a functor that is traversable into any functor.The  superclass is given because of the limitations of the Haskell class system.  traverseF actually implies functoriality.Minimal complete definition:  traverseF or  distributeF.%Decorations commute into any functor. traverseF is the defining property.3Decorations compose. (Thus, they form a category.)%The identity functor is a decoration.0A typical decoration is pairing with some stuff. '%& %'&    !None( #&()+,/159<=>?? (bag ! a) finds all elements equal to a(. O(log n). Total function, returns [] if none are.Return the multiplicity of the given element. O(log n + count _ _).!Returns the bag, with duplicates.O(1) !fromList = unions . map singleton:Returns the elements of the bag, grouped by equality (==). "insert a b = union b (singleton a)#Returns the bag without duplicates.O(n). O(log n). O(log n).Is the bag empty?O(1)7Number of elements in the bag. Duplicates count. O(n).!Returns the bag, with duplicates.A set with duplicates. Faithfully stores elements which are equal with regard to (==).%The list contains all occurrences of a (not just the duplicates!). Hence, the invariant: the list is never empty.   ! $  "+(c) Sven Panne 2002-2005, Andreas Abel 2025 BSD-styleNone( #&()+,/159<=>?Process the command-line, and return the list of values that matched (and those that didn't). The arguments are:The order requirements (see )The option descriptions (see )9The actual command line arguments (presumably got from ). returns a triple consisting of the option arguments, a list of non-options, and a list of error messages.This is almost the same as , but returns a quadruple consisting of the option arguments, a list of non-options, a list of unrecognized options, and a list of error messages.Return a string describing the usage of a command, derived from the header (first argument) and the options described by the second argument.Describes whether an option takes an argument or not, and if so how the argument is injected into a value of type a.no argument expectedoptional argumentoption requires argument.What to do with options following non-options.*freely intersperse options and non-options+no option processing after first non-optionwrap non-options into optionsEach  describes a single option.The arguments to  are:list of short option characters*list of long option strings (without "--")argument descriptorexplanation of option for user description of a single options:2Kind of command line argument (internal use only): an optionan un-recognized option a non-option!end-of-options marker (i.e. "--")something went wrong...Take a look at the next cmd line arg and decide what to do with it.Handle long option.Handle short option.non-option handlingoption descriptorsthe command-line arguments &(options, non-options, error messages)non-option handlingoption descriptorsthe command-line arguments 4(options, non-options, unrecognized, error messages)#minimal width of long option columnheaderoption descriptors'nicely formatted description of optionslist of short option characters*list of long option strings (without "--")argument descriptorexplanation of option for user   ? ?  ) )#None( #&()+,/159<=>?#Importing a whole module qualified.Should not be used when  could be used.Should only be used in let or where.7Unstructured pragma (Andreas, 2017-08-23, issue #2712). ) )> >7 7/ / 2 2, ,         ; ; $None( #&()+,/159<=>?6 The function  makes every function argument and case and generator pattern strict (except for those patterns that are marked as irrefutable, and anything in a  or ). Note that only the outermost patterns are made strict, and that  bindings are not made strict.  8 8  ? ? () ) . - -; ; None) #&()+,/159<=>?%None( #&()+,/159<=>?NReturns a close function for the file together with the contents.&None( #&()+,/159<=>?copyDirContent src dest recursively copies directory src onto dest.First, a to-do list of copy actions is created. Then, the to-do list is carried out.This avoids copying files we have just created again, which can happen if src and dest( are not disjoint. (See issue #2705.)copyIfChanged src dst makes sure that dst' exists and has the same content as dst.Search a directory recursively, with recursion controlled by a RecursionPredicate. Lazily return a unsorted list of all files matching the given FilterPredicate. Any errors that occur are ignored, with warnings printed to stderr.=Action to be carried out for copying a directory recursively.Create directory if missing.Copy file if changed.copyDirContentDryRun src dest; creates a to-do list for recursively copying directory src onto dest.Perform scheduled .&Control recursion into subdirectories.,Decide whether a file appears in the result.Directory to start searching.Files that matched the FilterPredicate.'None( #&()+,/159<=>?RCreates a temporary file, writes some stuff, and returns the filepath(None) #&()+,/159<=>?Reads a UTF8-encoded text file and converts many character sequences which may be interpreted as line or paragraph separators into 'n'.&If the file cannot be decoded, then a  is raised.Reads a UTF8-encoded text file and converts many character sequences which may be interpreted as line or paragraph separators into 'n'.&If the file cannot be decoded, then a  is raised.Writes a UTF8-encoded text file. The native convention for line endings is used.Writes a UTF8-encoded text file. The native convention for line endings is used.*A kind of exception that can be thrown by  and .#Decoding failed for the given file.Converts many character sequences which may be interpreted as line or paragraph separators into 'n'.,Strip the byte order mark (BOM) from a Text. (https://github.com/agda/agda/issues/6524 https://github.com/haskell-hvr/cassava/issues/106#issuecomment-3739861768 8!6 6)None( #&()+,/159<=>?ERead +, modify it strictly, and return old value. *None( #&()+,/159<=>? +Atomically modify the contents of a strict 3. Both the stored value and the result are forced.Modify a strict ? by a applying a function to the value stored in the reference.1This will force the value to WHNF before writing.Create a new strict .This will force the value to WHNF before creating the reference.Read the contents of a strict .Write to a strict .1This will force the value to WHNF before writing.Strict IO references.+None( #&()+,/159<=>?ySemiring with idempotent  == dioidE.g. +neutral element of compose , e.g. zero ,None) #&()+,/159<=>?6 Throw an 1 error reporting the location where you place . Throw an * error reporting the *caller's* call site. Throw an  Unreachable error reporting the *caller's* call site. Note that this call to "withFileAndLine" will be filtered out due its filter on the srcLocModule.Construct a value of 8 reporting the location where you call this function.Abort by throwing an "impossible" error. You should not use this function directly. Instead use  IMPOSSIBLEMonads in which we can catch an "impossible" error, if possible. Catch any  exception. Catch only # exceptions selected by the filter. Version of , with argument order suiting short handlers. Version of , with argument order suiting short handlers."Impossible" errors, annotated with a file name and a line number corresponding to the source code location of the error.We reached a program point without all the required primitives or BUILTIN to proceed forward. (ImpMissingDefinitions neededDefs forThis7We reached a program point which should be unreachable. Impossible with a different error message. Used when we reach a program point which can in principle be reached, but not for a certain run.  ) )2 2/ /, ,-None( #&()+,/159<=>?toImpossible e extracts the  Impossible value raised via  IMPOSSIBLE to create the element e of type Empty. It proceeds by evaluating e to weak head normal form and catching the exception. We are forced to wrap things in a Maybe because of catchImpossible's type.Values of type  are not forced, because ' is used as a constructor argument in .    .None( #&()+,/159<=>?The empty set.not . member b.A singleton set.toSingleton s == Just b iff s == singleton b. The full set.Isomorphic to Set .-"-)-- - -----/None( #&()+,/159<=>?The default termination depth.Cut off structural order comparison at some depth in termination checker?c >= 0( means: record decrease up to including c+1."Numeric literals and addition for . , , ( (0None( #&()+,/159<=>?Inserts a number of new bindings. The last element in the list will have de Bruijn index 0.Converts a list to an <. The last element in the list will have de Bruijn index 0.The  invariant. An empty map.Inserts a new binding, which will have de Bruijn index 0, and shifts other bindings one step.Maps from de Bruijn indices.(Is the index in range for the given map?*Converts a de Bruijn index to a map index.  %1None( #&()+,/159<=>?¨èĨŨƨǨȨɨʨ˨̨ͨΨϨШѨҨӨԨը֨רب٨ڨۨܨݨިߨ2None( #&()+,/159<=>?= All integers `>= n`All integers `< n` No integers. All integers. Invariant. MembershipA single integer.'If finite, return the list of elements.Represents a set of integers. Invariants: - All cannot be the argument to  or  - at most one  IntsBelow - at most one  IntsAbove - if `Below lo` and `Below hi`, then `lo < hi` - if `Below lo .. (Some xs)` then `all (> lo) xs` - if `Above hi .. (Some xs)` then `all (< hi - 1) xs`From a list of integers.       None( #&()+,/159<=>?=?Modify a part of the state monadically, and return some result.Strictly modify a part of the state monadically, and return some result.Modify a part of the state.$Strictly modify a part of the state.'Modify a part of the state monadically.0Strictly modify a part of the state monadically.Write a part of the state.#Strictly write a part of the state.Get inner part i of structure o as designated by  Lens' o i. Focus on given element in a set.#Build a lens out of an isomorphism."Access a map value at a given key.(Build a lens from a getter and a setter.&Only sound if the lenses are disjoint!/Modify a part of the state in a subcomputation.#Modify a part of the state locally.Modify inner part i of structure o using a function i -> i.Strictly modify inner part i of structure o using a function i -> i.Set inner part i of structure o as designated by  Lens' o i.Strictly set inner part i of structure o as designated by  Lens' o i.Read a part of the state.Read part of the environment.Van Laarhoven style homogeneous lenses. Mnemoic: "Lens outer inner", same type argument order as 'get :: o -> i'.2+&A2&A+  " & * . " & * . & * . * . .3None* #&()+,/12359<=>?[ !All indices into an indexed list./Turning an indexed list back into a plain list.!Indices are just natural numbers.>If you have an index you can get a lens for the given element.)Looking up an element in an indexed list./Constructing an indexed list from a plain list.Mapping over an indexed list.Unpacking a wrapped value.4Lists indexed by a type-level list. A value of type All p [xA..xA]% is a sequence of values of types p xA, .., p xA. An index into a type-level list.&Existential wrapper for indexed types.4None( #&()+,/159<=>?P(View source:) This is how you implement a lens for a record field.None( #&()+,/159<=>?)6 A variant of  that might provide more informative error messages if the index is out of bounds.4Precondition: The index should not be out of bounds.*Lookup function (safe). O(min n index).Spine-strict (++).Analogous to zip, combines two lists by taking the union using These (strict).Check whether all consecutive elements of a list satisfy the given relation. O(n).Remove the first representative for each list element. Thus, returns all duplicate copies. O(n log n).&allDuplicates xs == sort $ xs \ nub xs.Checks if all the elements in the list are equal. Assumes that the 6 instance stands for an equivalence relation. O(n). A version of  that avoids a final #. It is right-folding just like .-Precondition: the right-unit law holds, i.e. m  | A.empty = m.A right-folding ( for nonempty lists, never producing .Strict .Breaks a list just after1 an element satisfying the predicate is found.breakAfter even [1,3,5,2,4,7,8]([1,3,5,2],[4,7,8])Breaks a list just after1 an element satisfying the predicate is found. breakAfter1 even 1 [3,5,2,4,7,8](1 :| [3,5,2],[4,7,8]).Break a list when the given predicate returns Just b and place b< as pivot between the prefix (where the predicate returns Nothing) and the suffix.)Crashes when the predicate holds nowhere.5Case distinction for lists, with list first. O(1).Cf. R.5Case distinction for lists, with list first. O(1).Cf. R. Spine-strict catMaybe.2Chop up a list in chunks of a given length. O(n).Chop a list at the positions when the predicate holds. Contrary to wordsBy, consecutive separator elements will result in an empty segment in the result. O(n). *intercalate [x] (chopWhen (== x) xs) == xs6Compute the common prefix of two lists. O(min n m).4Compute the common suffix of two lists. O(n + m).Strict .Strict Check whether all elements in a list are distinct from each other. Assumes that the - instance stands for an equivalence relation.O(n) in the worst case distinct xs == True.downFrom n = [n-1,..1,0] . O(n).Drops from both lists simultaneously until one list is empty. O(min n m).*Drop from the end of a list. O(length). &dropEnd n = reverse . drop n . reverseForces the whole list even for n==0.dropFrom marker xs drops everything from xs starting with (and including) marker.If the marker does not appear, the string is returned unchanged.+The following two properties hold provided marker has no overlap with xs:  dropFrom marker (xs ++ marker ++ ys) == xs dropFrom marker xs == xs Returns an (arbitrary) representative for each list element that occurs more than once. O(n log n).*Implemented using dynamic programming and  Data.Array . O(n*m).Implemented using tree recursion, don't run me at home! O(3^(min n m)).An optimised version of . O(n log n)./Precondition: The list's length must fit in an .Strict .Like , but additionally return the last partition of the list where the predicate is False everywhere. O(n).,Find the longest suffix of the first string xs* that is a prefix of the second string ys. So, basically, find the overlap where the strings can be glued together. Returns the index where the overlap starts and the length of the overlap. The length of the overlap plus the index is the length of the first string. Note that in the worst case, the empty overlap  (length xs,0) is returned.)Worst-case time complexity is quadratic:  O(min(n,m)) where  n = length xs and  m = length ys.There might be asymptotically better implementations following Knuth-Morris-Pratt (KMP), but for rather short lists this is good enough.Find an element satisfying a predicate and return it with its index. O(n) in the worst case, e.g. findWithIndex f xs = Nothing.%TODO: more efficient implementation!?The more efficient implementation. We return a CPS's Maybe result for reliable inlining.A generalised variant of  elemIndex. O(n).Check membership for the same list often. Use partially applied to create membership predicate hasElem xs :: a -> Bool. First time:  O(n log n) in the worst case.Subsequently: O(log n).Specification: hasElem xs == ( xs).Head function (safe). Returns a default value on empty lists. O(1). >headWithDefault 42 [] = 42 headWithDefault 42 [1,2,3] = 17All ways of removing one element from a list. O(n).Lookup function with default value for index out of range. O(min n index).The name is chosen akin to .& of non-empty list, safe. O(n). init1 a as = init (a:as) and  in one go, safe. O(n). Spine-strict . and & of non-empty list, safe. O(n). *initLast1 a as = (init (a:as), last (a:as) Spine-strict .init, safe. O(n).init, safe. O(n).3Last element of non-empty list (safe). O(n). last1 a as = last (a : as)"Last two elements (safe). O(n). last2' x y zs# computes the last two elements of x:y:zs . O(n).Last element (safe). O(n).Last element (safe). Returns a default list on empty lists. O(n).4Case distinction for lists, with list last. O(1). Strict map.Spine-strict map.Strict .Like , but additionally return the last partition of the list where the function always returns Nothing . O(n).Maybe cons. O(1). "mcons ma as = maybeToList ma ++ asPartition a list into first and later occurrences of elements (modulo some quotient given by a representation function).Time: O(n log n).Specification: nubAndDuplicatesOn f xs = (ys, xs List.\\ ys) where ys = nubOn f xs A variant of  that is parametrised by a function that is used to select which element from a group of equal elements that is returned. The returned elements keep the order that they had in the input list. maybe (Left a) Right (f a))Note:  f = snd . partitionMaybe f. Spine-strict .Append a single element at the end. Time: O(length); use only on small lists.Monadic version of sortOn?. The effect is executed exactly once for each list element.&Check whether a list is sorted. O(n).Assumes that the % instance implements a partial order.Split off the largest suffix whose elements satisfy a predicate. O(n).spanEnd p xs = (ys, zs) where  xs = ys ++ zs and all p zs and #maybe True (not . p) (lastMaybe yz).A generalized version of span. O(length . fst . spanJust f).Spine-strict splitAt.#splitExactlyAt n xs = Just (ys, zs) iff  xs = ys ++ zs and genericLength ys = n.Check if a list has a given prefix. If so, return the list minus the prefix. O(length prefix).&stripReversedSuffix rsuf xs = Just pre iff xs = pre ++ reverse suf . O(n).stripSuffix suf xs = Just pre iff xs = pre ++ suf. O(n).Returns a list with one boolean for each non-empty suffix of the list, starting with the longest suffix (the entire list). Each boolean is  exactly when every element in the corresponding suffix satisfies the predicate. An example:    AbCde( = [False, False, False, True, True] For total predicates p and finite and total lists xs the following holds:   p xs =  ( p) ( ( xs)) Tail function (safe). O(1).Tail function (safe). Returns a default list on empty lists. O(1). Spine-strict . -takeExactly a n as == take n (as ++ repeat a)Strict .A generalized version of  takeWhile . (Cf. mapMaybe vs. filter#). @O(length . takeWhileJust f)."takeWhileJust f = fst . spanJust f.Efficient variant of nubBy for finite lists. O(n log n). uniqOn f == 'List.sortBy' (compare `'on'` f) . 'nubBy' ((==) `'on'` f),If there are several elements with the same f--representative, the first of these is kept./Update nth element of a list, if it exists. O(min index n). Precondition: the index is >= 0.:Update the first element of a list, if it exists. O(1).9Update the last element of a list, if it exists. O(n).Spine-strict zipping.Strict . Spine-strict .Like  but keep the rest of the second list as-is (in case the second list is longer). O(n).  zipWithKeepRest f as bs == zipWith f as bs ++ drop (length as) bs 5Requires both lists to have the same length. O(n). Otherwise, Nothing is returned.$Internal state for stripping suffix.Error.+"Positive string" (result). Non-empty list.8"Negative string" to remove from end. List may be empty.The values returned by this function are used to determine which element from a group of equal elements that is returned: the smallest one is chosen (and if two elements are equally small, then the first one is chosen).Two elements are treated as equal if this function returns the same value for both elements. The list before the split point.The list after the split point.""`None( #&()+,/159<=>?0 Return Just x if it's a finite number, otherwise return Nothing.Decode a Double to its mantissa and its exponent, normalised such that the mantissa is the smallest possible number without loss of accuracy.Denotational equality for floating point numbers, checks bitwise equality.NOTE: Denotational equality distinguishes NaNs, so its results may vary depending on the architecture and compilation flags. Unfortunately, this is a problem with floating-point numbers in general.I guess "denotational orderings" are now a thing? The point is that we need an Ord instance which provides a total ordering, and is consistent with the denotational equality.NOTE: The ordering induced via * is total, and is consistent with . However, it is *deeply* unintuitive. For one, it considers all negative numbers to be larger than positive numbers..Encode a mantissa and an exponent as a Double.$Decode a Double to an integer ratio.Checks whether or not the Double is within a safe range of operation.$Encode an integer ratio as a double.Remove suffix .0$ from printed floating point number.The smallest representable mantissa. Simultaneously, the smallest integer which can be represented as a Double without loss of precision.The largest representable mantissa. Simultaneously, the largest integer which can be represented as a Double without loss of precision.$The smallest representable exponent.#The largest representable exponent.++5None( #&()+,/159<=>?There is only one meaningful way to concatenate a finite and an infinite list, justifying the name append = prependList.pad as b! implements the frequent pattern as ++ repeat b. &splitAt n as == (take n as, drop n as)upFrom n = [n..] as properly infinite list. Update the n#th element of an infinite list. (n).Precondition: the index n is >= 0.6None) #&()+,/159<=>?;Update monadically the value at one position (must exist!). Wrapper for  for convenience. Version of forM_ that deigns to be properly lambda-lifted for State, Reader, etc. Version of  insertWith2 that's willing to be properly inlined. The extra c argument is passed down to the insertions unchanged. It can be used to avoid closure creation for the loop.#Check whether a map is a singleton."Filter a map and rewrite the keys.partitionKeys m s =  ( s) m2 but with potential for efficient implementation.partitionMap m m' =  ( m') m2 but with potential for efficient implementation.  7None( #&()+,/159<=>?Map both keys and values where the map is monotonic for the keys.A function that maps both keys and values while preserving the map structure is missing in Data.Map.NonEmpty<. We implement it simplistically here as a combination of  and .A more general type would be )Null m => Map k a -> (Map1 k a -> m) -> m but this type is problematic as we do not have a general %instance Applicative m => Null (m ()).9None+ #&()+,/159<=>?:None( #&()+,/159<=>?"Simple, non-reentrant memoisation.Recursive memoisation, second argument is the value you get on recursive calls.;None) #&()+,/159<=>?       <None( #&()+,/159<=>?  =None( #&()+,/159<=>?p/Function composition in the diagrammatic order./Maximum of on-negative (small) natural numbers. !%    >None( #&()+,/159<=>?Any  is a .Embed .%Represent a non-empty disjunction of s as .8Comparing the information content of two elements of '. More precise information is smaller.Includes equality: x  x == True. Opposites.related a po b iff related b (oppPO po) a.Combining two pieces of information (picking the least information). Used for the dominance ordering on tuples.orPO1 is associative, commutative, and idempotent. orPO has dominant element POAny, but no neutral element.+Are two elements related in a specific way? related a o b holds iff comparable a b is contained in o.Chains (transitivity)  x R y S z.seqPO1 is associative, commutative, and idempotent. seqPO has dominant element POAny and neutral element (unit) POEQ.A ! information is a disjunction of  informations.Inclusion comparison wrapper.Decidable partial orderings.6The result of comparing two things (of the same type).No information (incomparable).EqualGreater or equal. Greater than.Less or equal than. Less than.Pointwise comparison wrapper.1Partial ordering forms a monoid under sequencing.$Partial ordering for disjoint sums: Left _ and Right _ are unrelated.(Sets are partially ordered by inclusion.Sublist for ordered lists. and  _ are unrelated.Partial ordering for Maybe a is the same as for  Either () a..Less is ``less general'' (i.e., more precise).4The pointwise ordering for lists of the same length.There are other partial orderings for lists, e.g., prefix, sublist, subset, lexicographic, simultaneous order.&Pointwise partial ordering for tuples.related (x1,x2) o (y1,y2) iff related x1 o x2 and related y1 o y2.$   #  #  1 /   . $ 4 ; ?None( #&()+,/159<=>?hasLeftAdjoint x checks whether  x^-1 := x  mempty is such that x  y == x^-1 <> y for any y.?Completing POMonoids with inverses to form a Galois connection.Law: composition and inverse composition form a Galois connection. & related (inverseCompose p x) POLE y  == related x POLE (p <> y) Partially ordered monoid."Law: composition must be monotone.  related x POLE x' && related y POLE y' ==> related (x <> y) POLE (x' <> y') Partially ordered semigroup."Law: composition must be monotone.  related x POLE x' && related y POLE y' ==> related (x <> y) POLE (x' <> y') @None( #&()+,/159<=>? Semirings ( &https://en.wikipedia.org/wiki/Semiring).Star semirings ( 5https://en.wikipedia.org/wiki/Semiring#Star_semirings). * ( (2% %ANone( #&()+,/159<=>?     BNone/ #&()+,/159<=>?          &   8   # & ) ,      CNone, #&()+,/159<=>?Strict traversal.   (0&/ /,  2=DNone( #&()+,/159<=>? ENone( #&()+,/159<=>?[ O(log n). Find the given element and return the copy contained in the set. ©éĩũƩǩȩɩʩ˩̩ͩΩϩЩѩҩөԩթ֩שة٩ک۩ܩݩީߩ None( #&()+,/159<=>?  Lossless  . Opposite of  . A more general type would be %Null m => Set a -> (Set1 a -> m) -> m but this type is problematic as we do not have a general %instance Applicative m => Null (m ()). /. /.FNone* #&()+,/159<=>?        GNone* #&()+,/159<=>?        None+ #&()+,/159<=>?          .  *  1  8  6 0 0(  2  ,    " : :0  6  '   8  )  7  =  /None. #&()+,/159<=>?   ( ( ! !  -  +    5  '  /  +  7 7 7   .  &    7HNone- #&()+,/159<=>?    !   . .None. #&()+,/159<=>?    !   ??! ? ?    ?#?( ?6?=   ??? ?*?4 #( ) ).  <INone( #&()+,/159<=>?S  Converts 'A'-'A' to '0'-'9'.-Precondition: The digit needs to be in range. 'Is the character one of the subscripts 'A'-'A'? Increase the suffix by one.  Print suffix.  Parse suffix.  Converts '0'-'9' to 'A'-'A'-Precondition: The digit needs to be in range. &Classification of identifier variants. Identifier ends in number Integer (ordinary digits). Identifier ends in Integer many primes. Identifier ends in number Integer (subscript digits). JNone( #&()+,/159<=>?  Convert a   tagged thing into an  . Partition a list into 3 groups.)Preserves the relative order or elements. Partition a list into 3 groups.)Preserves the relative order or elements. Disjoint sum of three. Enum type with 3 elements.     #  % ) " "   ""    ""   None( #&()+,/159<=>?{ Strict pairing. Monadic ~. Monadic version of @. Monadic .  Order a pair. ~A@ @A~      '  )1   %   3>None( #&()+,/159<=>? Lookup keys in the same association list often. Use partially applied to create partial function apply m :: k -> Maybe v. First time:  O(n log n) in the worst case.Subsequently: O(log n).Specification:  apply m == (# m). O(n). Delete a binding. The key must be in the domain of the finite map. Otherwise, an internal error is raised. O(1). Add a new binding. Assumes the binding is not yet in the list. 9O(n). Get the domain (list of keys) of the finite map. O(n). Named in analogy to . To preserve the invariant, it is sufficient that the key transformation is injective (rather than monotonic). ?+ Strict version of (&&&).   KNone+ #&()+,/12359<=>? All p as ensures that the constraint p is satisfied by all the types in as. (Types is between scare-quotes here because the code is actually kind polymorphic) Arrows [a1,..,an] r corresponds to a1 -> .. -> an -> r | Products [a1,..,an] corresponds to (a1, (..,( an, ())..))  Currying as b# witnesses the isomorphism between  Arrows as b and Products as -> b. It is defined as a type class rather than by recursion on a singleton for as so all of that these conversions are inlined at compile time for concrete arguments. Using IsBase we can define notions of Domains and  CoDomains. which *reduce* under positive information IsBase t ~ 'True even though the shape of t is not formally exposed On Lists  Version of Foldr taking a defunctionalised argument so that we can use partially applied functions.  On Booleans$ $   /    ;  LNone) #&()+,/1359<=>? A known boolean is one we can obtain a singleton for. Concrete values are trivially known. "Singleton for type level booleans.      MNone) #&()+,/159<=>?( Checks if two arguments are equal as pointers in memory. Please note, that this function is a hack, and it can worsen the behavior of compiler. See  https://gitlab.haskell.org/ghc/ghc/-/blob/d151546e59a50158f25c3df6728b00d3c27bb4b9/compiler/GHC/Builtin/primops.txt.pp#L3455.  NNone( #&()+,/159<=>? Mark a computation as dirty. Map a  ( computation (monad transformer action). Run a  0 computation, returning result plus change flag. Run a  0 computation, returning result plus change flag. Blindly run an updater. Blindly run an updater. Replace result of updating with original input if nothing has changed. The ChangeT monad transformer. The class of change monads. Like , but preserving sharing. Like  Bifunctor, but preserving sharing.Eval an updater (using  ). 8A mock change monad. Always assume change has happened. -Mark computation as having changed something.  = sharing . updater1        %%! % % 2 2, %#%(    . %6%? %% %*%4 * *#        ONone* #&()+,/159<=>? Take the bitwise AND of the first argument with the complement of the second. 2Are the bit representations of two words disjoint? )Get the bit-index of the highest set bit. (Get the bit-index of the lowest set bit.  Create a  with the i th bit set.The result of   is undefined when i is not in the range [0..WORD_SIZE_IN_BITS]. &Clear a single bit in an unboxed word.The result of   is undefined when i is not in the range [0..WORD_SIZE_IN_BITS]. $Set a single bit in an unboxed word.The result of   is undefined when i is not in the range [0..WORD_SIZE_IN_BITS]. %Test a single bit in an unboxed word.The result of   is undefined when i is not in the range [0..WORD_SIZE_IN_BITS].  Create a  where the first n bits are 1.The result of   is undefined when i is not in the range [0..WORD_SIZE_IN_BITS]. wordFoldlBits# f a w, performs a lazy left fold over the bits of w. !wordFoldlBitsOffset# offset f a w, performs a lazy left fold over the bits of w", with every bit index passed to f offset by offset. 'wordFoldrBitsOffsetStrict# offset f a w/ performs a strict right fold over the bits of w", with every bit index passed to f offset by offset. wordFoldlBitsStrict# f a w. performs a strict left fold over the bits of w. wordFoldrBits# f a w- performs a lazy right fold over the bits of w. !wordFoldrBitsOffset# offset f a w( performs a right fold over the bits of w", with every bit index passed to f offset by offset. 'wordFoldrBitsOffsetStrict# offset f a w/ performs a strict right fold over the bits of w", with every bit index passed to f offset by offset. wordFoldrBitsStrict# f a w/ performs a strict right fold over the bits of w.  PNone, #&()+,/159<=>?P  Check if two s are bitwise disjoint. 4Perform a lazy left fold over the bit indicies of a . 6Perform a strict left fold over the bit indicies of a . 5Perform a lazy right fold over the bit indicies of a . 7Perform a strict right fold over the bit indicies of a .  Check that if the set bits of a  are a subset of another .  Construct a  consisting of n 1 bits.#byteArrayFillOnes# mwa start end st will fill a  with ones from start to end - 1.  QNone* #&()+,/159<=>?5 Infix operator for  . -Take a relative complement of a variable set. $Delete an index from a variable set. $Set difference of two variable sets. (Check if two variable sets are disjoint. The empty variable set. Filter a variable set to elements that are greater than or equal to an index. Filter a variable set to elements that are greater than to an index. Filter a variable set to elements that are less than or equal to an index. Filter a variable set to elements that are less than to an index. Lazily fold over the elements of a variable set in descending order.)This does not have the same deficiencies /, as we can start the fold at the back of the  . Strictly fold over the elements of a variable set in descending order. Lazily fold over the elements of a variable set in ascending order. Strictly fold over the elements of a variable set in ascending order.)This does not have the same deficiencies /, as we can start the fold at the back of the  . Construct a set of variables from a list of indices sorted in descending order. This can be more efficient than  , as we only need to perform a single to determine that elements of the list are smaller than 64.The precondition that the variables are sorted in descending order is not checked by  . 4Construct a set of variables from a list of indices. 3Construct a variable set that contains the indices [0..n-1]. inRange lo hi vs$ determines if all the variables in vs are within the range [lo+1 .. hi-1]. $Insert an index into a variable set. "Insert a list of variables into a VarSet. =Insert a list of variables sorted in descending order into a  #. This can be more efficient than  , as we only need to perform a single to determine that elements of the list are smaller than 64.The precondition that the variables are sorted in descending order is not checked by  . +Take the intersection of two variable sets. isSubsetOf vs1 vs2 determines if vs1 is a subset of vs2. +Find the largest index in the variable set. ,Find the smallest index in the variable set. Retrieve the smallest index in the variable set along with the set sans that element, or  if the set was empty. $Is a variable a member of a var set? Retrieve the smallest index in the variable set along with the set sans that element, or  if the set was empty. Is this the empty set? 3Construct a variable set that contains the indices  [lo+1..hi-1]. (A variable set with only a single entry. *The number of entries in the variable set. Split a variable set into elements that are strictly smaller than n' and elements that are strictly larger.Note that this is strict in both components of the pair. If you only need one half, use   or  . Remove the first n entries from the variable set, and shift the indices of all other entries down by n. 7Convert a variable set to an ascending list of indices. 7Convert a variable set to a descending list of indices. Union two variable sets. -Union a collection of variable sets together. ,Shift all indices in the variable set up by n. "A set of de Bruijn indices/levels. A variable set whose maximum entry is greater than or equal to 64. >A small variable set whose maximum entry is less than than 64. mempty is  . (<>) is  Slow path for  .Slow path for  .Slow path for  .Slow path for  .Fast path for   that omits bounds checking.Slow path for  .Slow path for  . Convert a  to a variable set, upholding the invariant that all word-sized variable sets should use  .1Trace the size of a variable set to the eventlog.* *                 RNone( #&()+,/159<=>? Disjunction (interpreting null _ as False).  Satisfying null empty == True. The default implementation of   compares with  9, first trying pointer equality, then falling back to  equality. Viewing  as  (), a boolean is   when it is false.  is seen as error monad. A  is  ' when it corresponds to the empty list.       (  )    %      7        %            4  7      6    (  2  <          SNone) #&()+,/1359<=>? Provided that the default value is a known boolean (in practice we only use True or False), we can collapse a potentially uninitialised value to a boolean. Focus, overwriting  . Update, but keep  ! when new value is default value. The main mode of operation of these flags, apart from setting them explicitly, is to toggle them one way or the other if they hadn't been set already. We don't want to have to remember for each flag whether its default value is True or False. So we bake it into the representation: the flag's type will mention its default value as a phantom parameter. %The null value of 'WithDefault b' is  .    ' '# - -! None) #&()+,/159<=>?  Time O(1).  Time O(n).  Time O(1).  Time O(1).  Time O(n). The empty set. Time O(1).  Time O(n).  Time O(n).  Time O(n).  Time O(1).  Time O(1).  Time O(1). not . member a . Time O(1).  Time O(1). A singleton set. Time O(1).  Time O(n).  Time O(n). The full set. Time O(1).  Time O(n). An element in a small set.This must implement  and  , and contain at most 64 values.    ; ;    ;;" > > ;; ;;UNone( #&()+,/159<=>? 0Create-only collection with at most one element. A create-only possibly empty collection is a monoid with the possibility to inject elements.  Overloaded  singleton constructor for collections.    #      $  ?  5  ?  5  (  ; = =' : :( 7 7* 4 4!  %  =  7  =  5  9  >  7      &  &  '  !  "  $    !  !  $    VNone( #&()+,/159<=>?_ Given a function f :: a -> NonEmpty c9 which returns a non-empty list of characteristics of a, partition a list of as into groups such that each element in a group shares at least one characteristic with at least one other element of the group. Partition a list of as paired with a non-empty list of characteristics into groups such that each element in a group shares at least one characteristic with at least one other element of the group. Given a function f :: a -> NonEmpty c9 which returns a non-empty list of characteristics of a , partition a non-empty list of as into groups such that each element in a group shares at least one characteristic with at least one other element of the group. Partition a non-empty list of as paired with a non-empty list of characteristics into groups such that each element in a group shares at least one characteristic with at least one other element of the group.:Lift a function on non-empty lists to a function on lists. Duplicate of .  TNone( #&()+,/159<=>?  Version of   with different argument ordering. Often, we want to case on a  %, do something interesting in the  ( case, but only a default action in the  * case. Then, the argument ordering of  caseMaybe is preferable. (caseMaybe m err f = flip (maybe err) m f Monadic version of  . That is,  $ with a different argument ordering. Filtering a singleton list. filterMaybe p a =   ( p [a])  Version of  " with different argument ordering. Monadic version of  .   with flipped branches. Monadic version of  .  unionWith for collections of size <= 1. Unzipping a list of length <= 1.A more telling name for  for the   collection type. Or:   without the   case.  without the   case.Note that strict Maybe is an  only modulo strictness. The laws only hold in the strict semantics. Eg. pure f  * pure _|_ = _|_#, but according to the laws for  it should be  pure (f _|_)3. We ignore this issue here, it applies also to  and .      % %WNone( #&()+,/159<=>?*Adjust value at key, leave subtree intact.Disclaimer: may return a non-canoncial trie because it does not clean up subtries that become empty..Delete value at key, but leave subtree intact.Disclaimer: may return a non-canoncial trie because it does not clean up subtries that become empty.everyPrefix k v! is a trie where every prefix of k (including k itself) is mapped to v.Filter a trie..Insert. Overwrites existing value if present. %insert = insertWith ( new old -> new)6Insert with function merging new value with old value.8Returns the value associated with the given key, if any.&Collect all values along a given path.(Get the subtrie rooted at the given key.Create new values based on the entire subtrie. Almost, but not quite comonad extend.%Is the given key present in the trie?%Prefix every key by the given prefix.Singleton trie.Convert to ascending list.Convert to ascending list.Convert to list where nodes at the same level are ordered according to the given ordering.Left biased union.#union = unionWith ( new old -> new)./Pointwise union with merge function for values. Key lens.Finite map from [k] to v.With the strict  type,  is also strict in v. Empty trie."Helper function used to implement  and .  00 55448 83< <// XNone( #&()+,/159<=>?WLazy version of allJust  . sequence. (allJust = mapM for the Maybe/ monad.) Only executes monadic effect while isJust.Retain object when tag is . Version of  with different argument ordering. Often, we want to case on a %, do something interesting in the ( case, but only a default action in the * case. Then, the argument ordering of  caseMaybe is preferable. $caseMaybe m d f = flip (maybe d) m fMonadic version of . That is, $ with a different argument ordering.Filtering a singleton list. filterMaybe p a =  ( p [a]) Version of " with different argument ordering.Monadic version of .Run a  with a default value for . with flipped branches. with flipped branches.Lift a maybe to an Alternative.Monadic version of . Unwrap a  value, returning  for .,Retain object when it passes the given test.Like , takes the prefix of a list satisfying a predicate. Returns the run of s until the first , and the tail of the list. unionWith for collections of size <= 1. unionsWith for collections of size <= 1. Unzipping a list of length <= 1.A more telling name for  for the  collection type. Or:  without the  case. without the  case. Pendent to . without the  case."\None( #&()+,/159<=>? minus xs ys! computes the difference between xs and ys<: the result contains those positions which are present in xs but not in ys.*Linear in the lengths of the input ranges. iff the ranges overlap.)The ranges are assumed to be well-formed.The  invariant.(Converts a range to a list of positions.The  invariant./Converts several ranges to a list of positions.Character ranges. The first character in the file has position 1. Note that the 4 position is considered to be outside of the range. Invariant:   ..Zero or more consecutive and separated ranges.    1 1& &11" "   ! %11]None( #&()+,/159<=>? -3Converts a list of pairs of ranges and values to a . The ranges have to be non-overlapping and non-empty, and earlier ranges have to precede later ones.,Inserts a value, along with a corresponding  , into a . No attempt is made to merge adjacent ranges with equal values.The function argument is used to combine values. The inserted value is given as the first argument to the function. Returns a > overlapping the given range, as well as the rest of the map.Invariant for .8The ranges must not be empty, and they must not overlap.Restricts the  to the given range.Like , but with several  instead of only one. The value of  p f is a pair (f1, f2)! which contains everything from f. All the positions in f1 are less than p, and all the positions in f2 are greater than or equal to p.A class that is intended to make it easy to swap between different range map implementations.Note that some , operations are not included in this class.?Returns the smallest range covering everything in the map (or , if the range would be empty).Note that the default implementation of this operation might be inefficient.The map  rs x contains the ranges from rs9, and every position in those ranges is associated with x.Converts the map to a list. The ranges are non-overlapping and non-empty, and earlier ranges precede later ones in the list.Converts range maps to s from positions to values.*Maps containing non-overlapping intervals.The implementation does not use IntMap, because IntMap does not come with a constant-time size function.Note the invariant which s should satisfy ().The keys are starting points of ranges, and the pairs contain endpoints and values.Merges s by inserting every "piece" of the smaller one into the larger one.Merges s by inserting every "piece" of the smaller one into the larger one. A variant of . If a range in the middle was split into two pieces, then those two pieces are returned. The number of ranges in the map.%This function should not be exported. ( , / (   None) #&()+,/159<=>? #Checks if all the elements in the list are equal. Assumes that the 6 instance stands for an equivalence relation. O(n).Breaks a list just after1 an element satisfying the predicate is found.breakAfter even [1,3,5,2,4,7,8](1 :| [3,5,2],[4,7,8])Like .(Concatenate one or more non-empty lists. Strict filterLike .List - but with a base case for the singleton list.Safe version of .More precise type for . A variant of : which applies the predicate to consecutive pairs. O(n). [a] -> (List1 a -> m) -> m often causes type inference to fail, as we do not in general have %instance Applicative m => Null (m ()).Like .Like .6Update the first element of a non-empty list. O(1).5Update the last element of a non-empty list. O(n).Split a list into sublists. Generalisation of the prelude function words . Same as  and , but with the non-emptyness guarantee on the chunks. O(n). words xs == wordsBy isSpace xsLike .Like .$Default value if convertee is empty.&List to convert, supposedly non-empty.Converted list.uN{|gCO^behjnmqkolpILRSV\t]KBFvwirs}`_XZY[MWPyQzfcJTUadxGEHD(78$44uN{|gCO^behjnmqkolpILRSV\t]KBFvwirs}`_XZY[MWPyQzfcJTUadxGEHD78$454(YNone( #&()+,/159<=>?Cache the size of an object.,The size of a collection (i.e., its length).*Lazily compute a (possibly infinite) size.1Use when comparing a size against a fixed number.Strict size computation.Anti-patterns:  size xs == n where n is 0, 10 or another number that is likely smaller than size xs. Similar for  size xs >= 1 etc. Use  instead.See  https://wiki.haskell.org/Haskell_programming_tips#Don.27t_ask_for_the_length_of_a_list_when_you_don.27t_need_it .Thing decorated with its size. The thing should fit into main memory, thus, the size is an Int.Return the cached size.    '9 9: :; ; 6 6= => >8 8< <? ?7 7 [None( #&()+,/159<=>?( 1Adds a final newline if there is not already one.$Adds hyphens around the given stringputStrLn $ delimiter "Title"<@@@@ Title @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@Turns the string into a Haskell string literal, avoiding escape codes.-Indents every line the given number of steps.Remove leading whitespace. Append an "s"5 to the second argument if the first has cardinality /= 1. adds double quotes around the string, replaces newline characters with n, and escapes double quotes and backslashes within the string. This is different from the behaviour of : >  $  "\x2200" "\8704" >  $  "\x2200" "D" (The code examples above have been tested using version 4.2.0.0 of the base library.)Remove trailing whitespace.6Show a number using comma to separate powers of 1,000.'Remove leading and trailing whitesapce., but remove empty words first.   ? <  ? > _None) #&()+,/159<=>?  Print an  without the call stack.Catch s in an extension of the  monad."Upon exception, the error is lost. Alias of  for the IO monad.#Upon exception, the state is reset.+Upon exception, the written output is lost. , % %+ ,^None( #&()+,/159<=>?Turn a possible non-surjective permutation into a surjective permutation. 2permute (compose p1 p2) == permute p1 . permute p2 deleteP i  deletes the value i from the output of .9Pick the elements that are not picked by the permutation. expandP i n  in the domain of  replace the ith element by n elements.8permPicks (flipP p) = permute p (downFrom (permRange p)) or permute (flipP (Perm n xs)) [0..n-1] = permute (Perm n xs) (downFrom n)Can be use to turn a permutation from (de Bruijn) levels to levels to one from levels to indices.See .Identity permutation. invertP err p is the inverse of p) where defined, otherwise defaults to err. composeP p (invertP err p) == pliftP k takes a  Perm {m} n to a Perm {m+k} (n+k). Analogous to ?, but Permutations operate on de Bruijn LEVELS, not indices. lookupP  i applies  to i. lookupRP  i applies  invertP  to i.'permute [1,2,0] [x0,x1,x2] = [x1,x2,x0] More precisely, permute indices list = sublist , generates sublist from list1 by picking the elements of list as indicated by indices. *permute [1,3,0] [x0,x1,x2,x3] = [x1,x3,x0]Agda typing: ,permute (Perm {m} n is) : Vec A m -> Vec A nPrecondition for  ( _ is) xs: Every index in is must be non-negative and, if xs is finite, then every index must also be smaller than the length of xs.The implementation is supposed to be extensionally equal to the following one (if different exceptions are identified), but in some cases more efficient:  permute ( _ is) xs =  (xs ) is  ?permute (reverseP p) xs == reverse $ permute p $ reverse xs Example:  permute (reverseP (Perm 4 [1,3,0])) [x0,x1,x2,x3] == permute (Perm 4 $ map (3-) [0,3,1]) [x0,x1,x2,x3] == permute (Perm 4 [3,0,2]) [x0,x1,x2,x3] == [x3,x0,x2] == reverse [x2,x0,x3] == reverse $ permute (Perm 4 [1,3,0]) [x3,x2,x1,x0] == reverse $ permute (Perm 4 [1,3,0]) $ reverse [x0,x1,x2,x3] With reverseP, you can convert a permutation on de Bruijn indices to one on de Bruijn levels, and vice versa."Restrict a permutation to work on n elements, discarding picks >=n.Stable topologic sort. The first argument decides whether its first argument is an immediate parent to its second argument.%Things that support delayed dropping.)Delayed dropping which allows undropping.Where to drop from.&Non-negative number of things to drop.3Invert a Permutation on a partial finite int map. inversePermute perm f = f' such that permute perm f' = f!Example, with map represented as  [Maybe a]:  f = [Nothing, Just a, Just b ] perm = Perm 4 [3,0,2] f' = [ Just a , Nothing , Just b , Nothing ]  Zipping perm with f gives  [(0,a),(2,b)], after compression with  catMaybes. This is an IntMap9 which can easily written out into a substitution again.Partial permutations. Examples:)permute [1,2,0] [x0,x1,x2] = [x1,x2,x0] (proper permutation).&permute [1,0] [x0,x1,x2] = [x1,x0] (partial permuation).,permute [1,0,1,2] [x0,x1,x2] = [x1,x0,x1,x2]- (not a permutation because not invertible).Agda typing would be: 9Perm : {m : Nat}(n : Nat) -> Vec (Fin n) m -> Permutation m is the  of the permutation.Perform the dropping. Drop more.Pick up dropped stuff.    ) )%-#)) - - , ,; ;7 7+ +3 3/:ZNone( #&()+,/159<=>?O(length first list).O(length first list).2Concatenate at least 2 lists of length at least 1.O(1). Unsafe! O(1).Any  is either a singleton or a . O(1). Safe. O(1). Safe. O(1). Safe. O(1). Safe. O(n).O(n). Safe. O(1). Safe. O(1). Inverse of . O(1).Lists of length D2. is unsafe." ""%"-""#' ' &"""""/": None( #&()+,/159<=>?kReturns  input_with_tags_stripped if all elements are to the , and otherwise .Returns  input_with_tags_stripped2 if all elements are to the right, and otherwise .  allRight xs == if all isRight xs then Just (map ((Right x) -> x) xs) else Nothing Monadic version of $ with a different argument ordering. Analogue of . Analogue of X. Analogue of . Analogue of X.)Groups a list into alternating chunks of  and  values'Either _ b' is a functor.'Either a' is a functor.Safe projection from . 8maybeLeft (Left a) = Just a maybeLeft Right{} = NothingSafe projection from . = 4.10.0.0 already present in . Loop while we have an exception.,-,-None) #&()+,/159<=>? H Strict ap Binary bind.Lazy monadic disjunction with Either> truth values. Returns the last error message if all fail.Lazy monadic conjunction.;Bracket without failure. Typically used to preserve state.Generalises the & function from lists to an arbitrary .Handle errors thrown in .A monadic version of  dropWhileEnd :: (a -> Bool) -> [a] -> m [a]:. Effects happen starting at the end of the list until p becomes false.A monadic version of  :: (a -> Bool) -> [a] -> [a].Finally for the Error class. Errors in the finally part take precedence over prior errors.Generalized version of 3for_ :: Applicative m => [a] -> (a -> m ()) -> m ()The for version of .The for version of . Translates  to .Monadic guard.Like -, but raise given error when condition fails.Monadic if-then-else. ifNotM mc = ifM (not  $ mc) Restore state after computation.Generalized version of 8traverse_ :: Applicative m => (a -> m ()) -> [a] -> m () Executes effects and collects results in left-to-right order. Works best with left-associative monoids.!Note that there is an alternative !mapM' f t = foldr mappend mempty  $ mapM f tthat collects results in right-to-left order (effects still left-to-right). It might be preferable for right associative monoids. Variant of  which gets compiled to good code, assuming that we're mapping over an actual runtime list and don't intend for list fusion to fire. Variant of  which gets compiled to good code, assuming that we're mapping over an actual runtime list and don't intend for list fusion to fire.A monadic version of  :: (a -> Maybe b) -> [a] -> [b]. A version of ' with a computation for the input list.Lazy monadic disjunction.Lazy monadic disjunction with accumulation of errors in a monoid. Errors are discarded if we succeed.A `monadic' version of @ partition# :: (a -> Bool) -> [a] -> ([a],[a])/Performing an action for an inclusive range of -s, counting up by one."Branch over elements of a monadic  data structure.Output a single value.1Run a command, catch the exception and return it.Try a computation, return  if an Error occurs.Acquires resource. Run first.Releases resource. Run last. Computes result. Run in-between.?;:9><=01%)3?;:9><=01)3 %aNone) #&()+,/159<=>?XLazy monadic conjunction of lazy monadic list, effects left-to-rightLazy monadic disjunction of lazy monadic list, effects left-to-right Case distinction over lazy list.The join operation of the ListT m monad.Consing a value to a lazy list. Monadic cons.+Folding a lazy list, effects left-to-right. Change from one monad to anotherBoilerplate function to lift  through the  transformer. Extending a monadic function to .!Alternative implementation using .The empty lazy list.We can `run' a computation of a  as it is monadic itself.8Force all values in the lazy list, effects left-to-rightSingleton lazy list.Monadic singleton. Inverse to ..Lazy monadic computation of a list of results.  , ,  ( & * * 6 4  ' *bNone( #&()+,/159<=>?>Is the NO_COLOR environment variable unset?cNone* #&()+,/159<=>? Make a copy.An empty hash table.Iterate over key-value pairs in IO. Caution: don't modify the table while iterating over it!Iterate over key-value pairs in IO while accummulating a value. Caution: don't modify the table while iterating over it!Inserts the key and the corresponding value into the hash table.Look up a key in the table. If it's already there, proceed with the first '(v -> m a) argument. Otherwise run the (m v) argument, insert the result value in the table and pass it to the second @(v -> m a) argument.Tries to find a value corresponding to the key in the hash table.)Properly inlinable CPS-d lookup function."Converts the hash table to a list.5The order of the elements in the list is unspecified.Hash tables. A very limited amount of (possibly outdated) testing indicates that, for the use in Agda's serialiser/deserialiser, Data.HashTable.IO.CuckooHashTable is somewhat slower than Data.HashTable.IO.BasicHashTable, and that Data.HashTable.IO.LinearHashTable and the hashtables from Data.Hashtable are much slower. However, other (also possibly outdated) testing suggests that Data.HashTable.IO.CuckooHashTable is quite a bit faster than Data.HashTable.IO.BasicHashTable for 64-bit Windows. Some more recent, also limited, testing suggests that the following hash table implementation from Data.Vector.Hashtables is quite a bit faster than Data.HashTable.IO.BasicHashTable (see issue #5966).-Hashtable with lifted keys and lifted values..Hashtable with lifted keys and unboxed values..Hashtable with unboxed keys and lifted values.'Hashtable with unboxed keys and values.dNone( #&()+,/159<=>?5The defaultWarningMode is a curated set of warnings covering non-fatal errors and disabling style-related onesWarnings enabled by  --exact-split.The flag corresponding to a warning is precisely the name of the constructor minus the trailing underscore.'Both of these warnings are disabled by -WnoUnusedImports. warningUsage generated using warningNameDescriptionwarningModeUpdate str computes the action of str over the current  WarningMode: it may reset the set of warnings, add or remove a specific flag or demand that any warning be turned into an errorCommon sets of warningsA  WarningMode has two components: a set of warnings to be displayed and a flag stating whether warnings should be turned into fatal errors.Invariant: When # is in the warning set, so must be .2Some warnings are errors and cannot be turned off. Warning that cannot be disabled.-WnoUnusedImports=all is not supported, use -WnoUnusedImports instead.Unknown warning.The  WarningName data enumeration is meant to have a one-to-one correspondance to existing warnings in the codebase.'Some warning could not be set or unset.9From user-given directives we compute WarningMode updates WarningName descriptions used for generating usage information Leave String empty to skip that name.The description should be a completion of the sentence "This warning is about ...". So, typically the subject is in plural.(/"&<< << 18> > !  << eNone( #&()+,/159<=>? %-#   "/:fNone) #&()+,/159<=>? Makes the path absolute.This function may raise an __IMPOSSIBLE__ error if " does not return an absolute path.!Resolve symlinks etc. Preserves .Case-sensitive  for Windows.This is case-sensitive only on the file name part, not on the directory part. (Ideally, path components coming from module name components should be checked case-sensitively and the other path components should be checked case insensitively.) Extract the  to be used as .True if the first file is newer than the second file. If a file doesn't exist it is considered to be infinitely old.Makes a path relative to a root without assuming that either path is canonical. Constructs s.2Precondition: The path must be absolute and valid.A partial version of & with flipped arguments, returning 6 if the given path cannot be relativized to the given root.Tries to establish if the two file paths point to the same file (or directory). False negatives may be returned. Generalizes .%Paths which are known to be absolute.Note that the  and  instances do not check if different paths point to the same files or directories.(The absolute path we seek to relativize.The root for relativization.The relative path, if any.  ----$-&-,-.-2--- -gNone, #&()+,/159<=>?[-Hashing a module name for unique identifiers.Hashes a piece of .  hNone( #&()+,/159<=>?r Compare a new set of favorites to an old one and discard the new favorites that are dominated by the old ones and vice verse. (Skewed conservatively: faithful to the old favorites.) 'compareFavorites new old = (new', old')Gosh, got some pretty a here, compare with my current favorites! Discard it if there is already one that is better or equal. (Skewed conservatively: faithful to the old favorites.) If there is no match for it, add it, and dispose of all that are worse than a.We require a partial ordering. Less is better! (Maybe paradoxically.)Construct favorites from elements of a partial order. The result depends on the order of the list if it contains equal elements, since earlier seen elements are favored over later seen equals. The first element of the list is seen first.%Compare, then insert accordingly. :insert a l = insertCompared a l (compareWithFavorites a l))After comparing, do the actual insertion.=Insert all the favorites from the first list into the second.;Result of comparing a candidate with the current favorites.Great, you are dominating a possibly (empty list of favorites) but there is also a rest that is not dominated. If null dominated, then  notDominated2 is necessarily the complete list of favorites..Sorry, but you are dominated by that favorite.!A list of incomparable favorites.Equality checking is a bit expensive, since we need to sort! Maybe use a Set! of favorites in the first place? forms a  under   and 'union. # 07 . 1!#.iNone) #&()+,/159<=>?a Render a  ann to a  ann" using standard layout parameters. Render a  ann to a  ann) with the given layout parameters. E.g.  width=100 fill=1.5.Generic  linearization. Linearize a  to  with the given -rendering of the annotations. Linearize a  to  dropping all annotations./A rendered document with annotations from type ann.Stuff annotated by ann.Atom.0Annotated stuff waiting for the opening bracket.ªLinearizer. We need forward function composition because we process nodes left-to-right.ê Linearizer.ĪLinearizer state.ŪCurrent position.ƪ;The top of the stack is the currently active annotation(s).ǪAccumulated text.Ȫ#Accumulated annotation information.ɪLinearizer state.ʪCurrent position.˪Accumulated text.̪#Accumulated annotation information.ͪ.State of the right-to-left conversion to tree.ΪAccumulator for text.ϪA nonempty stack of annotated trees with their closing annotation bracket, waiting for the opening bracket.Ъ)Run linearizer with given initial offset.Ѫ)Run linearizer with given initial offset.Ҫ2Initial linearizer state with configurable offset.Ӫ2Initial linearizer state with configurable offset.Ԫ2Adding an annotation to the currently active ones.ժ?#Turn a trie into a compressed trie.*Is the trie starting with a single branch?&Singleton tree with value at the root.A single branch with the given subtree. Precondition: the given subtree has a value at the root.Singleton trie.Singleton tree with empty root.The number of labeled nodes.0The number of nodes that are labeled or leaves..:Modify the leaves (input and output may be non-canonical).Convert to ascending list.Convert to ascending list.!Truncate tree at given depth.  truncate 0 t returns the root.Truncate the tree so that it has at most the given size according to the given sizing function. truncateSize sizing 0 t returns the trie  truncate 0 t. truncateSize sizeWithLeaves1Turn a compressed trie into an uncompressed trie.Finite map from [k] to v.With the strict  type,  is also strict in v.;Invariant: only the root of the tree may be of the form !Trie Nothing (Map.singleton ks t). A node inside of the trie of that form must be fused into its branch. Empty trie.77 <<;;? ?3 66  &kNone( #&()+,/159<=>?  %-#    !/:lNone( #&()+,/159<=>?;Modifies the value at the given position, if any. O(log n).Precondition: See .The precondition for  f k m is that, if the value v is inserted into m, and  v% is defined, then no key other than k may map to a value v' for which  v' =  v.Modifies the value at the given position, if any. If the function returns &, then the value is removed. O(log n).Precondition: See .Modifies the value at the given position, if any. If the function returns &, then the value is removed. O(log n).The precondition for  f k m is that, if the value v is inserted into m, and  v% is defined, then no key other than k may map to a value v' for which  v' =  v.The precondition for  f k m is that, if the value v is inserted into m, and  v% is defined, then no key other than k may map to a value v' for which  v' =  v.The invariant for .>The values, ordered according to the corresponding keys. O(n).Conversion from two lists that contain distinct keys/tags, with the keys/tags in ascending order. O(n).Precondition: See .Conversion from lists of pairs. Later entries take precedence over earlier ones. O(n log n).Precondition: See .0Insertion. Overwrites existing values. O(log n).Precondition: See .Inserts a binding into the map. If a binding for the key already exists, then the value obtained by applying the function to the key, the new value and the old value is inserted, and the old value is returned.Precondition: See .The precondition for  f k v m is that, if the value v' is inserted into m, and  v'% is defined, then no key other than k may map to a value v'' for which  v'' =  v'.The precondition for  k v m: If v has a  ( v D ), then m must not contain any mapping k' C v' for which k D k' and  v =  v'.Inverse lookup. O(log n).#The keys, in ascending order. O(n).Lookup. O(log n).Changes all the values using the given function, which is also given access to keys. O(n log n).Precondition: See .Changes all the values using the given function, which is also given access to keys. O(n).Precondition: See ". Note that tags must not change.The precondition for  f m is that, if m maps k to v, then  (f k v) ==  v.The precondition for  f m!: For any two distinct mappings kA C vA, kA C vA in m for which the tags of f kA vA and f kA vA are defined the values of f must be distinct (f kA vA D f kA vA). Furthermore  must be injective for { f k v | (k, v) D m }.Singleton map. O(1).$Is the value a source key? O(log n).Checks if the function  is injective for the values in the given list for which the function is defined.$Is the value a target key? O(log n).Generates input suitable for . O(n).Conversion to lists of pairs, with the keys in ascending order. O(n).0Left-biased union. For the time complexity, see .Precondition: See .Modifies the value at the given position, if any. If the function returns &, then the value is removed. O(log n).Precondition: See .The precondition for  f k m is that, if the value v is inserted into m, and  v% is defined, then no key other than k may map to a value v' for which  v' =  v.Finite maps from k to v!, with a way to quickly get from v to k for certain values of type v (those for which  is defined).&Every value of this type must satisfy .0Partial injections from a type to some tag type.The idea is that ( should be injective on its domain: if  x =  y =  i, then x = y. However, this property does not need to hold globally. The preconditions of the 3 operations below specify for which sets of values  must be injective.'' (   + .mNone( #&()+,/159<=>?Was this module name constructed from a file name rather than declared in the file?The range is not forced.=The record selector is not included in the resulting strings.   3 3(-- / /,9 9. > >, $6 6) - -nNone( #&()+,/159<=>?WParse and add a profiling option to a set of profiling options. Returns  with a helpful error message if the option doesn't parse or if it's incompatible with existing options. The special string "all" adds all options compatible with the given set and prefering the first of incompatible options. So `--profile=all` sets  over  and 0, but `--profile=modules --profile=all` sets  and not .Check if a given profiling option is present in a set of profiling options.#The empty set of profiling options.Use only for serialization.Use only for serialization.Strings accepted by Various things that can be measured when checking an Agda development. Turned on with the `--profile` flag, for instance `--profile=sharing` to turn on the  option. , , and  are mutually exclusive.NOTE: Changing this data type requires bumping the interface version number in .+Collect statistics about constraint solving,Collect statistics about conversion checking3Measure time spent on individual (Agda) definitions(Collect statistics about instance search$Measure time of interactive commandsMeasure time taken by various parts of the system (type checking, serialization, etc)%Count number of created metavariables/Measure time spent on individual (Agda) modules-Collect statistics about section applications/Collect detailed statistics about serialization!Measure things related to sharing A set of s -"-)-- --33-+-2/ /3333#--- -3 3oNone/ #&()+,/159<=>?A5Constructor tag (maybe omitted) and argument indices.; ;   pNone* #&()+,/1359<=>?=Killing the range of an object sets all range information to .%Backup the position by one character.(Precondition: The character must not be 'n'. beginningOf r is an empty range (a single, empty interval) positioned at the beginning of r. If r" does not have a beginning, then  is returned.Are the intervals consecutive and separated, do they all point to the same file, and do they satisfy the interval invariant??Returns the shortest continuous range containing the given one.0Removes gaps between intervals on the same line.4Finds the least interval which covers the arguments.Precondition: The ranges must point to the same file (or be empty).fuseRanges r r' unions the ranges r and r'.!Meaning it finds the least range r0 that covers r and r'.Precondition: The ranges must point to the same file (or be empty).The length of an interval.*Interleaves two streams of ranged elementsIt will report the conflicts as a list of conflicting pairs. In case of conflict, the element with the earliest start position is placed first. In case of a tie, the element with the earliest ending position is placed first. If both tie, the element from the first list is placed first.0Converts a file name and an interval to a range.8Turns a file name plus a list of intervals into a range.Precondition: .*Remove ranges in keys and values of a map.A smart constructor for .?Advance the position by one character. A newline character ('n') moves the position to the first character in the next line. Any other character moves the position to the next column.!Advance the position by a string.  movePosByString = foldl' movePos$Ranges between two unknown positionsConverts a file name and two positions to an interval. Sort the positions ascendingly."Converts two positions to a range.;Precondition: The positions have to point to the same file.2Converts a file name and two positions to a range.;The position after the final position in the range, if any.;The position after the final position in the range, if any.*The initial position in the range, if any.*The initial position in the range, if any."The file the range is pointing to.7Range pointing to the first position in the given file.The intervals that make up the range. The intervals are consecutive and separated ().Range invariant.*The range's top-level module name, if any.*The range's top-level module name, if any.If there is no range, then ? is returned. If there is a range without a module name, then   is returned.Converts a range to an interval, if possible. Note that the information about the source file is lost.-Converts a range to an interval, if possible.%Conflate a range to its right margin.;The first position in a file: position 1, line 1, column 1.;The first position in a file: position 1, line 1, column 1.x `withRangeOf` y sets the range of x to the range of y.Return an empty range (a single, empty interval) at the beginning of the file.5Things that have a range are instances of this class.Things that have a  are instances of this class.An interval. The iEnd* position is not included in the interval.4Note the invariant which intervals have to satisfy: .&Tolerably efficient representation of  Represents a point in the input.If two positions have the same  and  components, then the final two components should be the same as well, but since this can be hard to enforce the program should not rely too much on the last two components; they are mainly there to improve error messages for the user.4Note the invariant which positions have to satisfy: .:Line and position numbers as Word32, both counting from 1.Position, counting from 1.File.1Wrapper to indicate that range should be printed.A range is a file name, plus a sequence of intervals, assumed to point to the given file. The intervals should be consecutive and separated.1Note the invariant which ranges have to satisfy: .File information used in the ,  and  types.1The file's top-level module name (if applicable).This field is optional, but some things may break if the field is not instantiated with an actual top-level module name. For instance, the  and ( instances only make use of this field.The field uses  rather than  because it should be possible to instantiate it with something that is not yet defined (see ).>This '(TopLevelModuleName' Range)' should not contain a range.The file's path.;If it is also possible to set the range, this is the class.Instances should satisfy  ( r x) == r.beginningOfFile r is an empty range (a single, empty interval) at the beginning of r's starting position's file. If there is no such position, then an empty range is returned. Only the  component is compared.Precondition: The ranges of the list elements must point to the same file (or be empty).Precondition: The ranges of the list elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Precondition: The ranges of the tuple elements must point to the same file (or be empty).Overlaps with  KillRange [a]. Only the  component is compared.تPrecondition: The ranges must point to the same file (or be empty).٪The intervals that make up the range. The intervals are consecutive and separated (). & !  #  "   %-&# <-45<  ;  $ * * ) *  . 4       "  1 :   ?  # .         . ' . +  = /  + >  ;. , 3 , 4 , *3  / 8      # & $  % $  '  &   " $  $ * (  .  # &  /: +(3qNone( #&()+,/159<=>? <& Compute the  which (possibly) contain a ! for the given thing-with-range.#Non-code contents in literate Agda.Delimiters used to separate the Agda code blocks from the other contents in literate Agda.: Is the name an operator part?Text occurring in pragmas that does not have a more specific aspect. Things like Set and Prop. Symbols like forall, =, ->, etc.,Uniform Resource Locator aka clickable link.6Syntactic aspects of the code. (These cannot overlap.)Meta information which can be associated with a character/character range.The definition site of the annotated thing, if applicable and known.This note, if not null, can be displayed as a tool-tip or something like that. It should contain useful information about the range (like the module containing a certain identifier, or the fixity of an operator).Is this entry token-based?#A pretty name for the HTML linking. Has this DefinitionSite/ been created at the defining site of the name?The defining module.The file position in that module. File positions are counted from 1.NameKind(s are figured out during scope checking.!Named argument, like x in {x = v}Bound variable.%Inductive or coinductive constructor. Record field.Generalizable variable. (This includes generalizable variables that have been generalized).Macro. Module name. Primitive. Record type.Other aspects, generated by type checking. (These can overlap with each other and with s.)$Nothing serious, just a beauty flaw.Used for highlighting unreachable clauses, unreachable RHS (because of an absurd pattern), etc..A warning that is considered fatal in the end.Unusable instance etc.1Function declaration without matching definition.8Used for shadowed repeated variable names in telescopes.!Code which is being type-checked.Unsolved constraint not connected to meta-variable. This could for instance be an emptyness constraint.Is the highlighting "token-based", i.e. based only on information from the lexer?NameKind in Name can get more precise.Some #s are more informative than others.??$$+"( (   << ((<< -4           ((<<  #None( #&()+,/159<=>? a  ? b = hang a 2 balign max rows lays out the elements of rows in two columns, with the second components aligned. The alignment column of the second components is at most max2 characters to the right of the left-most column.Precondition: max > 0.$Only adds an annotation node if the  is non- .Attach a simple , rather than a full set of , to a document.?The current time.Measure the time of a computation. Of course, does not work with exceptions."CPU time in pico (10^-12) seconds. Timestamps.(Print CPU time in milli (10^-3) seconds. '''+' ''-'5'!'%'7'=''''. .''sNone+ #&()+,/159<=>?_Precedence of atoms.Precedence of >>=.Precedence of  |.Uses the given document as the printed representation of the given parser. The document's precedence is taken to be ..Parses a token satisfying the given predicate.Precedence of  *.Precedence of E and +.Parses a given token.Parses a single token.(Documents paired with precedence levels.The parser type.The parameters of the type Parser k r tok a have the following meanings: kType used for memoisation keys.rThe type of memoised values. (Yes, all memoised values have to have the same type.)tokThe token type.aThe result type.Uses the given function to modify the printed representation (if any) of the given parser.&Tries to print the parser, or returns , depending on the implementation. This function might not terminate.Memoises the given parser./Every memoised parser must be annotated with a unique key. (Parametrised parsers must use distinct keys for distinct inputs.)Memoises the given parser, but only if printing, not if parsing./Every memoised parser must be annotated with a unique key. (Parametrised parsers must use distinct keys for distinct inputs.)Runs the parser.Parses a token satisfying the given predicate. The computed value is returned.An extended parser type, with some support for printing parsers.۪This must be a lazy tuple so that we don't generate the docs eagerly.ܪList of positions and values with much better memory layout than  [(Pos, v)].ݪContinuations.ުThe extended parser type computes one top-level document, plus one document per encountered memoisation key. is used to mark that a given memoisation key has been seen, but that no corresponding document has yet been stored.ߪState monad used by the parser. Positions.Memoised values.A helper function.The constructor. Pretty-prints a memoisation key.A helper function.  & & 1 1 " -  + 9 .tNone( #&()+,/159<=>?0Returns True iff the graph is acyclic.'Combines each node label with a unique .Precondition: The number of nodes in the graph must not be larger than  :: .Time complexity: O(n + e log n).Removes   edges. O(n + e).Transitive closure ported from Agda.Termination.CallGraph.%Relatively efficient, see Issue 1560. Version of  that produces a list of intermediate results paired to the left with a difference that lead to the new intermediat result.The last element in the list is the transitive closure, paired with the empty graph. (complete g = snd $ last $ completeIter gcomposeWith times plus g g' finds all edges s --c_i--> t_i --d_i--> u with s --c_i--> t_i in g and t_i --d_i--> u in g', and constructs the result graph from !edge(s,u) = sum_i (c_i times d_i).Complexity: For each edge s --> t in g' we look up all edges starting with t in g'.>Precondition: The two graphs must have exactly the same nodes. Constructs a  structure. O(n + e log n). invariant.All self-loops.  O(n log n).Checks whether the graph is discrete (containing no edges other than   edges). O(n + e).The graph's edges. O(n + e).edgesFrom g ns is a list containing all edges originating in the given nodes (i.e., all outgoing edges for the given nodes). If ns does not contain duplicates, then the resulting list does not contain duplicates. O(|ns| log |n| + |edgesFrom g ns|). edgesTo g ns is a list containing all edges ending in the given nodes (i.e., all incoming edges for the given nodes). If ns does not contain duplicates, then the resulting list does not contain duplicates. O(|ns | n log n)."Empty graph (no nodes, no edges). O(1).0Keep only the edges that satisfy the predicate. O(n + e). The graph filterNodes p g# contains exactly those nodes from g that satisfy the predicate p=. Edges to or from nodes that are removed are also removed. O(n + e).Removes the nodes that do not satisfy the predicate from the graph, but keeps the edges: if there is a path in the original graph between two nodes that are retained, then there is a path between these two nodes also in the resulting graph.(Precondition: The graph must be acyclic.Worst-case time complexity:  O(e n log n)) (this has not been verified carefully). fromEdges es$ is a graph containing the edges in es=, with the caveat that later edges overwrite earlier edges. O(|es| log n).fromEdgesWith f es$ is a graph containing the edges in es. Later edges are combined with earlier edges using the supplied function. O(|es| log n).Constructs a completely disconnected graph containing the given nodes. O(n).Constructs a completely disconnected graph containing the given nodes.  O(n log n).-Computes the transitive closure of the graph.Uses the Gauss-Jordan-Floyd-Warshall-McNaughton-Yamada algorithm (as described by Russell O'Connor in "A Very General Method of Computing Shortest Paths"  'http://r6.ca/blog/20110808T035622Z.html), implemented using , and with some shortcuts:Zero edge differences are not added to the graph, thus avoiding some zero edges.Strongly connected components are used to avoid computing some zero edges.The graph's strongly connected components (in reverse topological order) are returned along with the transitive closure.-Computes the transitive closure of the graph.Uses the Gauss-Jordan-Floyd-Warshall-McNaughton-Yamada algorithm (as described by Russell O'Connor in "A Very General Method of Computing Shortest Paths"  'http://r6.ca/blog/20110808T035622Z.html), implemented using matrices.4The resulting graph does not contain any zero edges.This algorithm should be seen as a reference implementation. In practice ! is likely to be more efficient. Inserts an edge into the graph. O(log n). Inserts an edge into the graph. O(log n). A variant of . O(log n).insertWith f s t new inserts an edge from s to t3 into the graph. If there is already an edge from s to t with label old6, then this edge gets replaced by an edge with label  f new old%, and otherwise the edge's label is new. O(log n).Internal invariant.*Nodes without incoming or outgoing edges. O(n + e log n).Constructs a graph g', with the same nodes as the original graph g. In g' there is an edge from n1 to n2> if and only if there is a (possibly empty) simple path from n1 to n2 in g. In that case the edge is labelled with all of the longest (in terms of numbers of edges) simple paths from n1 to n2 in g), as well as the lengths of these paths.Precondition: The graph must be acyclic. The number of nodes in the graph must not be larger than  :: .>Worst-case time complexity (if the paths are not inspected):  O(e n log n)( (this has not been verified carefully).1The algorithm is based on one found on Wikipedia.If there is an edge from s to t, then  lookup s t g is  e, where e is the edge's label. O(log n).All self-loops.  O(n log n).Only transform the self-loops. A variant of < that provides extra information to the function argument. O(n + e).neighbours u g consists of all nodes v" for which there is an edge from u to v in g-, along with the corresponding edge labels.  O(log n + |neighbours u g|).neighboursMap u g consists of all nodes v" for which there is an edge from u to v in g-, along with the corresponding edge labels. O(log n). All nodes. O(n).The opposite DAG.'The nodes reachable from the given SCC.reachableFrom g n/ is a map containing all nodes reachable from n in g. For each node a simple path to the node is given, along with its length (the number of edges). The paths are as short as possible (in terms of the number of edges).Precondition: n must be a node in g<. The number of nodes in the graph must not be larger than  :: .Amortised time complexity (assuming that comparisons take constant time):  O(e log n), if the lists are not inspected. Inspection of a prefix of a list is linear in the length of the prefix.reachableFromSet g ns/ is a set containing all nodes reachable from ns in g.Precondition: Every node in ns must be a node in g<. The number of nodes in the graph must not be larger than  :: .Amortised time complexity (assuming that comparisons take constant time): O((|ns | + e) log n).removeEdge s t g removes the edge going from s to t , if any. O(log n).removeNode n g removes the node n% (and all corresponding edges) from g. O(n + e).removeNodes ns g removes the nodes in ns% (and all corresponding edges) from g. O((n + e) log |ns|).Renames the nodes.6Precondition: The renaming function must be injective.Time complexity: O((n + e) log n).Renames the nodes.$Precondition: The renaming function ren" must be strictly increasing (if x  y then ren x  ren y).Time complexity: O(n + e).Constructs a DAG containing the graph's strongly connected components.Constructs a DAG containing the graph's strongly connected components.The graph's strongly connected components, in reverse topological order.The time complexity is likely O(n + e log n) (but this depends on the, at the time of writing undocumented, time complexity of ).The graph's strongly connected components, in reverse topological order.The time complexity is likely O(n + e log n) (but this depends on the, at the time of writing undocumented, time complexity of ).5A graph with two nodes and a single connecting edge. O(1).Nodes with outgoing edges. O(n).Nodes with incoming edges. O(n + e log n).The transitive closure. Using . NOTE: DO NOT USE () AS EDGE LABEL SINCE THIS MEANS EVERY EDGE IS CONSIDERED A ZERO EDGE AND NO NEW EDGES WILL BE ADDED! Use 'Maybe ()' instead.The transitive reduction of the graph: a graph with the same reachability relation as the graph, but with as few edges as possible.Precondition: The graph must be acyclic. The number of nodes in the graph must not be larger than  :: .Worst-case time complexity:  O(e n log n)) (this has not been verified carefully).1The algorithm is based on one found on Wikipedia..The opposite graph (with all edges reversed). O((n + e) log n).Reverses an edge. O(1).Left-biased union.Time complexity: See .Union. The function is used to combine edge labels for edges that occur in both graphs (labels from the first graph are given as the first argument to the function).Time complexity:  O(nA log (nAnA + 1) + eA log eA), where nA/ is the number of nodes in the graph with the smallest number of nodes and nA0 is the number of nodes in the other graph, and eA is the number of edges in the graph with the smallest number of edges and eA+ is the number of edges in the other graph."Less complicated time complexity: O((n + e) log n (where n and e refer to the resulting graph).Union. O((n + e) log n (where n and e refer to the resulting graph).Union. The function is used to combine edge labels for edges that occur in several graphs. O((n + e) log n (where n and e refer to the resulting graph).Unzips the graph. O(n + e).#walkSatisfying every some g from to% determines if there is a walk from from to to in g/, in which every edge satisfies the predicate every(, and some edge satisfies the predicate some. If there are several such walks, then a shortest one (in terms of the number of edges) is returned.Precondition: from and to must be nodes in g<. The number of nodes in the graph must not be larger than  :: .Amortised time complexity (assuming that comparisons and the predicates take constant time to compute): O(n + e log n). SCC DAGs.0The maps map SCC indices to and from SCCs/nodes.Edges.Edge label (weight).Outgoing node.Incoming node. Graph n e, is a type of directed graphs with nodes in n and edges in e.At most one edge is allowed between any two nodes. Multigraphs can be simulated by letting the edge type e be a collection type.The graphs are represented as adjacency maps (adjacency lists, but using finite maps instead of arrays and lists). This makes it possible to compute a node's outgoing edges in logarithmic time (O(log n)). However, computing the incoming edges may be more expensive.Note that neither the number of nodes nor the number of edges may exceed  :: .Forward edges.Various kinds of nodes.!All nodes, with or without edges.Nodes with outgoing edges.Nodes with incoming edges.WithUniqueInt n consists of pairs of (unique) s and values of type n.2Values of this type are compared by comparing the s. with a more precise type.Used to implement  and .*The graph's strongly connected components.     3 ; .!% 5 uNone( #&()+,/159<=>?topoligical sort with smallest-numbered available vertex first | input: nodes, edges | output is Nothing if the graph is not a DAG Note: should be stable to preserve order of generalizable variables. Algorithm due to Richard Eisenberg, and works by walking over the list left-to-right and moving each node the minimum distance left to guarantee topological ordering.vNone( #&()+,/159<=>?Graph structureNone( #&()+,/159<=>?   None( #&()+,/159<=>?#2! #2! wNone( #&()+,/159<=>?;Register a new file identifier or retrieve an existing one. Register a new file identifier () or retrieve an existing one ().;Register a new file identifier or retrieve an existing one.If . is returned, the file was already registered.Unique identifier of a file..Translate a file to an ID; mapping must exist.-Translate a ID to a file; mapping must exist.-%-)- -77--#  #    # 2 4 4 0 1 ; 4 : 3        -+-.----xNone( #&()+,/159<=>?"Add to specified CPU time account..Bill a pure computation to a specific account.Bill a computation to a specific account. Works even if the computation is aborted by an exception.;Bill a CPS function to an account. Can't handle exceptions.Semantic editor combinator.Semantic editor combinator.Semantic editor combinator..Resets the account and the timing information.Turn benchmarking on/off.Bill current account with time up to now. Switch to new account. Return old account (if any).(Account we can bill computation time to.Benchmark structure is a trie, mapping accounts (phases and subphases) to CPU time spent on their performance.Are we benchmarking at all?!What are we billing to currently?/The accounts and their accumulated timing bill.3Record when we started billing the current account.'Monad with access to benchmarking data.We need to be able to terminate benchmarking in case of an exception.$Initial benchmark structure (empty).2Print benchmark as three-column table with totals.Maybe new account.Maybe old account.   1 1 2 . 9 2 1 > *    3yNone( #&()+,/159<=>? % (+) m1 m2 adds m1 and m2, using (+) to add values.  O(n1 + n2).Returns a matrix of size  m1 m2. x m adds a new column to m, after the columns already existing in the matrix. All elements in the new column get set to x. x m adds a new row to m, after the rows already existing in the matrix. All elements in the new row get set to x.#Constructs a matrix from a list of (index, value) -pairs. O(n) where n is size of the list.!Precondition: indices are unique. sz rs constructs a matrix from a list of lists of values (a list of rows). O(size) where size = rows  cols.Precondition:  rs   sz and  (( sz ) . ) rs."Association list intersection.  O(n1 + n2). interAssocWith f l l' = { (i, f a b) | (i,a) D l and (i,b) D l' }Used to combine sparse matrices, it might introduce zero elements if f( can return zero for non-zero arguments. f m1 m2! build the pointwise conjunction m1 and m2 . Uses f to combine non-zero values.  O(n1 + n2).Returns a matrix of size  infSize m1 m2.Returns  iff the matrix is empty. (i,)  $ f a), and same for gs and g.?General pointwise combination function for sparse matrices.  O(n1 + n2). m extracts the diagonal of m.For non-square matrices, the length of the diagonal is the minimum of the dimensions of the matrix.%Type of matrix indices (row, column). Column index 1 <= col <= cols. Row index, 1 <= row <= rows.6Type of matrices, parameterised on the type of values.Sparse matrices are implemented as an ordered association list, mapping coordinates to values.Dimensions of the matrix.!Association of indices to values.Size of a matrix.Number of columns, >= 0.Number of rows, >= 0.Transposable things.Diagonal of sparse matrix.O(n) where n2 is the number of non-zero elements in the matrix.Pointwise comparison. Only matrices with the same dimension are comparable.Transposing coordinates.Matrix transposition. O(n log n) where n2 is the number of non-zero elements in the matrix.Size of transposed matrix.Turn a sparse vector into a vector by inserting a fixed element at the missing positions. O(size) where size is the dimension of the vector.?iMultiplication of .s. (Corresponds to sequential composition.)Smart constructor for Decr k :: Order which cuts off too big values.Possible values for k:  - ?cutoff  k  ?cutoff + 1.$Raw decrease which does not cut off.Decreasing and usable?$Raw increase which does not cut off.%The infimum of a (non empty) list of $s. Gets the worst information. & is the least element, thus, dominant.Matrix-shaped order is decreasing if any diagonal element is decreasing.le, lt,  decreasing, unknown4: for backwards compatibility, and for external use.Usable decrease.*Turn any increase into infinite increase ().Smart constructor for matrix shaped orders, avoiding empty and singleton matrices.We use a record for semiring instead of a type class since implicit arguments cannot occur in instance constraints, like +instance (?cutoff :: Int) => SemiRing Order.+The supremum of a (possibly empty) list of ;s. More information (i.e., more decrease) is bigger. # is no information, thus, smallest.A partial order, aimed at deciding whether a call graph gets worse during the completion.:In the paper referred to above, there is an order R with   Le  Lt.This is generalized to   'Decr k' where Decr 1 replaces Lt and Decr 0 replaces Le. A negative decrease means an increase. The generalization allows the termination checker to record an increase by 1 which can be compensated by a following decrease by 2 which results in an overall decrease.However, the termination checker of the paper itself terminates because there are only finitely many different call-matrices. To maintain termination of the terminator we set a cutoff point which determines how high the termination checker can count. This value should be set by a global or file-wise option.See Call for more information.9TODO: document orders which are call-matrices themselves.2Decrease of callee argument wrt. caller parameter.The Bool indicates whether the decrease (if any) is usable. In any chain, there needs to be one usable decrease. Unusable decreases come from SIZELT constraints which are not in inductive pattern match or a coinductive copattern match. See issue #2331.UPDATE: Andreas, 2017-07-26: Feature #2331 is unsound due to size quantification in terms. While the infrastructure for usable/unusable decrease remains in place, no unusable decreases are generated by TermCheck.&Matrix-shaped order, currently UNUSED.No relation, infinite increase, or increase beyond termination depth./We assume the matrices have the same dimension.It does not get worse then ` increase'. If we are still decreasing, it can get worse: less decreasing.Information order:  is least information. The more we decrease, the more information we have.When having comparable call-matrices, we keep the lesser one. Call graph completion works toward losing the good calls, tending towards Unknown (the least information).(, , ) forms a semiring, with  as zero and Le as one.Pick the worst information. collapse mWe assume that m codes a permutation: each row has at most one column that is not Unknown.To collapse a matrix into a single value, we take the best value of each column and multiply them. That means if one column is all Unknown, i.e., no argument relates to that parameter, then the collapsed value is also Unknown.,This makes order multiplication associative.'Can two matrices be multplied together?      {None) #&()+,/159<=>? Insert into a call matrix set.Non-augmented call matrix./Convert into a list of augmented call matrices.Union two call matrix sets.0Call matrix indices = function argument indices.Machine integer  is sufficient, since we cannot index more arguments than we have addresses on our machine.Sets of incomparable call matrices augmented with path information. Use overloaded  ,  ,  , .0Call matrix multiplication and call combination.Call matrices.A call matrix for a call f --> g has dimensions  ar(g)  ar(f).9Each column corresponds to one formal argument of caller f9. Each row corresponds to one argument in the call to g.In the presence of dot patterns, a call argument can be related to several different formal arguments of f. See e.g. testsucceedDotPatternTermination.agda:  data D : Nat -> Set where cz : D zero c1 : forall n -> D n -> D (suc n) c2 : forall n -> D n -> D n f : forall n -> D n -> Nat f .zero cz = zero f .(suc n) (c1 n d) = f n (c2 n d) f n (c2 .n d) = f n d 'Call matrices (without guardedness) are  -1 -1 n < suc n and n < c1 n d ? = c2 n d <= c1 n d = -1 n <= n and n < c2 n d ? -1 d < c2 n d Here is a part of the original documentation for call matrices (kept for historical reasons):This datatype encodes information about a single recursive function application. The columns of the call matrix stand for source function arguments (patterns). The rows of the matrix stand for target function arguments. Element (i, j)0 in the matrix should be computed as follows: (less than) if the j-th argument to the target; function is structurally strictly smaller than the i-th pattern. (less than or equal) if the j-th argument to the target+ function is structurally smaller than the i-th pattern. otherwise.,Call matrix augmented with path information.Meta info, like call path."The matrix of the (composed call).1Call matrix set product is the Cartesian product.Call matrix multiplication.f --(m1)--> g --(m2)--> h is combined to f --(m2  m1)--> h9Note the reversed order of multiplication: The matrix c1 of the second call g-->h in the sequence  f-->g-->h is multiplied with the matrix c2 of the first call.Preconditions: m1 has dimensions  ar(g)  ar(f). m2 has dimensions  ar(h)  ar(g).Postcondition:  m1 >*< m2 has dimensions  ar(h)  ar(f).%Augmented call matrix multiplication. 0  8 1 .  %-#%& ('+< * .  6-/:|None) #&()+,/159<=>?"Call graph comparison. A graph cs' is `worse' than cs if it has a new edge (call) or a call got worse, which means that one of its elements that was better or equal to Le moved a step towards Un.A call graph is complete if combining it with itself does not make it any worse. This is sound because of monotonicity: By combining a graph with itself, it can only get worse, but if it does not get worse after one such step, it gets never any worse. cs completes the call graph cs. A call graph is complete if it contains all indirect calls; if f -> g and g -> h are present in the graph, then f -> h should also be present.!Inserts a call into a call graph."Returns all nodes with self-loops.!Make a call with a single matrix.Make a call with empty cinfo.Returns all the nodes with incoming edges. Somewhat expensive. O(e).Converts a call graph to a list of calls with associated meta information.#Takes the union of two call graphs.Calls are edges in the call graph. It can be labelled with several call matrices if there are several pathes from one function to another.A call graph is a set of calls. Every call also has some associated meta information, which should be al so that the meta information for different calls can be combined when the calls are combined.Call graph nodes.Machine integer  is sufficient, since we cannot index more than we have addresses on our machine. is a monoid under . : checks whether the call graph is completely disconnected.?Displays the recursion behaviour corresponding to a call graph.Call graph combination.Application of  to all pairs (c1,c2) for which  c1 =  c2.)Converts a list of calls with associated meta information to a call graph.The original call graph.The current completion.    3 % ". 5   2  2}None) #&()+,/159<=>? *< c: should not make any parameter-argument relation worse.Use guardedness?Only consider calls whose source and target satisfy this predicate.Callgraph augmented with cinfo.A bad call path of type cinfo%, if termination could not be proven.Use guardedness?Only consider calls whose source and target satisfy this predicate.Callgraph augmented with cinfo.A bad call path of type cinfo%, if termination could not be proven.    ")&)-) )$) ))) ! ! ))~None( #&()+,/159<=>?Return the glyph set based on a given (unicode or ascii) glyph modePicking the appropriate set of special characters depending on whether we are allowed to use unicode or have to limit ourselves to ascii.We want to know whether we are allowed to insert unicode characters or not.'false: Stick to ASCII.!: Unicode characters are allowed./Choose the glyph set based on the unsafe IORef.3Are we allowed to use unicode supscript characters?& & ""$"""""&"-+ +$ $" "None( #&()+,/159<=>?Create a keyword range.5Range dedicated to a keyword or fixed token sequence.Motivation: by lacking a 0 instance we indicate that it cannot be updated.   % % ( (None( #&()+,/159<=>?-Writes a response command to standard output.Formats a response command. Replaces 'n'= with spaces to ensure that each command is a single line.Simple Emacs Lisp expressions.Atom.List.  %None( #&()+,/159<=>?fFCombine inferred . The unit is . # forms a pointwise additive monoid.Combine inferred  .Combine inferred  . The unit is  .!. forms an additive monoid with zero Quantity0.Combine inferred !. The unit is !.Compose with cohesion flag from the left. This function is e.g. used to update the cohesion information on pattern variables a- after a match against something of cohesion rel.Compose with modality flag from the left. This function is e.g. used to update the modality information on pattern variables a- after a match against something of modality q.Compose with polarity flag from the left. This function is e.g. used to update the polarity information on pattern variables a- after a match against something of polarity pol.Compose with quantity flag from the left. This function is e.g. used to update the quantity information on pattern variables a- after a match against something of quantity q.Compose with relevance flag from the left. This function is e.g. used to update the relevance information on pattern variables a! after a match against something rel. can be embedded into !.)Prefer user-written over system-inserted. composition.  is dominant,  is neutral.Composition of values of type . is dominant.  is neutral.Right-biased for the origin.(Multiplicative monoid (standard monoid).  composition.  composition.   is dominant,   is neutral.+Composition of quantities (multiplication).! is dominant. ! is neutral.Right-biased for origin.! composition. ! is dominant, !+ is neutral. Composition coincides with ./The default Modality terms are checked against.:Default Cohesion is the identity element under compositionThe default value of type  : not erased.Default is directive is private% (use everything, but do not export).The default Modality Beware that this is neither the additive unit nor the unit under composition, because the default quantity is .+Default used when not caring about polarityAbsorptive element! This differs from Relevance and Cohesion whose default is the multiplicative unit.;Default Relevance is the identity element under compositionIs []-cong allowed?:Are unrestricted erased matches allowed for indexed types?! can be projected onto .Does an argument arg fit the shape dom of the next expected argument?The hiding has to match, and if the argument has a name, it should match the name of the domain. should be , so use as @ fromMaybe  IMPOSSIBLE $ fittingNamedArg arg dom @ Check for !. Check for !. Check for !. arguments are hidden.Left division by a 3. Used e.g. to modify context when going into a rel argument.Left division by a  3. Used e.g. to modify context when going into a m argument.3Note that this function does not change quantities.Left division by a  3. Used e.g. to modify context when going into a pol argument.Left division by a !3. Used e.g. to modify context when going into a q argument.Left division by a !3. Used e.g. to modify context when going into a rel argument.inverseComposeCohesion r x returns the least y such that forall x, y we have (x `moreCohesion` (r `composeCohesion` y) iff /(r `inverseComposeCohesion` x) `moreCohesion` y1 (Galois connection). The above law fails for  r = Squash.inverseComposeModality r x returns the least modality y such that forall x, y we have .x `moreUsableModality` (r `composeModality` y) iff 5(r `inverseComposeModality` x) `moreUsableModality` y (Galois connection).inverseComposePolarity r x returns the least y such that forall x, y we have x `morePolarity'\` (r `composePolarity` y) iff ,(r `inverseComposePolarity` x) `morePolarity'\` y (Galois connection).inverseComposePolarity r x returns the least y such that forall x, y we have x `morePolarity'\` (r `composePolarity` y) iff ,(r `inverseComposePolarity` x) `morePolarity'\` y (Galois connection).inverseComposeQuantity r x returns the least quantity y such that forall x, y we have (x `moreQuantity` (r `composeQuantity` y) iff /(r `inverseComposeQuantity` x) `moreQuantity` y (Galois connection).inverseComposeRelevance r x returns the most irrelevant y such that forall x, y we have )x `moreRelevant` (r `composeRelevance` y) iff 0(r `inverseComposeRelevance` x) `moreRelevant` y (Galois connection).Irrelevant function arguments may appear non-strictly in the codomain type.isDefaultImportDir implies null, but not the other way round.Is the value "erased"?Monoidal composition of  information in some data. Alias for Mixed polarity.Information ordering. Flat `moreCohesion` Continuous `moreCohesion` Sharp `moreCohesion` SquashmorePolarity' x y is True whenever a variable of polarity x can be used anywhere where a variable of polarity y is expected. Note that morePolarity' x y actually means x <= y.m moreUsableQuantity m' means that an m can be used where ever an m' is required.Information ordering. Relevant `moreRelevant` ShapeIrrelevant `moreRelevant` Irrelevantm  m' means that an m can be used where ever an m' is required.Get the content of a  .,Equality of argument names of things modulo  and  . Alias for   polarity.An abbreviation: noPlaceholder =   .*Did the user supply a quantity annotation?Non-inlined equality that's sometimes useful to prevent GHC from ballooning code size. and  arguments are  notVisible.Like partitionEithers.Extract the positional modality components (cohesion and polarity) for checks regarding only them.prettyHiding info visible doc# puts the correct braces around doc according to info info and returns  visible doc% if the we deal with a visible thing./Equality ignoring origin. TODO: add origin to .Equality ignoring origin.Ignores  .Equality ignoring origin.,Equality of argument names of things modulo  and  .Equality for polarities.Equality ignoring origin.Equality ignoring origin. ,setNamedArg a b = updateNamedArg (const b) aApplied when working on types (unless --experimental-irrelevance).splittablePolarity pol == False& iff we cannot split on a variable of pol."Absorptive element under addition."Absorptive element under addition."Absorptive element under addition.Absorptive element is ."Absorptive element under addition.Identity under compositionIdentity under compositionIdentity under composition."Identity element under composition"Identity element under compositionThing with no range info.The functor instance for  8 would be ambiguous, so we give it another name here.usableCohesion rel == False! iff we cannot use a variable of rel.usablePolarity pol == False! iff we cannot use a variable of pol.9A thing of quantity 0 is unusable, all others are usable.usableRelevance rel == False! iff we cannot use a variable of rel. arguments are visible.xs `withArgsFrom` args translates xs into a list of s, using the elements in args to fill in the non- fields.5Precondition: The two lists should have equal length.4 forms a monoid under addition, and even a semiring.Identity under addition 4 forms a monoid under addition, and even a semiring.Identity element under addition!4 forms a monoid under addition, and even a semiring.Access modifier. Store the   of the private block that lead to this qualifier. This is needed for more faithful printing of declarations.  is the range of the private keyword.)What kinds of erased matches are allowed?What kinds of erased matches, if any, are allowed for single-constructor, indexed data types?.Erased matches are allowed for the empty type.Erased matches are allowed for single-constructor, non-indexed data types.What kinds of erased matches are allowed for indexed, single-constructor data types?[]-cong is allowed.All erased matches are allowed. A variant of : that supports default values that depend on other flags. The flag --erased-matches& has been given with (valid) options.No flag has been given, the default is used. (The default depends on whether the K rule is allowed or not.) The flag --erased-matches has been given without any options, the "default on" value is used. (The default depends on whether the K rule is allowed or not.)We have a tuple of annotations, which might not be fully orthogonal.Fitch-style dependent right adjoints. See Modal Dependent Type Theory and Dependent Right Adjoints, arXiv:1804.05236."Is any element of a collection an .4A function argument can be hidden and/or irrelevant.Sometimes we want a different kind of binder/pi-type, without it supporting any of the Modality interface.Names in binders and arguments.Associativity..Positions of variables in syntax declarations.The position (in the left-hand side of the syntax declaration) of the hole in which the variable is bound, counting from zero (and excluding parts that are not holes). For instance, for  syntax  A ( x C B) = B , A , x the number for x is 1, corresponding to B (0 would correspond to A).The position in the list of variables for this particular variable, counting from zero, and including wildcards. For instance, for "syntax F ( x _ y C A) = y ! A ! x the number for x is 0, the number for _ is 1, and the number for y is 2.1 of the CATCHALL pragma for a clause, if any.  means no such pragma.Cohesion modalities see "Brouwer's fixed-point theorem in real-cohesive homotopy type theory" (arXiv:1509.07584) types are now given an additional topological layer which the modalities interact with.identity modality.=same points, discrete topology, idempotent comonad, box-like.same points, codiscrete topology, idempotent monad, diamond-like.single point space, artificially added for Flat left-composition.Where does the ConP or Con come from?#User wrote a constructor (pattern).User wrote a record (pattern).(Generated by interactive case splitting.8Inserted by system or expanded from an implicit pattern./Distinguish constructors from pattern synonyms.0Can we construct a record by copattern matching?!Coverage check? (Default is yes).Variants of Cubical Agda.Distinguish parsing a DISPLAY pragma from an ordinary left hand side.A special case of !: erased or not.Note that the 2 instance does *not* ignore the origin arguments.*Expression kinds: Expressions or patterns.Fixity of operators.&Range of the whole fixity declaration.The notation is handled as the fixity in the renamer. Hence, they are grouped together in this type.Range of the name in the fixity declaration (used for correct highlighting, see issue #2140).$Fixity level declared as the number.No fixity declared.8Force record type to have eta equality? (Default is no).Pattern and copattern matching is allowed in the presence of eta.In the absence of eta, we have to choose whether we want to allow matching on the constructor or copattern matching with the projections. Having both leads to breakage of subject reduction (issue #4560).%Does a record come with eta-equality?The things you are allowed to say when you shuffle names between name spaces (i.e. in import,  namespace, or open declarations). Only for open. Exports the opened names from the current module. Range of the public keyword.3An imported name can be a module or a defined name.Imported module name of type m.Imported name of type n.Abstract or concrete.9Does a datatype have path constructors, i.e. is it a HIT?Functions can be defined in both infix and prefix style. See .0Is this definition eligible for instance search? Range of the instance keyword.Is this a macro definition?Opaque or transparent.This definition is opaque, and it is guarded by the given opaque block.4Monoid representing the combined opaque blocks of a * containing possibly-opaque declarations.%More than one opaque block was found.Nothing here is opaque.= 0. Number >= 1. Notation as provided by the syntax declaration. Notation parts. A hole: a place where argument expressions can be written. For instance, for _+_) the two underscores are holes, and for  syntax  A ( x C B) = B , A , x the variables A and B are holes. The number is the position of the hole, counting from zero. For instance, the number for A is 0, and the number for B is 1. &An identifier part. For instance, for _+_ the only identifier part is +. A bound variable.The first range is the range of the variable in the right-hand side of the syntax declaration, and the second range is the range of the variable in the left-hand side. /A wildcard (an underscore in binding position). The unique identifier of an opaque block. Second argument is the top-level module identifier. Origin of arguments. &Produced by an interactive case split. Inserted by the conversion checker in an argument spine at the position where they differ.Indicates that the argument at this position should always be reified, even if the visibility/modality would be skipped with the current flags.  An expanded hidden argument pun. &Inserted by the generalization process E.g. inserted hidden arguments. Inserted to stand for the record "self" variable when checking a declaration inside a record module. %Produced by the reflection machinery. Named application produced to represent a substitution. E.g. "?0 (x = n)" instead of "?0 n" /From the source file / user input. (Preserve!)  Origin of !. User wrote ".". User wrote nothing. User wrote "@irr". User wrote "@irrelevant".  Origin of !. User wrote nothing. User wrote "@relevant".  Origin of !. User wrote "..". User wrote nothing. User wrote "@shirr". User wrote "@shape-irrelevant". The possible overlap modes for an instance, also used for instance candidates. No user-written overlap pragma. This instance can be overlapped by an OVERLAPPING instance, and it can overlap OVERLAPPABLE instances. 'Overlapping instances in record fields. User-written INCOHERENT pragma: both overlappable and overlapping; and, if there are multiple candidates after all overlap has been handled, make an arbitrary choice. User-written OVERLAPPABLE pragma: this candidate can *be removed* by a more specific candidate. User-written OVERLAPPING pragma: this candidate can *remove* a less specific candidate. User-written OVERLAPS pragma: both overlappable and overlapping. /Can we pattern match on the record constructor? =For a record without eta, which type of matching do we allow? 5Can copattern match using the projections. (Default.) $Can match on the record constructor. #The actual polarity of the variable The locks of the variable (= composition of all denominators the variable has been left divided by) ,The original polarity annotation by the user 4The position of a name part or underscore in a name. ;The following underscore is at the beginning of the name: _foo. 4The following underscore is at the end of the name: foo_. 8The following underscore is in the middle of the name: foo_bar. #Positivity check? (Default = True).  Precedence levels for operators. A "problem" consists of a set of constraints and the same constraint can be part of multiple problems. "Where does a projection come from?  User wrote a postfix projection. User wrote a prefix projection. 'Projection was generated by the system.  Origin of !. User wrote "@0". User wrote "@erased". User wrote nothing.  Origin of !.!User wrote "@1".!User wrote nothing.!User wrote "@linear".!Quantity for linearity.A quantity is a set of natural numbers, indicating possible semantic uses of a variable. A singleton set {n}= requires that the corresponding variable is used exactly n times.! Zero uses {0}, erased at runtime.! Linear use {1} (could be updated destructively). Mostly TODO (needs postponable constraints between quantities to compute uses).!Unrestricted use B.! Origin of !.!User wrote "@".!User wrote nothing.!User wrote "@plenty".!String with range info.!Thing with range info.!A RawName is some sort of string.!:A function argument can be relevant or irrelevant. See Agda.TypeChecking.Irrelevance.!3The argument is irrelevant at compile- and runtime.!4The argument is (possibly) relevant at compile-time.!Like !, the argument may never flow into evaluation position. So it is irrelevant at run-time, yet treated relevantly during equality checking.Unlike !, it is used to type !* arguments in functions: If you enable --experimental-irrelevance, then the type of an irrelevant function is forced to be shape-irrelevant. See: -  (https://doi.org/10.2168/LMCS-8(1:29)2012 example 2.8 (Not enforcing shape-irrelevant codomains can break subject reduction!) -  &https://dl.acm.org/doi/10.1145/3110277 - 'https://doi.org/10.1145/3209108.3209119!New fixity of ! (optional).!Rename from this name.!#To this one. Must be same kind as !.!The range of the "to" keyword. Retained for highlighting purposes.!RewriteEqn' qn p e represents the rewrite and irrefutable with clauses of the LHS. qn stands for the QName of the auxiliary function generated to implement the feature nm/ is the type of names for pattern variables p is the type of patterns e is the type of expressions! with p <- e in eq!  using p <- e!  rewrite e!0Termination check? (Default = TerminationCheck).!#Skip termination checking (unsafe).!Treat as non-terminating.!/Treat as terminating (unsafe). Same effect as !.!Run the termination checker.!2Skip termination checking but use measure instead.!;Type wrapper to indicate additive monoid/semigroup context.!Type wrapper to indicate composition or multiplicative monoid/semigroup context.!!Universe check? (Default is yes).!The using clause of import directive.!No using clause given.!using the specified names.!Decorating something with  information.!Decorating something with   information.! Default is ."Ignores range.$,Composition is left-biased, taking the left  if both have one.$, is an idempotent partial monoid, with unit .  and  are incompatible.$+Semigroup computes if any of several is an .$Conjunctive semigroup ( is absorbing).$Right-biased composition, because the left relevance acts as context, and the right one as occurrence.$Right-biased composition, because the left relevance acts as context, and the right one as occurrence.$ Just for the 9 instance. Should never combine different overlapping.$Right-biased composition, because the left quantity acts as context, and the right one as occurrence.$Right-biased composition, because the left quantity acts as context, and the right one as occurrence.$Right-biased composition, because the left quantity acts as context, and the right one as occurrence.$'' is the additive unit.$ " forms a semigroup under addition.% is the additive unit.%" forms a semigroup under addition.%Pointwise additive unit.%Pointwise addition.% Continous is the multiplicative unit.% % forms a semigroup under composition.% Continous is the multiplicative unit.%% forms a semigroup under composition.%! is the unit under composition.%!% forms a semigroup under composition.%In the absense of finite quantities besides 0,  is the unit. Otherwise, 1 is the unit.%+Composition of quantities (multiplication).! is dominant. ! is neutral.Right-biased for origin.%Pointwise composition unit.%Pointwise composition.%Ranges are not forced.%Ranges are not forced.%Ranges are not forced.% 5 shall mean no information, not even origin or range.%null for import directives holds when everything is imported unchanged (no names are hidden or renamed).% 0 means no information, not even origin or range.% 0 means no information, not even origin or range.&2Order is given by implication: flatter is smaller.&Ignores range.&More relevant is smaller.&Flatter is smaller.&The derived Ord instance for ModalPolarity is just used for serialisation and has no particular meaning. The actual order on modalities is a partial order.&Dominance ordering.&Note that the order is  D 0,1, more options is smaller.&More relevant is smaller.&Ignores range.'?The record selectors are not included in the resulting strings.%!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!! ! !!! !!! !!! !! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! ! ,! 2! "! .! 4! #!;! &!!  !#! ! ! ! !&!")!")!  #!&-"  #"&-"$+"")"")"")"!"#"")"  #" /" )" 5" " " !"%" "" " "#"" " " % )" $" % )"" $" "" " " " " "%)"" " % )"" " " """"""! !" """ """ "  "!!" " " " "! !" " " """ " " """ """" """"" " " """""""""" "" " """"  "" " " " " """" " " " "&"%-"'"'/"$""*" ("%-"%-"#""#  # ######%##  #(/#+2## + 2# ###  #### + 2#%####### ####-4#%###  #  #  ##*#+2#+2###  ##  ## + 2# $# # # (# # # # # # ,# # )# # # # # 5# # /#! !# # ## !# (# %# ## # # # # # 6# # ># #! !# ;# /# /# # # ###"*# # # # # # "#+-## # # *# # $# # # # !# 4# #! !$# # # "# !# .# # # # # !# # # # # # # 7# # # $" " $ $ $ $$ "$ )$ $ &$ $$ #$ $ $ $ $ $ $ 8$ $ $ $! !$ 7$ !$ >$ 1$ 1$ $ 6$ 8$ .$ 9$ /$ 8$ .$ 8$ .$ #$  $  $ $ $ $ $ $ $ $ $ $ #$ #$ )$ $ $ $ 1$ #$ #$ $ $ $ $ #$ #$ $$ ,$ $ $ $ *$ $ "$ $ $ $ #$ $ $ $ $ $ $  $ !$  $  $ #$ %$ ($ ,$ /$ 1$ 4$ $ $ $ !$! !!$! !$$ $ "$ $ !$ $ $ '$ *$ $ $ $  $ !$ $$ $ "$ &$ )$ $  $ $ #$ $ $ $ $ $ $ 1$ 4% )% ,% *% -% )% ,% )% ,% 4% 7% ,% /% -% 0% ,% /% ,% /% % !% %  % % %% ,% 1% % $% % !%" "&% % % % ,% % % %! !!% % % % % % % (% % ?% <%% % % % % % % % 1% % % % :%" "% % % !% % &% % % #% !% %17% % % % % % '% 2% % 8% % % 1% % 5% +% +% % % % %! !% % % % % % %% % % % % % % $% % % % % % % .% % % % %%,/%%%%%%%&!!& &&  &  && &&  &&&&&&&&&&&& #&/2&&&&&&&! !&&&&&&&&&& #& #& #& #& !& & &&&  &&& 3& +& ,& +& +& 6& .& /& .& .& 9& 1& 2& 1& 1& & "& & %& & &&& -& '& *& 3& & $& & & ,& & & & & & & ?& <& & & & & & & & '&" "& & !& & && & !& & & & & & '& & 8& & & 5& +& +& -& (& & /&" "& #& !& (& #& ' ' ' ' ' ' /' /'''''''''' '!!'  '' ' '  '' '' '! !''' ' ''  '' ' '''''''' '' '' ' '6:' '''!%''! !'!%' ' ' ' ' ' ' '' '' ' ' ' ' ' ' ''  '' '  ''59';?'  '''  '(3'/:')4'1<'&1',7' * 5'/:'/:' ' ' None( #&()+,/159<=>?*'Blanks the non-code parts of a given file, preserving positions of characters corresponding to code. This way, there is a direct correspondence between source positions and positions in the processed result.'Returns True& if the role corresponds to Agda code.'Returns True! if the layer contains Agda code.''List of valid literate file extensions.'Preprocessor for Markdown.The ! parameter controls whether only ```agda- blocks are treated as Agda code. When True , only blocks explicitly marked ```agda are considered code. When False, both unmarked ``` and ```agda blocks are code (default).'$Preprocessor for Org mode documents.'List of valid extensions for literate Agda files, and their corresponding preprocessors.If you add new extensions, remember to update test/Utils.hs so that test cases ending in the new extensions are found.The ! parameter controls whether only ```agda blocks are treated as Agda code in Markdown/Typst files. When True, only blocks marked ```agda are considered code. When False, both ``` and ```agda blocks are code (default).'"Preprocessor for reStructuredText.'Preprocessor for literate TeX.'9A sequence of characters in a file playing the same role.' Role of a character in the file.'A list of contiguous layers.'/Type of a literate preprocessor: Invariants:  f : Processorproposition> f pos s /= []*proposition> f pos s >>= layerContent == s7Annotates a tokenized string with position information.#Preprocessor for Forester documents6Replaces non-space characters in a string with spaces.Returns a tuple consisting of the first line of the input, and the rest of the input.2Canonical decomposition of an empty literate file.*Check if a character is a blank character.Create a regular expression that: - Must match the whole string - Works across line boundaries'''''''''''''''''''''''''''''''''''''''''''**'8 8#'22'* *None( #&()+,/159<=>? '*Does a function application need brackets?'*Does a function application need brackets?'#Argument context preferring parens.(Does a lambda-like thing (lambda, let or pi) need brackets in the given context? A peculiar thing with lambdas is that they don't need brackets in certain right operand contexts. To decide we need to look at the stack of precedences and not just the current precedence. Example: mA >>= ( x C x) >>= mA (for _>>=_ left associative).(Do we need to bracket an operator application of the given fixity in a context with the given precedence.(Do we need to bracket an operator application of the given fixity in a context with the given precedence.($Does a function space need brackets?(&Does a with application need brackets?(*Do we prefer parens around arguments like  x C x or not? See (.((Precedence is associated with a context.(When printing we keep track of a stack of precedences in order to be able to decide whether it's safe to leave out parens around lambdas. An empty stack is equivalent to (. Invariant: `notElem TopCtx`.(Decorating something with Fixity'.''''((((((((((((((((((((((((((((((((((((((((((((((''(((''(((($ $(55(( ($$#(55 ( 6( )( ((& & (7 7($$(9 9($$(55(-1( +None* #&()+,/159<=>?W (Uses the given document as the printed representation of the given parser. The document's precedence is taken to be atomP.(&Tries to print the parser, or returns empty, depending on the implementation. This function might not terminate.(Memoises the given parser./Every memoised parser must be annotated with a unique key. (Parametrised parsers must use distinct keys for distinct inputs.)(Memoises the given parser, but only if printing, not if parsing./Every memoised parser must be annotated with a unique key. (Parametrised parsers must use distinct keys for distinct inputs.)(Runs the parser.(.Parses a token satisfying the given predicate.(Parses a token satisfying the given predicate. The computed value is returned.(Memoisation keys.(The parser monad.(((((((((((((((((((((((((((((((((((((0 0(3 3(00( ( (00(33None( #&()+,/159<=>? P%(Get the first version of the concrete name that does not satisfy the given predicate.(-Is the name an operator? Needs at least 2 (s.(An open mixfix identifier is either prefix, infix, or suffix. That is to say: at least one of its extremities is a Hole(Is the name (un)qualified?(:Check whether a name is a simple identifier without holes.($Zoom on the last non-hole in a name.(Don't use on 'NoName{}'.((Lens for the unqualified part of a QName(Get a raw version of the name with all suffixes removed. For instance, nameRoot "xAAA" = "x".(Lens for accessing and modifying the suffix of a name. The suffix of a NoName is always Nothing, and should not be changed.(,Split a name into a base name plus a suffix.(?)Print list of errors.)Extra information for error ).)What kind of declaration? See also .)Name of a data type.)Name of a function.)Name of a record type.)Nicifier errors.)The reason for an ErasedDatatype error.)Erased matches are disabled for indexed, single-constructor types.),Erased matches are disabled for empty types.)Erased matches are disabled for non-indexed, single-constructor types.)There are several constructors.)Symbolic name of an Agda error.+Reasons for error +.+Reasons for error +.+#Things not allowed in dot patterns.)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))********************************************************************************************************************************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))+,,+++++++))))))))))))))))))))))))********************************************************************************************************************************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++)))))))))))))))+++++++++++++++++++++++++,,,,,,,,,,))))))++++,,,,,,,,,,,,,,,,)))))))))))))))))))))),"),"),"),,.".),,"),,"),,,,"),"),"),"),5"5),,"), , , , ,,.. , ,55 , , , , , , , , , ,,, ,,1,,,,,..,,,,,,,55,,  , %, $, ', (, , , , ,. ., , , , , , , , , ,5 5, , None( #&()+,/159<=>?,Arbitrary JS code.--+,,,,,,,,,,,,,,,,,,,,,,,,,-------------------,,,,,,,,,,,,,,,,,,,,,-------,,,,--------------66-;;-''-6 6-3 3-; ;- - - "- (- (- - 2- -33-' '- -66-33-;;- - - - - "- )- 4None( #&()+,/159<=>?----------------------------------None( #&()+,/159<=>?-Separate by blank line.-1Separate by space that will be removed by minify.For non-removable space, use d <> " " <> d'.-Check if a string is a valid JS identifier. The check ignores keywords as we prepend z_ to our identifiers. The check is conservative and may not admit all valid JS identifiers.-Apply - to - if boolean is true.-1Concatenate vertically, separated by blank lines.------------------------------------------------/---------------------------------------------------( (- - - - "- 4- (- - - %- - &- - - .None( #&()+,/159<=>?- .+Lookup a builtin by the string used in the BUILTIN pragma./Builtins that come without a definition in Agda syntax. These are giving names to Agda internal concepts which cannot be assigned an Agda type.,An example would be a user-defined name for Set.{-# BUILTIN TYPE Type #-} The type of Type would be Type : Level C Set which is not valid Agda./%Lookup a primitive by its identifier./A builtin name, defined by the BUILTIN pragma.1-The class of types which can be converted to 2.1Get the identifier for this builtin, generally used for error messages.1 Convert this value to a builtin.1!A primitive name, defined by the  primitive block.2 Either a / or 1, used for some lookups.--................................................................................................................................////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111122222222222222222222222222222222222222111//////////////////////////////////000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111/////////////////..////././/.//////////////...//////////////../////////////...//......././/////////....///......--.............................................................................................111111111111111111111111111111111111111111111111111111111111111111111111111111111122222222222222222222222222222222////.////..//.///2#2#2%)2%)2222+22+22#2 2 2 2 2 2& &2 2 2 2 2 2222 2 2 2 2 None( #&()+,/159<=>?24Drop anonymous modules at the end of the module name2Get the name if unambiguous.2%Get the first of the ambiguous names.2Is a name ambiguous.2A module is anonymous if the qualification path ends in an underscore.2/Is the first module a weak child of the second?20Is the first module a weak parent of the second?21Is the first module a proper child of the second?22Is the first module a proper parent of the second?2Is the name an operator?2Van Laarhoven lens on 2.2Van Laarhoven lens on 2.29Preserve lineage information from both maps, left-biased.29Get the next version of the concrete name. For instance, nextName "x" = "xA". The name must not be a NoName.2Turn a qualified name into a concrete name. This should only be used as a fallback when looking up the right concrete name in the scope fails.2 Convert a 3 to a 3 (add no module name).2Ignoring the suffix.2%Useful for debugging scoping problems2A singleton "ambiguous" name.2Sets the ranges of the individual names in the module name to match those of the corresponding concrete names. If the concrete names are fewer than the number of module name name parts, then the initial name parts get the range .C.D.E `withRangesOf` [A, B] returns C.D.E! but with ranges set as follows:C: .D: the range of A.E: the range of B.Precondition: The number of module name name parts has to be at least as large as the length of the list.2Like 2, but uses the name parts (qualifier + name) of the qualified name as the list of concrete names.2-A decoration of abstract syntax module names.2&Explanation where this name came from.2The resolved module name.2A decoration of .26The kind (definition, constructor, record field etc.).2&Explanation where this name came from.2Additional information needed during scope checking. Currently used for generalized data/record params.2The resolved qualified name.2Alternative in 2.23/ with lineage information, for error reporting.23 without lineage information.2?4Occurrence of the nth definition argument inside the definition.4&Definition site of a mutual definition4Subterm occurrences for positivity checking. The constructors are listed in increasing information they provide: 3Mixed <= JustPos <= StrictPos <= GuardPos <= Unused Mixed <= JustNeg <= Unused.4Guarded strictly positive occurrence (i.e., under D). For checking recursive records.4Negative occurrence.4/Positive occurrence, but not strictly positive.4-Arbitrary occurrence (positive and negative).4Strictly positive occurrence.4No occurrence.4in the type of a constructor4&in an endpoint of a higher constructor4)in the nth argument of a defined constant4'in the nth clause of a defined function4in the definition of a constant4"is an index of an inductive family4*in a sort, e.g. in the level of a universe4$in a datatype index of a constructor41matched against in a clause of a defined function4 as an argument of a metavariable4in the nth argument of a def in the current mutual block. (def given by Int index in the block)4'in the principal argument of built-in D4as an argument to a bound variable with given polarity. The polarity is only used for warning printing.41List of polarities stemming from POLARITY pragma.44* is a complete lattice with least element 4 and greatest element 4.&It forms a commutative semiring where  is meet (glb) and 0 is composition. Both operations are idempotent.For , 4 is neutral (zero) and 4 is dominant. For , 4 is neutral (one) and 4 is dominant.!444444444444444444444444444444444!4444444444444444444444444444444444&"&)4&& 4 4 4&&4 4 4#4 43 341 14 4 444&&4 4( (4 4 4 '4= =444& &4 44 !None( #&()+,/159<=>?4Each redundant field comes with a range of associated dead code.4Record type, fields not supplied by user, non-fields but supplied. The redundant fields come with a range of associated dead code.44444444444444444")4 444 $4 4 None( #&()+,/159<=>?"5Ranges are not forced. 44445555555 5445555554456 65 5 5 5 5 None( #&()+,/159<=>?m"5Unconditional layout keywords.Some keywords introduce layout only in certain circumstances, these are not included here.5Tokens which may appear qualified.5 qualified do5 qualified (|) or SS5 qualified (| or S,  if unicode5A "qualified token", i.e. a sequence of (module) names followed by one of the allowed (5) keywords/symbols.5-> or C5@@@5 |5 }5|) or S,  if unicode5 )5 #-}5layout-implied }5 :5 .5 ..5{{ or S,  if unicode5{{ or S,  if unicode5... or @5(|) or SS5A misplaced end-comment "-}".5 =5@ or @5 {5(| or S,  if unicode5 (5 {-#5layout-implied {5 ?5 ;5 _5layout-implied ;6Arbitrary string (not enclosed in double quotes), used in pragmas.5The token itself.Parts for the qualifying identifier, together with their ranges.#Range of the token being qualified.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556666666666666566666666666666555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555 6//6 6 6 66 !6 6 #6//6666None( #&()+,/159<=>? 6Drop 6 constructors. (Safe)6Drop 6 constructors. (Safe)6 Discards Proj f entries.6Drop 6 constructor. (Safe)6Only 6 variant.6Drop 6 constructors, fails with  IMPOSSIBLE if there's a non-6 entry.6Drop 6 constructor, fails with  IMPOSSIBLE on a projection.6Split at first non-665Eliminations, subsuming applications and projections.6 Application.6'IApply x y r, x and y are the endpoints6 Projection. 3 is name of a record projection.6This instance cheats on 6, use with care. 6s are always assumed to be  , since they have no . Same for IApply666666666666666666666666666666 6$66 6 ,6 6 &6 (6 6&1None( #&()+,/159<=>? 6When trying to reduce f es(, on match failed on one elimination e D es that came with info r :: NotBlocked.  stuckOn e r produces the new  NotBlocked info.6 must be propagated, as this is blockage that can be lifted in the future (as more clauses are added).6 e0 is also propagated, since it provides more precise information as  StuckOn e (as e0 is the original reason why reduction got stuck and usually a subterm of e). An information like %StuckOn (Apply (Arg info (Var i []))) (stuck on a variable) could be used by the lhs/coverage checker to trigger a split on that (pattern) variable.In the remaining cases for r$, we are terminally stuck due to  StuckOn e. Propagating 6 does not seem useful.64 must not be propagated, as this would mean that f es is underapplied, which is not the case (it is stuck). Note that 6 can only arise when projection patterns were missing to complete the original match (in e/). (Missing ordinary pattern would mean the e is of function type, but we cannot match against something of function type.)6Something where a meta variable may block reduction. Notably a top-level meta is considered blocking. This did not use to be the case (pre Aug 2020).6What is causing the blocking? Or in other words which metas or problems need to be solved to unblock the blocked computation/constraint.6 Unblock when function is defined6Unblock if meta is instantiated6Even if we are not stuck on a meta during reduction we can fail to reduce a definition by pattern matching for another reason.62We matched an absurd clause, results in a neutral Def.6We ran out of clauses for 3, all considered clauses produced an actual mismatch. This can happen when try to reduce a function application but we are still missing some function clauses. See  Agda.TypeChecking.Patterns.Match.6Reduction was not blocked, we reached a whnf which can be anything but a stuck Def.6The Elim' is neutral and blocks a pattern match.6 >,66 6 ,6 6 6* *6 6&1None, #&()+,/159<=>?A*6Constant level n7Absurd lambdas are internally represented as identity with variable name "()".76Make an absurd pattern with the given de Bruijn index.7Doesn't do any reduction.7Add 9 is it is not already a DontCare.7Context entries without a type have this dummy type. Note: use macro  DUMMY_DOM !7A dummy level to constitute a level/sort created at location. Note: use macro  DUMMY_LEVEL !7Construct a string representing the call-site that created the dummy thing.75A dummy sort created at location. Note: use macro  DUMMY_SORT !75A dummy term created at location. Note: use macro  DUMMY_TERM !7,Aux: A dummy term to constitute a dummy termlevel sort/type.75A dummy type created at location. Note: use macro  DUMMY_TYPE !7Build 8 from 8.7#A view distinguishing the neutrals Var, Def, and MetaV which can be projected.7Is this Dom annotated as a local rewrite rule and if so, has the rewrite been invalidated due to a substitution?7+Is this a Prop universe? Answers are yes ( ) or maybe ().74Is this a strict universe inhabitable by data types?7Given a constant m and level l , compute m + l7Lens to edit a 9 as a list.7)A traversal for the names in a telescope.7'Retrieve the PatternInfo from a pattern7 Retrieve the origin of a pattern7 Turn a known  sort into a  sort, leave others unchanged.7 Get the flavor of the universe.  could also mean "don't know".7Removing a topmost 9 constructor.7(Convert a list telescope to a telescope.7%Convert a telescope to its list form.7Build partial 8 from 87>Convert top-level postfix projections into prefix projections.7Convert 6/ projection eliminations according to their   into 9 projection applications.7An unapplied variable.7Binder.72: The bound variable might appear in the body. 7 is pseudo-binder, it does not introduce a fresh variable, similar to the const of Haskell.76The body has (at least) one free variable. Danger: 7! doesn't shift variables properly7Type of argument lists.7 'Blocked a without the a.7Newtypes for terms that produce a dummy, rather than crash, when applied to incompatible eliminations.73A clause is a list of patterns and the clause body.The telescope contains the types of the pattern variables and the de Bruijn indices say how to get from the order the variables occur in the patterns to the order they occur in the telescope. The body binds the variables in the order they appear in the telescope.  B.8Elaborated "@rewrite" equation/Will only be present if domain annotated with " rewrite" ( annRewrite is IsRewrite@) AND the type successfully elaborated into a rewrite rule.8 "@tactic e".8 Terms used for internal purposes8Collects applications to a 7.8Generic dummy term, the  generally describes where the term was generated (as well as giving a disambiguator).0Should not be used to convey actual information.8 NotHidden.8Builtin EQUALITY.8Hidden. Empty or Level.8 Range of the rewrite expression, if any.8 NotHidden.8Sort of this type.8Hidden.8View type as equality type.8A type of the form u D v4 decomposed into its parts. Used as type for the rewrite expression.8$A reduced type used as type for the with inspect idiom.8"A reduced type used as type for a with expression.8>A level is a maximum expression of a closed level and 0..n 94 expressions each of which is an atom plus a number.8Telescope as list.8 Extra information attached to a 9.8)Information on the origin of the pattern.8Time when this pattern was constructed during LHS checking. This field is used during pattern matching with the non-compiled clauses.8Undirected equational constraint ("the LHS and RHS must be convertible in the calling context"). Admits arbitrary substitution.8For the sake of reducing clauses before they have compiled, we keep a match priority in the constructors (and literals) of patterns that is computed during lhs checking and decides whether a mismatch should be treated as a hard No. Matches that get available earlier have a lower priority. Lower priority wins, meaning that if we combine a DontKnow with a No) we take the one with the lower priority.8Named pattern arguments.81Non-linear (non-constructor) first-order pattern.8Matches x es# where x is a lambda-bound variable8Matches f es8Matches  x C t8Matches  (x : A) C B8"Matches a sort of the given shape.8'Matches the term modulo  (ideally ).8Matches anything (modulo non-linearity) that only contains bound variables that occur in the given arguments. Tracks the definitional singularity of the surrounding pattern (not the type of the variable itself)9Wrapper for types that do not contain variables (so applying a substitution is the identity). Useful if you have a structure of types that support substitution mixed with types that don't and need to apply a substitution to the full structure.9Origin of the pattern: what did the user write in this position?9User wrote an absurd pattern9 User wrote a constructor pattern9User wrote a dot pattern9User wrote a literal pattern9User wrote a record pattern9Pattern generated by case split9+Argument to pattern generated by case split9Pattern inserted by the system9User wrote a variable pattern9User wrote a wildcard pattern9Pattern variables.9View type as path type.9reduced9Hidden9 NotHidden9 Builtin PATH.9 NotHidden9Sort of this type.9Hidden97Patterns are variables, constructors, or wildcards. QName is used in ConP rather than Name since a constructor might come from a particular namespace. This also meshes well with the fact that values (i.e. the arguments we are matching with) use QName.9c ps= The subpatterns do not contain any projection copatterns.9:Used for HITs, the QName should be the one from primHComp.9 .t9Path elimination pattern, like VarP but keeps track of endpoints.9E.g. 5, "hello".91Projection copattern. Can only appear by itself.9 x97Extract pattern variables in left-to-right order. A 9+ is also treated as variable (see docu for 7).9Elaborated "@rewrite" equation9="@rewrite" equation transformed into a directed rewrite rule.Nothing iff invalidated by a substitution. If we are checking against an "8rewrite" domain, this is fine, but if we are inside an "6rewrite" context, this is probably an internal error.9?de Bruijn index of head symbol (excluding rewContext variables)9Directed rewrite rules generic over the type of head symbol. Generally unstable under substitution.9#Constructing a singleton telescope.9Sorts.9A postulated sort.9A (part of a) term or type which is only used for internal purposes. Replaces the abuse of Prop for a dummy sort. The String typically describes the location where we create this dummy, but can contain other information as well.9(Sort of a (non-dependent) function type.9Prop:, (S)Set:.9 IntervalUniv+, a sort inhabited by the cubical interval.9 LevelUniv, a sort inhabited by type Level>. When --level-universe isn't on, this universe reduces to Set 09LockUniv, a sort for locks.9Sort metavariable.9Sort of the pi type  (x : A) C B#. The components are the domain A (as a bare term), the sort s1 of A, and the sort s2 of B in the context extended by x : A.The sort denoted by 9 A s1 s2 only depends on s1 and s2. The domain A0 is kept around so that we can rebuild the type 9 s1 A needed to extend the context when we have to work under the binder of s2; see e.g. reduceB' for sorts or  piSortEquals.9SizeUniv, a sort inhabited by type Size.9Prop B, Set B, SSet B.9(Sort of another sort ("successor sort").9Substitutions.9Substitution extension, `cons'.   E u : A  E  :  ----------------------  E u :#  : , A 9Empty substitution, lifts from the empty context. First argument is  IMPOSSIBLE. Apply this to closed terms you want to use in a non-empty context.  E EmptyS : ()9Identity substitution.   E IdS : 99Lifting substitution. Use this to go under a binder. Lift 1  == var 0 :# Wk 1 .   E  :  ------------------------- ,  E Lift ||  : ,  9/Strengthening substitution. First argument is  IMPOSSIBLE. In 'Strengthen err n  the number n must be non-negative. This substitution should only be applied to values t$ for which none of the variables 0 up to n - 1 are free in t[], and in that case n5 is subtracted from all free de Bruijn indices in t[].  E  :  || = n ---------------------------  E Strengthen n  : ,  @99Weakening substitution, lifts to an extended context.   E  :  ------------------- ,  E Wk ||  :  92Suggest a name if available (i.e. name is not "_")9 Drop the types from a telescope.9Sequence of types. An argument of the first type is bound in later types and so on.97 is never 7.9 Raw values.Def is used for both defined and undefined constants. Assume there is a type declaration and a definition for every constant, even if the definition is an empty list of clauses.9c es or record { fs = es } es allows only Apply and IApply eliminations, and IApply only for data constructors.9f es, possibly a delta/iota-redex9Irrelevant stuff in relevant position, but created in an irrelevant context. Basically, an internal version of the irrelevance axiom .irrAx : .A -> A.9A (part of a) term or type which is only used for internal purposes.The 8 describes why this dummy was created; typically, it is a string describing the source location that created it, but dummy terms are also used when *leaving* the type checker (through reification) to convey out-of-band information.The second field accumulates eliminations in case we apply a dummy term to more of them. Dummy terms should never be used in places where they can affect type checking, so syntactic checks are free to ignore the eliminators, which are only there to ease debugging when a dummy term incorrectly leaks into a relevant position.9+Terms are beta normal. Relevance is ignored9)dependent or non-dependent function space9x es neutral9The size of a term is roughly the number of nodes in its syntax tree. This number need not be precise for logical correctness of Agda, it is only used for reporting (and maybe decisions regarding performance).'Not counting towards the term size are:sort and color annotations, projections.9'Types are terms with a sort annotation.9(PropSetSSet):.9PropSetSSet B.:Ignores   and  and tactic.;A   clause is one with no patterns and no rhs. Should not exist in practice.;2The size of a telescope is its length (as a list).8#eliminations ordered left-to-right.9The  PatVarName is a name suggestion.::::2222222222222222222222222222222222222222222222222266677777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777776666666666666666666666666666666666666662222222222222233333333333333333333333333333333333333333333333333333333 (((((777777777777788888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999666666666666666666666666666666777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778888888888888888888888888888888888888888888888888888888888888888888888888888888888::88888:8888888888888888888888888888888888888888899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999:9999999999 9: : " ): *: : : : : :::  : :: :: : : :::  :: : ::$:$:$::$:$::%:::::$+:: '::: :  ::  :  :  :  : ::3:: ::  :  ::3:: : : +: :  : *: .: : #: : ": : <: -: ": 5:"+: : : : : /: : 1: .: : : ,: : +: : >: &:  : ": : &: &: #: : &: &: : &: ": ": #: (: (: : : : : $: :  : : : : .: : $: : : : ;-3; ; ; ;; ; ); ; ; ; ; ; ; .; %; ; ; ; ; ; ; ;  ; ; ;; -; (; *; $; (; ;  ; ; ; 3; ; *; ); ; ; .; +; ; ; ; ; %; #; ;<; ;)-;; ;; ;;; $; ;; ;; ;; ;  ; ; ; ;; ; ; ; ;; ; ; ;; "; ; ; ; ; ; ; ; ; ; ; 2; ;  ;";*;&1;&1;&1;;&1;&1None( #&()+,/159<=>?[;Things we can substitute for a variable. Needs to be able to represent variables, e.g. for substituting under binders.;(Produce a variable with name suggestion.;+Produce a variable without name suggestion.;=Are we dealing with a variable? If yes, what is its index?;We can substitute Terms for variables.;;;;;;;;;;;;;4 4;< <;, ,;8 8+;$ $; None( #&()+,/159<=>?;&The map contains bindings of the form  bound |-> ess?, satisfying the following property: for every non-empty list w, .  w  bound iff  [  every w   some w | (every, some) <- ess ].;+productOfEdgesInBoundedWalk occ g u v bound returns a value distinct from  iff there is a walk c (a list of edges) in g, from u to v, for which the product .  ( occ c)  bound&. In this case the returned value is  (.  c) for one such walk c.Preconditions: u and v must belong to g, and bound must belong to the domain of boundToEverySome.There is a property for this function in Internal.Utils.Graph.AdjacencyMap.Unidirectional.;Description of an occurrence.;The elements of the sequences, read from left to right, explain how to get to the occurrence. The second sequence includes the main information, and if the first sequence is non-empty, then it includes information about the context of the second sequence.;-One part of the description of an occurrence.;in the type of a constructor;&in an endpoint of a higher constructor;(in the nth argument of a define constant;'in the nth clause of a defined function;in the definition of a constant;"is an index of an inductive family;*in a sort, e.g. in the level of a universe;$in a datatype index of a constructor<1matched against in a clause of a defined function< as an argument of a metavariable<'in the principal argument of built-in D<#as an argument to a bound variable.;;;;;;;;;;;;;<<<<<;;;;;;;;;;;<<<<<;; <))<<))#<#<+ +< <- -<))<< < <) )< None) #&()+,/159<=>?<<<<<<<< <8 8<<. .<<6 6<< >< "< 8< >< &< !<> >!< < !None( #&()+,/159<=>?<< aggregation (additive operation of the semiring). For combining occurrences of the same variable in subterms. This is a refinement of the  operation for < which would work if < did not have the <* as an argument. Now, to aggregate two <$ occurrences, we union the involved <s.<< composition (multiplicative operation of the semiring). For accumulating the context of a variable.< is dominant. Once we are under a meta, we are flexible regardless what else comes. We taint all variable occurrences under a meta by this meta.<0 is next in strength. Destroys strong rigidity.< is still dominant over <.<0 is the unit. It is the top (identity) context.<First argument is the outer occurrence (context) and second is the inner. This multiplicative operation is to modify an occurrence under a context.<%What's the rigidity of a constructor?<$Extract a blocker from an occurrence<Absorptive for <.< Unit for <.<The absorptive element of variable occurrence under aggregation: strongly rigid, relevant.< Unit for <.<Depending on the surrounding context of a variable, it's occurrence can be classified as flexible or rigid, with finer distinctions.The constructors are listed in increasing order (wrt. information content).<7In arguments of metas. The set of metas is used by ' to generate the right blocking information. The semantics is that the status of a variable occurrence may change if one of the metas in the set gets solved. We may say the occurrence is tainted by the meta variables in the set.<3Under at least one and only inductive constructors.<In top position, or only under inductive record constructors (unit).<*In arguments to variables and definitions.<5Where should we skip sorts in free variable analysis?<Skip unconditionally.<Skip when annotation to a type.< Do not skip.<5A set of meta variables. Forms a monoid under union.<Representation of a variable set as map from de Bruijn indices to <.<Occurrence of free variables is classified by several dimensions. Currently, we have < and  .<Equality up to origin.< Access to < in <.<Proper monoid instance for VarMap rather than inheriting the broken one from IntMap. We combine two occurrences of a variable using .<The neutral element for variable occurrence aggregation is least serious occurrence: flexible, irrelevant. This is also the absorptive element for <, if we ignore the < in <.<The default way of aggregating free variable info from subterms is by adding the variable occurrences. For instance, if we have a pair (tA,tA) then and tA has oA the occurrences of a variable x and tA has oA/ the occurrences of the same variable, then (tA,tA) has  mappend oA oA occurrences of that variable.From counting !, we extrapolate this to < and !: we care most about about < ! occurrences. E.g., if tA has a < occurrence and tA a < occurrence, then (tA,tA) still has a < occurrence. Analogously, Relevant occurrences count most, as we wish e.g. to forbid relevant occurrences of variables that are declared to be irrelevant.< forms a semiring, and this monoid is the addition of the semiring.<A "set"-style  3 instance with default/initial variable occurrence.1<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<1<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<!< < <! !< < <  < (<< $< #< "< "< #<!(!.<!!&< < < +< .< *< .<!!< )</ /< (<<<!!<<< < (<# #"None* #&()+,/159<=>?p < Instances of <3 are inputs to the generic traveral implemented by = instances. The r type parameter denotes the   environment of the traversal.=The result type of the traversal. Most commonly, this is either a newtype wrapper on  or some instantiation of  StrictEndo from . The latter is used to efficiently accummulate sets or maps.='Do we want to skip over sorts of types?=?Update the environment when going under some number of binders.=Update the environment when descending into the spine of a constructor.=Update the environment when the rigidity of the current position changes, e.g. we switch to flexible mode when going into the spine of an unsolved metavariable. See the = instances for details. & has the identity action. NOTE: since   contains <0 information, if you implement a non-trivial < update, you must also implement a non-trivial modality update, in order to handle the < -s there!=4Update the environment when going under a modality.  has the identity action.=3Update the environment with relevance information. ) has the identity action. NOTE: since  3 contains relevances, if you implement non-trivial ! update, you must also implement a non-trivial modality update, to handle the relevances there!=Evaluating a single variable. NOTE: you have to disambiguate bound and free variables yourself! For example, when we collect all free variables in a set, we need to store an  in the reader environment to keep track of the size of the local scope, which allows us to distinguish bound and free vars.=Only computes free variables that are not pattern variables (see  nlPatVars) i.e., those in a 8 or 8s from the local context.=====<<<<<<<<<<<<==========<=============<<<<<<<==<<<<=  =  = =  = "= = = = = "= = = = "= '= = = = != = )= 4= ?= = "None* #&()+,/159<=>?=9Compute the conjunction of a predicate on free variables.=Same as =2 except occurrences in sorts of types are ignored.=9Compute the disjunction of a predicate on free variables.=Same as =2 except occurrences in sorts of types are ignored.=Is a term closed?=Variables occuring in arguments of metas. These are only potentially free, depending how the meta variable is instantiated. The set contains the id's of the meta variables that this variable is an argument to.='Check if single variable occurs freely.=Check if a single variable occurs freely outside of sorts of types.=0Return how many times each free variable occurs.=Compute a (possibly non-unique) list of free variables, in preorder traversal order.=-Return information about every free variable.=Return information about every free variable, but ignore occurrences in sorts of types.="Compute the set of free variables.=8Returns all variables that occur in local rewrite rules.=7Is the variable bound by the abstraction actually used?=?Does a variable occur relevantly and outside of sorts of types?=Rigid variables: either strongly rigid, unguarded, or weakly rigid.=Test for a set of variables whether each variable occurs relevantly and outside of sort annotations. Return the set of variables that don't occur.=?Variables under only and at least one inductive constructor(s).==Returns the variables that correspond to local rewrite rules.=Variables at top or only under inductive record constructors s and s. The purpose of recording these separately is that they can still become strongly rigid if put under a constructor whereas weakly rigid ones stay weakly rigid.=Compute < for a single variable.Local scope size.Returns two sets of variables: the first set contains all variables corresponding to local rewrite rules, and the second set includes all variables which occur in those rewrite rules.=========================<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<==<<<<<<==<<<<<<<<<<<<<<<<<<<<<=====<<<<===<<<<<<===============<===  = )= = = )= #= !=  = )=  = /= &= = "=  = 1= (= *= != = #= "= += 1= (= $= = 'None( #&()+,/159<=>? =/Instantiate an abstraction. Strict in the term.=#Apply to a single default argument.=Apply to two default arguments.= Apply to some default arguments.= applySubst ( =& ) v == applySubst  (applySubst  v)=   E  : ,  -------------------  E dropS ||  :  =Single substitution without disturbing any deBruijn indices.  , A,  E u : A --------------------------------- , A,  E inplace || u : , A,  =Checks whether the variable bound by the abstraction is actually used, and, if not, returns the term within, =ed to live in the context outside the abstraction. See also .=Instantiate an abstraction. Lazy in the term, which allow it to be  IMPOSSIBLE in the case where the variable shouldn't be used but we cannot use =. Used in Apply.=$Lift a substitution under k binders.=lookupS (listS [(x0,t0)..(xn,tn)]) xi = ti, assuming x0 < .. < xn.=9Instantiate an abstraction that doesn't use its argument.=   E reverse vs :  -----------------------------  E parallelS vs  : ,   Note the  in , .=   E  :   E reverse vs :  ----------------------------- (treating Nothing as having any type)  E prependS vs  : ,  =%Raise de Bruijn index, i.e. weakening= #, ,  E raiseFromS || || : , =To replace index n by term u, do applySubst (singletonS n u).  ,  E u : A --------------------------------- ,  E singletonS || u : , A,  = E (strengthenS E ||) : ,=A "smart" variant of 9. If =1 is applied to a substitution with an outermost 9 constructor, then the "error message" of that constructor is discarded in favour of the  argument of this function.=Replace de Bruijn index i by a 9 in something.=Replace what is now de Bruijn index 0, but go under n binders. %substUnder n u == subst n (raise n u).=(abstract args v) > args --> v[args].>Apply something to a bunch of arguments. Preserves blocking tags (application can never resolve blocking).>>' instance whose argument type is itself>Apply a substitution.>Simple constraint alias for a > instance a with arg type t.>>! instance whose argument type is 9>>! instance whose argument type is   (i.e. for things that can be weakened, but do not admit arbitrary substitution)=.Raise the looked up term/thing by this amount.The substitution.$Index to lookup in the substitution.The raised result.>>.===================================>>>>>>>>>>>0>>>>====>>>>>>>>>================================> +> None( #&()+,/159<=>?" >Merge a pair of discrimination trees. This function tries to build the minimal discrimination tree that yields the union of the inputs' results, though it does so slightly navely, without considerable optimisations (e.g. it does not turn single-alternative >s into >s).>Construct the case tree corresponding to only performing proper matches on the given key. In this context, a "proper match" is any > that is not >.>A 90-indexed associative data structure supporting  approximate, (conservative) lookup. Rather than using a Trie keyed by > directly, a >% is instead represented more like a case tree.This allows us to exploit the fact that instance selection often focuses on a small part of the term: Only that critical chain is represented in the tree. As an example, level parameters are unlikely to contribute to narrowing a search problem, so it would be wasteful to have an indirection in the tree for every >! standing for a level parameter.>Do case analysis on a term. > is scoped in the same way as fast case trees for the abstract machine: When matching actually succeeds, the variable that was matched gets replaced by its arguments directly in the context.>#Succeed with a given set of values.>The empty discrimination tree.>Constant lambdas.>Anything else.>Local variables.>Dependent function types. The domain will be represented accurately, for the case of a genuine dependent function type, the codomain will be a dummy.>Rigid symbols (constructors, data types, record types, postulates) identified by a QName.> Universes.>The variable to case on.The proper branches.0A further tree, which should always be explored. >>>>>>>>>>>>> >>>>>>>>>>>>> >>((> >((#> ;> )> ,> ,>* *> >((>>( (None( #&()+,/159<=>? 4>Expose the format  coerce f args.We fuse coercions, even if interleaving with applications. We assume that coercion is powerful enough to satisfy / coerce (coerce f a) b = coerce f a b >=Strip leading coercions and indicate whether there were some.>:The default strictness for constructors of the given kind.>The default strictness.>filterUsed used args drops those args which are labelled  ArgUnused in list used.Specification:  filterUsed used args = [ a | (a, ArgUsed) <- zip args $ used ++ repeat ArgUsed ]  Examples:  filterUsed [] == id filterUsed (repeat ArgUsed) == id filterUsed (repeat ArgUnused) == const [] >Introduces a new binding>4Usage status of function arguments in treeless code.>&Is this a match on an erased argument?>Is the matched type inductive (or non-recursive), or is it coinductive?>, if treeless usage analysis has not run yet.>The treeless compiler can behave differently depending on the target language evaluation strategy. For instance, more aggressive erasure for lazy targets.>Strict evaluation.>$Lazy evaluation. If the argument is >, then applications of inductive (or non-recursive) constructors are strict.> Strictness.>Matches on the given constructor. If the match succeeds, the pattern variables are prepended to the current environment (pushes all existing variables aArity steps further away)>Binds no variablesThe guard must only use the variable that the case expression matches on.>Code which could not be obtained because of a hole in the program. This should throw a runtime error. The string gives some information about the meta variable that got compiled.>Code which is unreachable. E.g. absurd branches or missing case defaults. Runtime behaviour of unreachable code is undefined, but preferably the program will exit with an error message. The compiler is free to assume that this code is unreachable and to remove it.>Compiler-related primitives. This are NOT the same thing as primitives in Agda's surface or internal syntax! Some of the primitives have a suffix indicating which type of arguments they take, using the following naming convention: Char | Type C | Character F | Float I | Integer Q | QName S | String??Treeless Term. All local variables are using de Bruijn indices.?Case scrutinee (always variable), case type, default value, alternatives First, all TACon alternatives are tried; then all TAGuard alternatives in top to bottom order. TACon alternatives must not overlap.?Used by the GHC backend?,A runtime error, something bad has happened.?Introduces a new (non-recursive) local binding. It can be strict or non-strict. Non-strict bindings should not be made more strict, this could lead to crashes. Sharing may happen, but is optional. It is also perfectly valid to just inline the bound term in the body.?5Checks if the given expression is unreachable or not.22222222222222222222222222222222222222222222222222>>>>>>>>>>>>>>>>>>>>>>>>2222222222222233333333333333333333333333333333333333333333333333333333(((((>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>??????????????????>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>??????????????????7?**???$$?<<?00?????**#?#?#?$$#?<<#?00#?#?#?#?#? ? ? ? ? ? #? ? ? ? ? ?**???$$?<<?00?????* *? ? ?$ $?< <?0 0? ? ? ? ? ? ? ? None( #&()+,/159<=>?9,Split alts into TAGuard alts and other alts.??None( #&()+,/159<=>?]?We lose track of @-patterns in the internal syntax. This pass puts them back.??? None( #&()+,/159<=>?/???????????????????????????????????????????????/???????????????????????????????????????????????? ? ?9 9?' '? @ @1 1None( #&()+,/159<=>? @Translate the clause patterns to terms with free variables bound by the clause telescope.%Precondition: no projection patterns.@Translate the clause patterns to an elimination spine with free variables bound by the clause telescope.@Computes the permutation from the clause telescope to the pattern variables.Use as  fromMaybe  IMPOSSIBLE . clausePerm to crash in a controlled way if a de Bruijn index is out of scope here.@Computes the permutation from the clause telescope to the pattern variables.Use as  fromMaybe  IMPOSSIBLE . dbPatPerm to crash in a controlled way if a de Bruijn index is out of scope here.The first argument controls whether dot patterns counts as variables or not.@Compute from each subpattern a value and collect them all in a monoid.@5Augment pattern variables with their de Bruijn index.@Turn a pattern into a term. Projection patterns are turned into projection eliminations, other patterns into apply elimination.@Traverse pattern(s) with a modification after the recursive descent.@Traverse pattern(s) with a modification before the recursive descent.@+Arity of a function, computed from clauses.@Label the pattern variables from left to right using one label for each variable pattern and one for each dot pattern.@Intended, but unpractical due to the absence of type-level lambda, is: labelPatVars :: f (Pattern' x) -> State [i] (f (Pattern' (i,x)))@Generic pattern traversal.Pre-applies a pattern modification, recurses, and post-applies another one.@ Fold pattern.@Traverse pattern.@Combine a pattern and the value computed from its subpatterns.@pre : Modification before recursion.post: Modification after recursion.@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@$@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ 8@ 4@ <@ '@. .@22/@**8@ :@ 2@ @ .@ 6@ <@ 2@ .@ 6@ $@ @ <@ @ +None( #&()+,/159<=>?@5Put it in a monad to make it possible to do strictly.@Generic term traversal.Note: ignores sorts in terms! (Does not traverse into or collect from them.)@Generic fold, ignoring sorts.@?Generic traversal with post-traversal action. Ignores sorts.@@@@@@@@@@@@@ (@: :(@? ?,@# #@/ /@; ;9@9 9*@ @' '@+ +@ @< <$@> >*@= =*@ @3 3@ @ )@ @ /@ 5@ @ @ /None( #&()+,/159<=>? @Check that the requirements on lazy matching (single inductive case) are met, and set lazy to False otherwise.@1Check whether a case tree has a catch-all clause.@5Check whether a case tree has any projection patterns@Data stored in @ nodes of the case tree. CCDone no mr xs b stands for the body b where the xs contains hiding and name suggestions for the free variables. This is needed to build lambdas on the right hand side for partial applications which can still reduce. The no is the number of the original 7$ this case tree leaf comes from. mr tells whether this body contains calls to the mutually recursive functions.@Branches in a case tree.@'(Possibly additional) catch-all clause.@Map from constructor (or projection) names to their arity and the case subtree. (Projections have arity 0.)@Eta-expand with the given (eta record) constructor. If this is present, there should not be any conBranches or litBranches.@?(if True) In case of non-canonical argument use catchallBranch.@Lazy pattern match. Requires single (non-copattern) branch with no lit branches and no catch-all.@!Map from literal to case subtree.@3We are constructing a record here (copatterns). @ lists projections.@The number of a 7+ (starting with 0) in the clause list of a  FunctionData.@Case tree with bodies.@ Case n bs stands for a match on the n(-th argument (counting from zero) with bs as the case branches. If the n+-th argument is a projection, we have only @ with arity 0.@Absurd case. Add the free variables here as well so we can build correct number of lambdas for strict backends. (#4280)%@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@%@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@)@#+@<<A#+A$$A A< <A A$ $A3:A<3<:A3:A$3$:A +A #A 0A "A 'A +A ,A 0A 'A %A 1A *A A 'A %A 1A *A-1A<-<1A-1A$-$1A +A )A 5A .A!A< <+A!A$ $+None( #&()+,/159<=>?AReturns A in a list. allMetasList = allMetas (:[]).Note: this resulting list is computed via difference lists. Thus, use this function if you actually need the whole list of metas. Otherwise, use A with a suitable monoid.A8Returns the first meta it find in the thing, if any. 'firstMeta == listToMaybe . allMetasList.A if thing contains no metas. noMetas = null . allMetasList.AA blocker that unblocks if any of the metas in a term are solved.AA blocker that unblocks if any of the metas in a term are solved.AReturns every meta-variable occurrence in the given type, except for those in sort annotations on types.AAAAAAAAA AAAAAAAAAA< <(A A *A! !A: :$A---A' 'A; ;*A" "A$ $:A* *A A )A A1 15A4 4A7 7A ;None( #&()+,/159<=>?AGet list of definitions, throw an error if any metavariable is encountered.AGetting the used definitions.Note: in contrast to  getDefs also collects from sorts in terms. Thus, this is not an instance of foldTerm.AgetDefs lookup emb a extracts all used definitions (functions, data/record types) from a, embedded into a monoid via emb7. Instantiations of meta variables are obtained via lookup."Typical monoid instances would be  Endo [QName] or  Set QName . Do not use [QName]8 because of obvious quadratic slowdown. Note that emb can also choose to discard a used definition by mapping to the unit of the monoid.AAAAAAA &A &A* *A &A (A A,A "A (A< <A A A A. .A 1A? ?None* #&()+,/1569<=>?-6ATurn an expression into a pattern, turning non-pattern subexpressions into C.ATurn an expression into a pattern. Fails if the expression is not a valid pattern.AReturn C if B is C.ASmart constructor for Pi: check whether the  Telescope is emptyASmart constructor for Lam: check for non-zero bindings.ASmart constructor for Let": check for non-zero let bindings.ASmart constructor for TLet": check for non-zero let bindings.A*Observe the hiding status of an expressionA2Observe various modifiers applied to an expressionA-Observe the relevance status of an expressionADrop type annotations and modalities from bindings. Also drop let, patterns, fixity, and tactics, but those should not be present in the first place when using this function, because all such cannot occur in data and record parameters.A We can get a  Telescope from  Parameters. If we have a type annotation already, we're happy. Otherwise we manufacture a binder with an underscore for the type.ASplits off allowed (= import) declarations before the first non-allowed declaration. After successful parsing, the first non-allowed declaration should be a module declaration.A#Parse outermost hiding information.AUnparse hiding information.AThe B is not an application.A.From the parser, we get an expression for the as-(#, which we have to parse into a (.AThe content of the as -clause of the import statement.AThe "as" name.AThe range of the "as" keyword. Retained for highlighting purposes.A A Binder x@p, the pattern is optionalBThe @finite- cannot be parsed, it comes from the builtin Partial only.BFrom @tactic attribute.BThe representation type of a declaration. The comments indicate which type in the intended family the constructor targets.B#lone data signature in mutual blockBOnly   is used in .B=Variables to be generalized, can be hidden and/or irrelevant.BThe ) here only refers to the range of the instance( keyword. The range of the whole block InstanceB r ds is fuseRange r ds.B  opaque ...BIn  Agda.Syntax.Concrete.Definitions we generate private blocks temporarily, which should be treated different that user-declared private blocks. Thus the  .B%lone record signature in mutual blockBnotation declaration for a nameB)Axioms and functions can be irrelevant. ( should be ) C makes only sense in B blocks.B  unfolding ...B %unquoteDecl data d constructor xs = eB unquoteDecl xs = eB unquoteDef xs = eBParameters supplied to data and record definitions (as opposed to their signatures) are stripped of their type information. They also cannot contain let* or pattern bindings or tactic attributes.B p C e where csBConcrete expressions. Should represent exactly what the user wrote.Bex: () or {}, only in patternsBex: \ ()Bex: e e, e {e}, or  e {x = e}Bex: x@p, only in patternsBex: do x <- m1; m2 The  is for the do keyword.Bto print irrelevant thingsBex: .p, only in patternsBex: ..A, used for parsing ..A -> BB...$, used internally to parse patterns.Bex: a = b, used internally in the parserBex: .\ { p11 .. p1a -> e1 ; .. ; pn1 .. pnz -> en }Bex: e -> e or .e -> e (NYI: {e} -> e)Bex: {e} or {x=e}BAn arbitrary expression bundled with highlighting information from abstract (or internal) syntaxBex: xBex: (| e1 | e2 | .. | en |) or (|)Bex: {{e}} or {{x=e}}BAn identifier coming from abstract syntax, for which we know a precise syntactic highlighting class (used in printing).BAn operator application coming from abstract syntax, for which we know a precise syntactic highlighting class (used in printing).Bex:  \x {y} -> e or \(x:A){y:B} -> eBex:  let Ds in e+, missing body when parsing do-notation letBex: 1 or "foo"Bex: e + e The ) is possibly ambiguous, but it must correspond to one of the names in the set.Bex: (e)Bex:  (xs:e) -> e or  {xs:e} -> eBex: ? or  {! ... !}Bex: quote, should be applied to a nameBex:  quoteTerm, should be applied to a termBbefore parsing operatorsBex: record {x = a; y = b}, or record { x = a; M1; M2 } The  is for the record keyword.Bex: record e {x = a; y = b} The  is for the record keyword.Bex:  @(tactic t)", used to declare tactic argumentsBex: _ or _A_5Bex: unquote&, should be applied to a term of type TermBex: e | e1 | .. | enBAn expression followed by a where clause. Currently only used to give better a better error message in interaction.B(Extended content of an interaction hole.B eB  (rewrite | invert) e0 | ... | enBThe things you are allowed to say when you shuffle names between name spaces (i.e. in import,  namespace, or open declarations).B3An imported name can be a module or a defined name.B;Left hand sides can be written in infix style. For example: +n + suc m = suc (n + m) (f D g) x = f (g x)We use fixity information to see which name is actually defined.BOriginal pattern (including with-patterns), rewrite equations and with-expressions.Be.g.  f ps | wpsB(rewrite e | with p <- e in eq) (many)Bwith e1 in eq | {e2} | ... (many)B:Processed (operator-parsed) intermediate form of the core f ps of B. Corresponds to B.B fBRecord projection.B+Pattern that was expanded from an ellipsis ....BMain argument.B psB-Patterns for record indices (currently none).B At least one (| p).B;A lambda binding is either untyped (domain free) or typed (C).B. x or {x} or .x or .{x} or {.x} or x@p or (p)B. (xs : e) or {xs : e}BPossibly empty sequence.C=Modules: Top-level pragmas plus other top-level declarations.C;All the other declarations, including the top-level module.C7The module name as inferred by the parser. Could be _7 if the parser inserted a top-level module declaration.CThe top-level OPTIONS pragmas.C  M {{...}}C tel M exprs where M exprs is a B just after parsing.CAn abstraction inside a special syntax declaration (see Issue 358 why we introduce this).C Range of the open keyword.C6Parameters are sequences of typed or untyped bindings.C9Concrete patterns. No literals in patterns at the moment.C ()Cp p' or  p {x = p'}C x@pC.e, the  is for the dot, the  for the whole thing (including the dot). If the dot pattern came from parsing e.g. .{e}# it cannot be a projection pattern.C...., only as left-most pattern. Second arg is Nothing before expansion, and Just p after expanding ellipsis to p.Ci = i1$ i.e. cubical face lattice generatorC{p} or {x = p}Cc or xIf the boolean is  , then the ) must not refer to a constructor or a pattern synonym. The value 2 is used when a hidden argument pun is expanded.C{{p}} or  {{x = p}}C0, 1, etc.Ceg: p => p' for operator _=>_ The ) is possibly ambiguous, but it must correspond to one of the names in the set.C (p)C quoteCp1..pn before parsing operatorsCrecord {x = p; y = q}. The  is for the record keyword.C _C| p, for with-patterns.C7Can a dot pattern be interpreted as projection pattern?CNo.CYes.C)Applies to the following function clause.C*Display lhs as rhs (modifies the printer).C/Applies to the following record type. Force  eta-equality for the attached record type for unguarded and  coinductive records.CRemoved, replaced by C.C6Throws an internal error in the scope checker. The +s are words to be displayed with the error.C9Mark a definition as injective for the conversion checkerCMark a definition as injective for the pattern matching unifier.CINLINE or NOINLINECApplies to the following function (and all that are mutually recursive with it) or to the functions in the following mutual block.C:Applies to the following data/record type or mutual block.C*Applies to the following data/record type.CApplies to the stated functionCApplies to the given name(s), which must be instance names (checked by the type checker).C$Second Range is for REWRITE keyword.CApplies to the following function (and all that are mutually recursive with it) or to the functions in the following mutual block.CApplies to the current moduleCApplies to the named functionC+No right hand side because of absurd match.C;Expressions usually instantiating module parameters as in % open import Monoid Carrier _==_  that might also code an as clause e.g. in  open import File as M  The parser does not distinguish these so we do it in the nicifier.C1Isolated record directives parsed as DeclarationsC Range of [no-]eta-equality keyword.CRange of keyword  [co]inductive.CIf declaration pattern is present, give its range.CA telescope is a sequence of typed bindings. Bound variables are in scope in later types.CJust type signatures.C(Just type signatures or instance blocks.CA typed binding.CBinding (x1@p1 ... xn@pn : A).C Let binding (let Ds) or  (open M args).Cwhere block following a clause.CThe generalization  WhereClause' is for the sake of Agda.Concrete.Generic.C Ordinary where.  of the where/ keyword. List of declarations can be empty.CNo where clauses.C Named where: module M where ds.  of the keywords module and where . The  flag applies to the ( (not the module contents!) and is propagated from the parent function. List of declarations can be empty.CType of where block following a clause.C Ordinary where.CNo where clauses.C Named where: module M where ....DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DRanges are not forced.DA C is   when the where keyword is absent. An empty list of declarations does not count as   here.Just field signatures)Generic expression to pattern conversion.&Default result for non-pattern things.The expression to translate.The translated pattern (maybe).AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA(((((((((((((((((((((((((((((((((AAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC((((((((((((((((((((((((((()))((BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCACCCAAAAAAAAAAAAACCCAAAAAABBBBAAABBBBBAACCCCCCBBBBBAACCCCCBBBBBBAACCCCCCCAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBACCCCCCCCCCCBCBCCBAAAAACCCCCCBBBBBCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBBBBBCCCCCCCCCCCCCBBABBBBCCCCCCCCCCCCCCCCCCCCCCCCCCCCC((BBBBAAC35CC C C C C35C C C C-/C C C C-/C C C C-/CC D-/D D D$D$DDDDDD(0DD"DDD D D D D D&D DDDD D D D D D D 5D D D D D $D #D *D  D D D D "D 'D D D D D D D D D 7D D D D %D $D ,D !D D D D #D?D D D D !D $D D D D D D D 1D D ,D D "D !D &D D D D %D DD .D -D D D #D D D D D D-1DDDDD&1D&1D +D +D +D +D +D2=D +D$/None( #&()+,/159<=>?D#Hashes a raw top-level module name.DA lens focusing on the .DTurns a top-level module name into a file name with the given suffix.DFinds the current project's "root" directory, given a project file and the corresponding top-level module name.8Example: If the module "A.B.C" is located in the file "fooABC.agda", then the root is "foo".2Precondition: The module name must be well-formed.DConverts a top-level module name to a raw top-level module name.D$Retrieves the top-level module name.D Computes the D corresponding to the given module name, which is assumed to represent a top-level module name.2Precondition: The module name must be well-formed.DTurns a qualified name into a D. The qualified name is assumed to represent a top-level module name.D0Turns a raw top-level module name into a string.DA corresponding . The range of each Name! part is the whole range of the E.DConverts a raw top-level module name and a hash to a top-level module name.This function does not ensure that there are no hash collisions, that is taken care of by .D:Raw top-level module names (with linear-time comparisons).EWas this module name constructed from a file name rather than declared in the file?E8Top-level module names (with constant-time comparisons).EThe  is not forced.DDDDDDDDDDDDDEEEEDDDDDDDDDDDDDEEEE E6 6"E44E (E *E )E &E9 9#E &E #E (E4 4E< <%E "None( #&()+,/159<=>? gECompute a value from each subpattern and collect all values in a monoid.E)Does the LHS contain projection patterns?ECompute the context in which the ellipsis occurs, if at all. If there are several occurrences, this is an error. This only counts ellipsis that haven't already been expanded.E9Does the pattern contain a with-pattern? (Shortcutting.)EIs C?EAppend patterns to B), separating with patterns from the rest.EAdd applicative patterns (non-projection / non-with patterns) to the right.EAdd with-patterns to the right.EConstruct the E" of the given list (if not empty).+Return the view and the remaining patterns.E?Map pattern(s) with a modification after the recursive descent.E Modify the C component in B.EEffectfully modify the C component in B.E2Count the number of with-subpatterns in a pattern?EView a pattern p as a list p0 .. pn where p04 is the identifier (in most cases a constructor).8Pattern needs to be parsed already (operators resolved).ECombine a pattern and the value computed from its subpatterns.E;Combine a pattern and the its recursively computed version.Epre : Modification before recursion.post: Modification after recursion.EEEE!EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE%EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE 0E =E ,E 2E 2E 4E 2E E E7 7E/ /E$ $E &E *E None( #&()+,/159<=>?E,Generic traversals for concrete expressions. Note: does not go into patterns!EThis corresponds to .EThis corresponds to .EThis corresponds to .ECollect declarations and subdeclarations, transitively. Prefix-order tree traversal.EUpdate declarations and their subdeclarations. Prefix-order traversal: traverses subdeclarations of updated declaration.E7Note: this instance discards top-level OPTIONS pragmas.EEEEEEEEEEEEE EEEEEEEEEEEEE+E (E E E E ;E E "E E E E $E *E *E 5E $E #E> >E /E *E *E E )E +E E 5E 5E E E 2E9 9E 1E /E E $E *E E *E 1E "E ,E 2E 2E 9None( #&()+,/159<=>? EInvariant for F hl%, parametrised by the invariant for hl.?Additionally the endofunction should be extensionally equal to (fs ) for some list fs.EThe invariant for F.?Additionally the endofunction should be extensionally equal to (fs ) for some list fs.EThe invariant for F.F4Conversion from classification of the scope checker.F A variant of  with  set to .FInvariant for F.F#Conversion between different types.F'Highlighting info with delayed merging.Merging large sets of highlighting info repeatedly might be costly. The idea of this type is to accumulate small pieces of highlighting information, and then to merge them all at the end.>Note the invariant which values of this type should satisfy (E).FHighlighting information.>Note the invariant which values of this type should satisfy (E).This is a type synonym in order to make it easy to change to another representation.FA type that is intended to be used when constructing highlighting information.>Note the invariant which values of this type should satisfy (E).This is a type synonym in order to make it easy to change to another representation."The type should be an instance of  ,  and &, and there should be an instance of F F F.FSyntax highlighting information, represented by maps from positions to .,The first position in the file has number 1.FA limited kind of syntax highlighting information: a pair consisting of  and .Note the invariant which Fs should satisfy (F).Merges meta information.EEEFFFFFFFFFFFFFFFFFFFFFFFFEFEFEFFFFF 6F =F ?F 3F 0F 7F ?J1F.Global variable to store benchmark statistics.F=Benchmark an IO computation and bill it to the given account.F>Benchmark a pure computation and bill it to the given account.FPhases to allocate CPU time to.F Subphase for F(: copying definitions for a module macroF Subphase for F.F Subphase for F.F Subphase for F: checking the LHSF Subphase for F : reducing overlapping instancesF Subphase for F: checking the RHSF Subphase for F: compacting interfaces.F Subphase for F.F Subphase for F.F0Coverage checking and compilation to case trees.FGenerating left inverses in LHS unification in cubical or cubical-compatible mode.FDead code elimination.F)Dead code reachable definitions subphase.FReading interface files.F Subphase for F": checking candidates for validityF Subphase for F: free variable computation.F Subphase for F: generalizing over variablesF Subphase for F.FGenerating highlighting info.FImport chasing.F Subphase for F: collecting initial candidatesFInjectivity checking.F Subphase for F: solving instance goalsF)Unfolding all metas before serialization.F Subphase for F.F Subphase for F.F Subphase for F!: occurs check for solving metas.F Subphase for F.F Subphase for F.F Subphase for F%: ordering candidates for specificityF#Happy parsing and operator parsing.FPolarity computation.FPositivity checking.F!Checking for projection likeness.F Subphase for F.F Subphase for F.F Subphase for F": evaluating elaborator reflectionF2Scope checking and translation to abstract syntax.FWriting interface files.F Subphase for F.FTermination checking.F Subphase for F: checking a type signatureF1Type checking and translation to internal syntax.F Subphase for F: unification of the indicesF Subphase for F.>FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF>FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF F#F FF F FNone( #&()+,/159<=>?=F Pretty-print G.F Pretty-print G.F#Compute a position position prefix.-Depending on the error to be printed, it willeither give the name of the  libraries file and a line inside it,or give the name of the  .agda-lib file.F)Does a parse error contain a line number?FThe special name "." is used to indicated that the current directory should count as a project root.FSplit a library name into basename and a list of version numbers. parseLibName "foo-1.2.3" == LibName "foo" [1, 2, 3] parseLibName "foo-01.002.3" == LibName "foo" [1, 2, 3]$Note that because of leading zeros,  parseLibName is not injective. (prettyShow . parseLibName would produce a normal form.)G Content of a  .agda-lib file.G3How many directories above the Agda file is the  .agda-lib file located?G Dependencies.G Path to this  .agda-lib file (not content of the file).G3Roots where to look for the modules of the library.G!The symbolic name of the library.G4Default pragma options for all files in the library.GA symbolic executable name.GThe executables file might not exist, but we may print its assumed location in error messages.GE.g. ~.agda executables.G5Cache locations of project configurations and parsed  .agda-lib files.G Contents of  .agda-lib% files that have already been parsed.G3Map from directories to paths of closest enclosing  .agda-lib files (or G if there are none).GCollection of Gs and Gs.G0Collected errors while processing library files.G1Raised when a library name is defined in several .agda-lib files.GThe  executables! file contains duplicate entries.GRaised when a library name could not successfully be resolved to an  .agda-lib file.GThe  .agda-lib file could not be parsed.G/The user specified replacement for the default  libraries file does not exist.G*An I/O Error occurred when reading a file.G.The given project root contains more than one  .agda-lib file.G Collects Gs and Gs.G$Collected errors when processing an  .agda-lib file.GThrows G exceptions, still collects Gs.GA symbolic library name.Library names are structured into the base name and a suffix of version numbers, e.g.  mylib-1.2.3". The version suffix is optional.GActual library name.GMajor version, minor version, subminor version, etc., all non-negative.GExceptions thrown by the  .agda-lib parser.GAt the given line number, an invalid field name is encountered before the :. (E.g., containing spaces.)G1An invalid library name, e.g., containing spaces.GAt the given line number, indented text (content) is not preceded by a field.G'These fields occur each more than once.G=At the given line number, the given field is not followed by :.G=At the given line number, a field name is missing before the :.GMissing these mandatory fields.GI/O error while reading file.GInformation about which  .agda-lib. file we are reading and from where in the  libraries file it came from.G Library file.GName of  libraries file.GLine number in  libraries file.GLibrary Warnings.GThe libraries file might not exist, but we may print its assumed location in error messages.GE.g. ~.agda libraries.GThe options from an OPTIONS pragma (or a  .agda-lib file).In the future it might be nice to switch to a more structured representation. Note that, currently, there is not a one-to-one correspondence between list elements and options.GThe range of the options in the pragma (not including things like an OPTIONS keyword).G The options.GA file can either belong to a project located at a given root containing an .agda-lib file, or be part of the default project.G0How many directories above the Agda file is the  .agda-lib file located?G .agda-lib file relative to G (filename only, no directory).GDirectory which contains the  .agda-lib file for the current project.GRanges are not forced.GIn comparisons, a missing version number is assumed to be infinity. E.g. +foo > foo-2.2 > foo-2.0.1 > foo-2 > foo-1.0.G? HParse  .agda-lib file.Sets F name and turn mentioned include directories into absolute pathes (provided the given  is absolute).H4Break a comma-separated string. Result strings are trimmed.H+Remove leading whitespace and line comment.Header line, like a field name, e.g. "include :". Cannot be indented. String is trimmed."Other line. Must be indented. String is trimmed.(Library file field format format [sic!].Name of the field.Is it optional?Content parser for this field.*The range points to the start of the file.Sets parsed content in G structure.E.g. field name. trimmed.E.g. field content. trimmed.The config files we parse have the generic structure of a sequence of field : content entries.Lines with line numbers.Parser monad: Can throw  LibParseErrors, and collects  LibWarning's library warnings.-...and trailing, but not leading, whitespace. .agda-lib& file format with parsers and setters.Ensure that there are no duplicate fields and no mandatory fields are missing.Find  with given , throw error if unknown.Parse  with  descriptors.Given a list of 5 descriptors (with their custom parsers), parse a  into the G structure.Checks mandatory fields are present; no duplicate fields, no unknown fields.Collect  and subsequent s into .Leading s? That's an error.Example:  parseGeneric "name:Main--BLAndepend:--BLAn standard-library--BLAninclude : . --BLAn src more-src n" == Right [("name",[Main]),("depend",["standard-library"]),("include",[".","src more-src"])] Parse file contents.Parse line into  and  components.Precondition: line comments and trailing whitespace have been stripped away. Example file:  name: Main depend: standard-library include: . src more-src This should give ' [ Header 1 "name" , Content 1 Main , Header 2 "depend" , Content 3 "standard-library" , Header 4 "include" , Content 4 "." , Content 5 "src more-src" ] The parsed file.The parsed file.The parsed file.HHHHHHHHH None( #&()+,/159<=>?yH Converts a  to a .H Converts a #, seen as a continuous range, to a .HH HHNone( #&()+,/159<=>?HHHHHHHHH %H !H H !H !H H H H H H3 3H8 8H !H H= =H None( #&()+,/159<=>? E!H Lens for  in H.HTarget argument position of a part (Nothing if it is not a hole).HIs the part a hole?HIs the part a binder?HIs the hole a binder?HCheck if a notation contains any lambdas (in which case it cannot be used in a pattern).H Analogue of (: prefix, infix, or postfix.HMerges Hs that have the same precedence level and notation, with two exceptions:Operators and notations coming from syntax declarations are kept separate.If all instances of a given H have the same precedence level or are "unrelated", then they are merged. They get the given precedence level, if any, and otherwise they become unrelated (but related to each other).If Hs that are merged have distinct associativities, then they get  as their associativity.Precondition: No 1 may occur in more than one list element. Every H must have the same H.Postcondition: No & occurs in more than one list element.H2From notation with names to notation with indices.An example (with some parts of the code omitted): The lists &["for", "x", "D", "xs", "return", "e"] and [H ("x" :| []) "e", H "xs"]- are mapped to the following notation:  [   "for" ,   ( 0 0) ,   "D" ,   1 ,   "return" ,   0 ] HIf an operator has no specific notation, then it is computed from its name.H'Converts a notation to a (non-)section.HFor non-sectioned operators this should match the notation's H.HEffective precedence level.  for closed notations.(HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH(HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH  H H H  H H H  HHH None) #&()+,/1359<=>?# HParses a split-up, unqualified name consisting of at least two name parts.The parser does not check that underscores and other name parts alternate. The range of the resulting name is the range of the first name part that is not an underscore.H0Parse the "operator part" of the given notation.Normal holes (but not binders) at the beginning and end are ignored.If the notation does not contain any binders, then a section notation is allowed.HRuns a parser. If sections should be parsed, then identifiers with at least two name parts are split up into multiple tokens, using   to record the tokens' original positions within their respective identifiers.H)Parse a specific identifier as a NamePartH,Parses a potentially pattern-matching binderHThe ) is possibly ambiguous, but it must correspond to one of the names in the set.HA singleton type for H (except for the constructor H).H"Used to define the return type of H.HShould sections be parsed?"HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH"HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH H +H H HNone( #&()+,/159<=>?HGet the fixities and polarity pragmas from the current block. Doesn't go inside modules and where blocks. The reason for this is that these declarations have to appear at the same level (or possibly outside an abstract or mutual block) as their target declaration.Subset of postulates within .Subset of private names within .While H and Polarities are not semigroups under disjoint union (which might fail), we get a semigroup instance for the monadic m (Fixities, Polarities)% which propagates the first error.&Mark all declared names as postulates.#Mark all declared names as private.Compute the names defined in a declaration. We stay in the current scope, i.e., do not go into modules.Add more fixities. Throw an exception for multiple fixity declarations. OR: Disjoint union of fixity maps. Throws exception if not disjoint.HHHHHIIIIIIIIIIHIIIIIIIIIIHHHHI I I !I 8I ;INone( #&()+,/159<=>?0܏IAdd a module to a scope.IAdd all associated name parts of a name (operator parts, notation parts) to the scope.IAdd a name to a scope.IReturn all names in a scope.I$The flat list of ambiguous names in J.I Apply an  to a scope: "rename keys (C.Name) according to renaming;for untouched keys, either ofa) remove keys according to hiding', or b) filter keys according to using.Both steps could be done in one pass, by first preparing key-filtering functions C.Name -> Maybe C.Name for defined names and module names. However, the penalty of doing it in two passes should not be too high. (Doubling the run time.)I Version of I that also returns sets of name and module name clashes introduced by renaming0 to identifiers that are already imported by using or lack of hiding.I?For ambiguous constructors, we might have both alternatives of !. In this case, we default to .I+Add first string only if list is non-empty.I?For ambiguous constructors, we might have both alternatives of !. In this case, we default to 3.I!Constructor and pattern synonyms.I:Get all concrete names in scope. Includes bound variables.I!All kinds of regular definitions.I3Disallow using generalized variables from the scopeIThe empty name space.IThe empty scope.IThe empty scope info.I Only return  [Co]ConName if no ambiguity.I&Returns the scope's non-private names.IFilter a scope keeping only concrete names matching the predicates. The first predicate is applied to the names and the second to the modules.I+Look up a single name in the current scope.This is equivalent to Map.lookup n . allNamesInScope', but more efficient when only a single name needs to be looked up.I2Find a concrete, possibly qualified name in scope s. The qualifiers are resolved to modules whose public scopes are searched.I inNameSpace> selects either the name map or the module name map from a J. What is selected is determined by result type (using the dependent-type trickery).I.Add an explanation to why things are in scope.IFind the concrete names that map (uniquely) to a given abstract module name. Sort by length, shortest first.IFind the concrete names that map (uniquely) to a given abstract qualified name. Sort by number of modules in the qualified name, unqualified names first.I A version of I that also delivers the 3. Used in highlighting.IIs the given module (or one of its parents) a member of the set?I$Is the given name alive in this set?Note: a qualified name can be kept alive by liveness of any of the modules it belongs to.I9Map functions over the names and modules in a name space.I&Map monadic function over a namespace.I4Map functions over the names and modules in a scope.IexportedNamesInScope . restrictPrivate == exportedNamesInScope.I0The current scope and the scopes of its parents.ILenses for ScopeInfo componentsILook up a name in the scopeIFor a qualified name x.q& resolving to one of the given things ys, find the modules x8 in the current scope (or its parents) through which q resolves to some of ys.Used to mark the qualifier x) as used for the unused-imports analysis.IGet a J from J.IThe scope of the given module.IUpdate a particular name space.IMove all names in a scope to the given name space (except never move from Imported to Public).I3Shadow a local name by a non-empty list of imports.I Lens for I.I A lens for JI`Monadic' lens (Functor sufficient).I Lens for I.JFilter privates out of a JJZip together two name spaces.JZip together two scopes. The resulting scope has the same name as the first scope.JSame as J but applies the same function to both the public and private name spaces.JUsed for instance arguments to check whether a name is in scope, but we do not care whether is is ambiguousJ9Ambiguous constructors, projections, or pattern synonyms.J:Why is a resolved name ambiguous? What did it resolve to?Invariant (statically enforced): At least two resolvents in total.J/The name resolves to at least 2 declared names.JThe name resolves both to a local variable and some declared names.JFor each bound variable, we want to know whether it was bound by a , , module telescope, pattern, or let.J (currently also used for  and module parameters)J  let ... inJBinding added to scope by one of context-manipulating reflection primitivesJf ... =. Remember  for pattern variables {x} and {{x}}. This information is only used for checking pattern synonyms. It is not serialized.J  | ... in qJ-Type class for some dependent-types trickery.J#Set of types consisting of exactly 2 and 2..A GADT just for some dependent-types trickery.J A set of 3, for the sake of I.JAll but these Kinds.JOnly these kinds.JA set of module and definition names that were explicitly referred to during scope checking.JAn interaction point can see this copy, so we should preserve every name.JWe encountered these names during scope-checking, so they should be preserved.JA local variable can be shadowed by an import. In case of reference to a shadowed variable, we want to report a scope error.J/Kind of binder used to introduce the variable (, let, ...).JIf this list is not empty, the local variable is shadowed by one or more imports.JUnique ID of local variable.JLocal variables.J"For the sake of highlighting, the J map also stores the 3 of an A.QName.J)Possible renderings of the abstract name.JThe 2.J%Non-dependent tag for name or module.JA failure in name resolution, indicating the reason that a name which is% in scope could not be returned from tryResolveName.J The name was Foo.constructor, and Foo& is in scope, but it is not a record.J4Ambiguous names are not supported in this situation.JA  NameSpace contains the mappings from concrete names that the user can write to the abstract fully qualified names that the type checker wants to read.JAll abstract names targeted by a concrete name in scope. Computed by I.J>Maps concrete module names to a list of abstract module names.JMaps name parts to a list of abstract names in which the name part occurs.JMaps concrete names to a list of abstract names. If this is part of a scope produced by an , the concrete names should (where possible) match those of the directive. E.g., if the directive mentions  using (x), then the concrete x in the map should be this x rather then the x from the original scope that is restricted by the import directive. This is important for the highlighting of the  UnusedImports warning.JSee .J1Things from open public, exported by this module.J#Things not exported by this module.J+Things defined and exported by this module.JInformation gathered during scope checking for the unused-imports warning when a module is opened.JModules among J that accompany a name in J (e.g. the module of a data type or record type) and are not mentioned explicitly in the opening directive. These are not reported individually when unused.J Whether the open statement comes with using or renaming.JModule we opened.JThe modules imported by the open statement. The keys () of this map should be the concrete names of the opening directive, if such was given.JThe names imported by the open statement. The keys () of this map should be the concrete names of the opening directive, if such was given.J5Parent module into which we merged the opened module.J of the open keyword.J,Names that are relevant to operator parsing.J.Are there any operators or notations in scope?JRelevant names in local scope.J#All relevant names in global scope.J Data or record constructor name.J&Function, data/record type, postulate.JRecord field name. Needs to be distinguished to parse copatterns.JName of pattern synonym.J Unbound name.J9Local variable bound by , , module telescope, pattern, let.JWhat kind of binder?JA scope is a named collection of names partitioned into public and private names.JThe complete information about the scope at a particular program point includes the scope stack, the local variables, and the context precedence.J&Maps concrete names C.Name to fixitiesJ(Maps concrete names C.Name to polaritiesJThe variables that will be bound at the end of the current block of variables (i.e. clause). We collect them here instead of binding them immediately so we can avoid shadowing between variables in the same variable block.JSet the 3 in an abstract name.JInformation gathered during scope checking for the unused-imports warning.JNames that were ambiguously resolved from a concrete name in the source. They are stored with their position in the file that is matched with disambiguation information produced by the type checker.JModules that were resolved from a concrete name in the source, either directly or as the qualifier of a qualified name.JLog of module open)s with the names they brought into scope.JNames that were unambiguously resolved from a concrete name in the source.J%When we get here we cannot have both using and hiding.KDecorate something with 3KWe show shadowed variables as prefixed by a ".", as not in scope.KInvariant: the 3 components should be equal whenever we have two concrete renderings of an abstract name.K/Sets the binding site of all names in the path.I4Merged scope, clashing names, clashing module names.J or  or both. isJust . I . 2 for all names.J2 can be DefName, 3, 3.J(3 ==) . 2 for all names.J(3 ==) . 2 for all names.K The name x this explanation is about.2The directory in which the current module resides.The local variable that x could denote, if any.The defined names that x could denote.The modules that x could denote.KIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJKKKKKJJJJJJJJJJJJJJIJIIIIIJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIIIIIJJJJJJJJJJJJJJJJIJJJJJJJJJJJJJIIJJJJJJJJJJJJJJJIIIIIIIIIIIIIJJJJIIIIKKKKJJJJJJJJJJJJJJJIJKJIJIIIIJIIIIIIIIJJIIIIIIIIIIIIIIIIIIIIIJJJIIIIIIJIIIIIIIIIIIIIIJJJJIIIIIIIIIIJJKIJJJJIK$K")KKK KK KKK K K K K KKK K KK'/K%KKK&-KKK+2KKK&-KK KKKKK  K K K K K K $K K #K K K K K K K K K K K K K K !K KKK K K K K K K K K K K K  K 'K %K 0K %K K 6K K  K K K K K KK KK $KK KK KK1<None( #&()+,/159<=>?K-Default is system inserted and prefer parens.KK with no range information.KDefault meta kind from its  context.KSame as  mkDefInfo but where we can also give the  IsInstanceKEmpty range for patterns.KInformation about applicationK6Do we prefer a lambda argument with or without parens?KConstructor pattern info.KDoes this pattern come form the eta-expansion of an implicit pattern?K:Has the constructor pattern a dotted (forced) constructor?KOrdinary constructor.KDotted constructor.LInformation associated to a meta variable in the abstract syntax.L+Kind of a meta: the method how to solve it.L(Meta variable solved by instance search.L.Meta variable solved by unification (default).LName suggestion for meta variable. Empty string means no suggestion.LThe "as" module name, if any. Retained for highlighting purposes.LThe range of the "as" and "to" keywords, if any. Retained for highlighting purposes.L Retained for abstractToConcrete of B.L;For a general pattern we remember the source code position.LDefault value for L.KKKKKKKKKKKKKKKKKKKKKKKKKLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLKLLLLLLLLKLLKKKKKKKKLLLLLLLLLLLLLLLLLLLKKKKKKLLLLLLLLLLLLKKKKKKKKKL #L $L#L%)LL L LLLLLLL%%L LL L#LL+2LLL LL%%LLL L L L L L L L L L L:L L L L  L L L L L L L L %L #L L"(L L L L L L )L#L L#L L* *L L LL LL LL L' 'L LLLL L L L L08L LMM M M MM M M% %MM M*.None( #&()+,/159<=>?M#Does not raise the retrieved entry!MAssumes the list of entries to be prepended follows the context ordering convention (earlier entries depend on later ones)MThe returned prefix follows the context ordering convention (earlier entries depend on later ones)MThe returned list of context entries follows the context ordering convention (earlier entries depend on later ones)MCollection of s of primitive modules.MThe Context is a stack of Ms. Unlike telescopes, later context entries are bound in earlier ones.MTranslation between  and . that also knows about Agda's builtin modules.MFor the known 9s, remember whether they refer to Agda's builtin modules.M!(Building a) translation between  and .MThe absolute path to the directory with the builtin modules. Needs to be set upon initialization.M;How much highlighting should be sent to the user interface?MThis includes both non-interactive highlighting and interactive highlighting of the expression that is currently being type-checked.M6How should highlighting be sent to the user interface?M Via stdout.MBoth via files and via stdout.MDatatype representing a single boundary condition: x_0 = u_0, ... ,x_n = u_n E t = ?n esM=Discern Agda's primitive modules from other file modules. isPrimitiveModule implies" IsBuiltinModuleWithSafePostulate implies isBuiltinModule%. Keep constructors in this order!MAgda.Primitive.MAgda.Primitive.Cubical.MAny builtin module.MSafe module, e.g. Agda.Builtin.Equality.MMaps top-level module names to the corresponding source file ids.M8For printing, we couple a meta with its name suggestion.M+Polarity for equality and subtype checking.MantitoneMmonotoneMno information (mixed variance)MconstantMM6s must exist and be registered in our file dictionary.MMMMMMMMMMMMMMEMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMME9M MMM M MM M,,,4M)1M,#,*M 'MM,,MM M$+M&M#MMM#MM "M $M $M (M $M $M $M $M M M %M  M /M M 1M,6,:M !MMMM"MMN, ,N NNNNN NN N,,!N,<,N3>None( #&()+,/159<=>?'N Interpret N as relation on N.NDefault polarity is N.NN acts as , N as .NReturns $ if the constraint is contradictory.N.Comparison operator, e.g. for size expression.ND.N<.N= 0.N*Type of solution wanted for each flexible.N)What type of solution are we looking for?N,Assigning a polarity to a flexible variable.NFixed size variables i.N2The rigid variables contained in a pice of syntax.N*Size expressions appearing in constraints.NConstant number n.NMeta variable X + n.N Infinity D.NVariable plus offset i + n.NSize metas in size expressions.NDe Bruijn indices.NPartial substitution from flexible variables to size expression.NExecuting a substitution.N)Make offsets non-negative by rounding up.NOffsets + n must be non-negativeN-An equality which ignores the meta arguments.N*An order which ignores the meta arguments.NComparison operator is ordered N < N.OAdd offset to size expression.NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN 'N N N)-N!$!(NN> >N N! !N N4 4NN N 4N !N N N 2N%-N08N#N'.NNNNN!!N%NN N, , N N :N "N N# #N 8N NN!!"N N>>N N!!NO44OO (O/ /#O 5O O :O O O) )O O 9O9 9O 8O O 7O +O  O )O O O O OO& &O6 6OOO O 3O 0O 6O 1O 0O/:O:O O (O O %None/ #&()+,/1359<=>? 'OCreates an empty dictionary.OThe actual logic of O is cold code, so it's out-of-line, to decrease code size and avoid cache pollution.Oicode( only if thing has not been seen before.OicodeN tag t a1 ... an serialises the arguments a1, ..., an of the constructor t together with a tag tag picked to disambiguate between different constructors. It corresponds to 0icodeNode . (tag :) =<< mapM icode [a1, ..., an]OicodeN' is the same as icodeN except that there is no tagO$Computing a key of an abstract name.O$Computing a key of a qualified name.OIncrease entry for a in O.Ovcase value ix decodes thing represented by  ix :: Word32 via the valu function and stores it in O. If ix is present in O, valu, is not used, but the thing is read from O instead.ODecoder arguments.O;Compact region where the decoded interface is allocated.OObtained from interface.O,Memoizes filepaths computed for RangeFile-s.OThe include directories.OObtained from interface.OObtained from interface.O 21s for std-lib).OWritten to interface file.OWritten to interface file.ONot written to interface file.OWritten to interface file.ONot written to interface file. Fresh UIDs and reuse statistics:OWritten to interface file.OWritten to interface file.OWritten to interface file. Andreas, 2026-08-29, issue #8697: The  dictionary is keyed by the  bit pattern of the /, because the 'Eq Double' instance identifies 0.0 and -0.0, which would make hash-consing conflate these two distinct literals. (This is the inconsistency of issue #2169, which is why 'Eq Literal' compares  s bitwise.)OicodeArgs proxy (a1, ..., an) maps icode over a1, ..., an* and returns the corresponding list of Word32.OAssociation lists mapping TypeRep fingerprints to values. In some cases values with different types have the same serialized representation. This structure disambiguates them.OWe need to distinguish s with different 3, so we complement the key   with that .OTwo 3s are equal if their NameId is equal.OMonad used by the decoder.TCM is not used because the associated overheads would make decoding slower.OMonad used by the encoder.OCollect statistics for icode calls?O Memo structure for thing of key a.Counter and statistics.Key to the thing.)Fallback computation to encode the thing.Encoded thing.OSerialization (worker).OSerialization (wrapper).ODeserialization.OPPOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOPPOOOOOOOOOOOOOOOOPPP P ;P P P =P 1P %P P :P P P ?PPPPPPPPPPPPPP#P P /P5P P P 0P P 5P P 6P P P P P+P &P 9P -P &P 'P &P 3P $P &P +P P P :P  >P P: :P =P P None( #&()+,/159<=>? PPPPPPPPPP PPPPPPPPPPP P%-P#PPP/:P P Data file location, and package version and installation directories.None) #&()+,/159<=>?The package version.If the argument is a filename, the result is the name of a corresponding file on the system on which the program is running, if the file were listed in the  data-files field of the package's Cabal package description file. No check is performed that the given filename is listed in that field.3The location of the directory specified by Cabal's --bindir option (where executables that the user might invoke are installed). This can be overridden at runtime using the environment variable Agda_bindir.3The location of the directory specified by Cabal's --libdir option (where object libraries are installed). This can be overridden at runtime using the environment variable Agda_libdir.3The location of the directory specified by Cabal's  --dynlibdir option (where dynamic libraries are installed). This can be overridden at runtime using the environment variable Agda_dynlibdir.3The location of the directory specified by Cabal's  --datadir option (where architecture-independent data files are installed). This can be overridden at runtime using the environment variable Agda_datadir.3The location of the directory specified by Cabal's  --libexedir option (where executables that are not expected to be invoked directly by the user are installed). This can be overridden at runtime using the environment variable Agda_libexedir.3The location of the directory specified by Cabal's  --sysconfdir option (where configuration files are installed). This can be overridden at runtime using the environment variable Agda_sysconfdir.None( #&()+,/159<=>?8PThe version of Agda.PThis package name. This is mainly intended for use in the test suites to filter ephemeral hash-fingerprinted package names like !Agda-2.6.2-5ceeWeguf1QFMaHLput4zw.PReturns a URL corresponding to the given section in the documentation for the current version.PPPPPPP!.!5None+ #&()+,/159<=>?P1Agda's version suffixed with the git commit hash.PInformation about current git commit, generated at compile time.PPPPNone+ #&()+,/159<=>?PGet the path to ~/.agda1 (system-specific). Can be overwritten by the AGDA_DIR environment variable./(This is not to be confused with the directory P for the data files that Agda needs (e.g. the primitive modules).)PThis overrides the P from ' Paths_Agda'#. See the documentation for the --print-agda-data-dir flag.PThis overrides the P from ' Paths_Agda'.PFalse: Check whether we need to setup Agda. This function can be called when starting up Agda.True.: force a setup e.g. when passing Agda option --setup.Copies the embedded data files to the designated data directory.The embedded contents of the Agda data directory, generated by Template Haskell at compile time.Spit out the embedded files into Agda data directory relative to the given directory. Lock the directory while doing so..Dump line of warning or information to stderr. Given the  Agda_datadir#, what should the Agda data dir be?PPPPPPPPNone( #&()+,/159<=>?: P2Tries to compile the Agda mode's Emacs Lisp files.PHelp topic for  --emacs-mode.PPrints out the path to the Agda mode's main file (using UTF-8 and without any trailing newline).P7Tries to set up the Agda mode in the given .emacs file.&Has the Agda mode already been set up?«Evaluates the given Elisp command using Emacs. The output of the command (whatever was written into the current buffer) is returned.Note: The input is not checked. The input is assumed to come from a trusted source.ëEscapes the string so that Emacs can parse it as an Elisp string.ī7Tries to find the user's .emacs file by querying Emacs.ūIf this string occurs in the .emacs file, then it is assumed that setup has already been performed.ƫA `monadic' version of @ partition# :: (a -> Bool) -> [a] -> ([a],[a])ǫLike ȫ but handles  by printing diagnostics (PATH ) before ɫ.ʫ2The string appended to the end of the .emacs file.ǫCommand to run.Arguments to command.PPPPPPPPPPPPPPPPNone( #&()+,/159<=>?9PUsage information generationPConversion functions to stringsPInterface to the help functionPGeneral usage informationP)Specialised usage information about TOPIC˫List of Help Topics NOTA BENE: You need to add each new topic together with its name to  allHelpTopicsPPPPPPPPPPPPP P& &PP&&P P( (PP&&None( #&()+,/159<=>?P Argument to --color.PPossible values for --color.P Argument to  --emacs-mode.PPossible values for  --emacs-mode.PThe argument to --erased-matches.PPossible values for --erased-matches.P Argument to --help.PPossible values for --help.P;Print the possible values of an argument of the given type.P Argument to  --profile.PPossible values for  --profile.P Argument to --trace-imports.PPossible values for --trace-imports.P Argument to  --warning.PPossible values for  --warning.PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPNone* #$&()+,/159<=>?PAll builtin modules.P(Non-empty) library names to be resolved to (lists of) pathes.2Resolved pathes (no duplicates). Contains "." if  [LibName] does.Ϋ8Candidate (initially: the directory Agda was called in).Actual root and  .agda-lib file for this project.ԫOverride the default  libraries file?׫Name of  libraries file for error reporting./Library files paired with their line number in  libraries.-Content of library files. (Might have empty LibNames.),PPQQQQQQQQQQQQFFGGGGGGGGGGGGGGGGGGGGGGGGGGGG,QQQQQQQQPPQQGFGGGGGGGGGGGGGGQGGGGGGGFGGGGGGQNone) #&()+,/1359<=>?nQ'The list should not contain duplicates.Q--build-library+: Build all modules in the current library.Q2In the absence of a path the project root is used.QUse ~/.agda/defaults.QConfigure colour output.Q3Emacs mode administration (formerly done by the  agda-mode' executable). Accepted subcommands: locate, setup, compile. Can be given several times, subcommands are accumulated in the set.Q%Exit if an interactive command fails.Q --interaction mode.Q Agda REPL (-I).Q--interaction-json mode.Q'In literate Markdown/Typst, only treat ```agda blocks as code.QShould the top-level module only be scope-checked, and not type-checked?Q Use this (if  ) instead of ~/.agda/libraries.Q+Should imports be type-checked in parallel?QPrint all options as a simple list (for implementing bash completion).Q$Force Agda to self-setup at startup.Q/Configure notifications about imported modules.QShould code points that are not supported by the locale be transliterated?Q3Map names of trusted executables to absolute paths.Q look for  .agda-lib files.Q If several  --emacs-mode commands are given, they are executed in the order as given in this datatype.Q Compile the .el files to .elc.Q#Print the installation location of agda2.el.Q Add the initialization lines to .emacs.QInfective or coinfective?Q%Options which can be set in a pragma.QAllow running external  executables from meta programs.QAutomatic compile-time inlining for simple definitions (unless marked NOINLINE).Q)Use call-by-name instead of call-by-need.Q&Are the cohesion modalities available?QTreat the module given at the command line or via interaction as main module in compilation?Q"Check confluence of rewrite rules?Q(Allow definitions by copattern matching?QCount extended grapheme clusters rather than code points when generating LaTeX.Q,Mark parameters of record modules as erased?Q)What kinds of erased matches are allowed?Q+irrelevant levels, irrelevant data matchingQ:Defer instance search based on discrimination tree resultsQUse the Agda abstract machine ( fastReduce)?QShould we speculatively unify function applications as if they were injective? Implies optRequireUniqueMetaSolutions.QCan we split on a  (@flat x : A) argument?Q0Allow recursion on forced constructor arguments.Q2Perform the forcing analysis on data constructors?QCan Agda.Builtin.Erased.Funext be used?QShould patterns of the form {x} or S x S be interpreted as puns?QShould every top-level module start with an implicit statement ,open import Agda.Primitive using (Set; Prop)?QShould case splitting and coverage checking try to discharge absurd clauses? Default: , but  might make coverage checking considerably faster in some cases.QDo not discard clauses constructed by the coverage checker (needed for some external backends).QShould case splitting replace variables with dot patterns (False) or keep them as variables (True).QAllow large indices, and large forced arguments in constructors.QShould we load the primitive modules at all? This is a stronger form of optImportSorts.Q*Can local rewrite rules be added and used?Q4Perform automated occurrence analysis for functions?Q0Is pattern matching allowed in the current file?QCan we use modal polarities (++,  +, etc.)?Q$Should system generated projections  ProjSystem0 be printed postfix (True) or prefix (False).Q6Perform the projection-likeness analysis on functions?QCan Agda.Builtin.Erased.Propext be used?Q?Should instance search consider instances with qualified names?RCan Agda.Builtin.Erased.Quotient be used?RForbid non-unique meta solutions allowed. For instance from INJECTIVE_FOR_INFERENCE pragmas.R$Can rewrite rules be added and used?R'Save meta-variables to interface files.R'Show generalized parameters in Pi typesRShow identity substitutions when pretty-printing terms (i.e. always show all arguments of a metavariable).RShould the conversion checker use the syntactic equality shortcut?  means that it should.  n, for a non-negative number n/, means that syntactic equality checking gets n units of fuel. If the fuel becomes zero, then syntactic equality checking is turned off. The fuel counter is decreased in the failure continuation of .RCut off structural order comparison at some depth in termination checker?ROptions  --version and --numeric-version (last wins).RPrint Agda version number.RPrint Agda version information.R is used if no verbosity options have been given, thus making it possible to handle the default case relatively quickly. Note that  corresponds to a trie with verbosity level 1 for the empty path.RRRQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQRRRRRRRRRRRRRRRRRRRRRRRRRRRRګ۫ ܫ ݫޫ߫# . #   # ! %   !      None( #&()+,/159<=>?R?Returns the command line options which are currently in effect.R9Returns the pragma options which are currently in effect.RRRRR % %0& &2' '2( (.) )/- -9* *2. .8+ +1/ /, ,>None( #&()+,/159<=>?RRRRR !R None+ #&()+,/1359<=>?>RChecks that the given options are consistent. Also makes adjustments (e.g. when one option implies another).RCommand line options of previous versions of Agda. Should not be listed in the usage info, put parsed by GetOpt for good error messaging.RSimple interface for Agda.Utils.GetOpt Could be moved to Agda.Utils.Options (does not exist yet)R"Infective and coinfective options. Note that --cubical[=full] and --cubical=erased are "jointly infective": if one of them is used in one module, then one or the other must be used in all modules that depend on this module.RLatex pragma options.RMap a function over the long options. Also removes the short options. Will be used to add the plugin name to the plugin options.SS is implied by S.SS is implied by S, S and S. S+ is also implied by an explicitly given --erased-matches# with an argument distinct from =none.SS is implied by S.SS requires S.SParse options for a plugin.S%Parse options from an options pragma.SThis function returns ! if the file should be rechecked.S?ZS$Print an annotated, pretty-printing " onto a VT100-compatible terminal.SSSSSSSSNone( #&()+,/159<=>?SHandle the option --bash-complete. It expects the index  COMP_CWORD as first argument that tells which of the following arguments  COMP_WORDS is supposed to be completed.5It either returns an error message or the result for  COMPREPLY.S%Complete the given word as an option.SCached trie of options.SPrint just the names of the given options (e.g. for bash completion scripts). For long options with finitely enumerable arguments, print all variants.S1The result of an invokation of (bash) completion.SIf  , the S" word cannot be further completed.SIf =, then the completion word cannot become a valid option ever.S Should the S4 be truncated to a given maximum number of prefixes?S/Truncate completions suggestions? To how many?Arguments following --bash-complete. Error or  COMPREPLY. SSSSSSSSSSSS SSSSSSSSSSSSNone( #&()+,/159<=>?RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSRRSSSSSSSSSSSSSSSSSSRRRQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSRRSSSSSSSSSSSSSSSSSSQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQRRRQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQRRRRRRRRRRRRRRRRRRRRRRRRRRRRNone( #&()+,/159<=>?SShow the attributes necessary to recover a modality, in long-form (e.g. using at-syntax rather than dots). For the default modality, the result is at- (rather than the empty document). Suitable for showing modalities outside of binders.*SSSSSSSSSSSSSSTTTTSSSSSSSSSSSSSSTTTT,T (T T T T 5T T 1T T T T T T 1T "T !T T T T T T  T 1T T 'T T T))-T%%T,,!T''#T55T00T((T11T++"T22!T66T44)T--(T&&-T..T//T**$T33#None( #&()+,/159<=>? TConvert a split tree into a  (for printing).TTag for labeling branches of a split tree. Each branch is associated to either a constructor or a literal, or is a catchall branch (currently only used for splitting on a literal type).TAbstract case tree shape.TA split is necessary.TNo more splits coming. We are at a single, all-variable clause.TArg. no to split at.T+The number of variables bound in the clauseTSub split trees.T for root of split treeTSplit tree branching. A finite map from constructor names to splittrees A list representation seems appropriate, since we are expecting not so many constructors per data type, and there is no need for random access.TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT55TT55#T#T22T T 1T T T +T55TT T +T /T5 5T T2 2None( #&()+,/159<=>? T Monoidal for T and T. Returns just first T discarding the second one.TOne clause in a function definition. There is no guarantee that the B actually declares the (#. We will have to check that later.T$The kind of the forward declaration.TName of a data typeTName of a function.TName of a record typeTNumbering declarations in an interleaved mutual block.Twe are nicifying a mutual blockT,we are nicifying decls not in a mutual blockTIn an inferred mutual block we keep accumulating nice declarations until all of the lone signatures have an attached definition. The type is therefore a bit span-like: we return an initial segment (the inferred mutual block) together with leftovers.T.Constructors associated to the data signature.T&Internal number of the data signature.TThe data signature.U6Function clauses associated to the function signature.UIn an `interleaved mutual' block we collect the data signatures, function signatures, as well as their associated constructors and function clauses respectively. Each signature is given a position in the block (from 0 onwards) and each set of constructor / clauses is given a *distinct* one. This allows for interleaved forward declarations similar to what one gets in a new-style mutual block.UExtra state for the Nice, monad to process interleaved mutual blocks.USeveral declarations expect only type signatures as sub-declarations. These are:U constructor, in interleaved mutual.Udata ... where=. Here we got a bad error message for Agda-2.5 (Issue 1698).Ufield. Ensured by parser.U postulate.U primitive.U1Termination measure is, for now, a variable name.UWhen processing a mutual block we collect the various checks present in the block before combining them.UOnly Us.UThe nice declarations. No fixity declarations and function definitions are contained in a single constructor instead of spread out between type signatures and clauses. The private,  postulate, abstract and instance modifiers have been distributed to the individual declarations. Observe the order of components:Range Fixity' Access IsAbstract IsInstance TerminationCheck PositivityCheckfurther attributes(Q)Namecontent (Expr, Declaration ...)U: argument: We record whether a declaration was made in an abstract block. argument: Axioms and functions can be declared irrelevant. ( should be .)UBlock of function clauses (we have seen the type signature before). The Bs are the original declarations that were processed into this U and are only used in notSoNiceDeclaration9. Andreas, 2017-01-01: Because of issue #2372, we add 6 here. An alias should know that it is an instance.UAn uncategorized function clause, could be a function clause without type signature or a pattern lhs (e.g. for irrefutable let). The B is the actual B.U (Maybe Range) gives range of the  'pattern' declaration.UOnly Us.TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUTTUUUUUTTTTTTUTTTTTTUUUUUUTTTUUUUUUTTTTTTTTTTTTTTTTTTTTU UU UUU#UU "U "U U U U U U U UU U  UU UUU None( #&()+,/159<=>?=