{-# OPTIONS_GHC -Wno-orphans #-} -- Outputable {-# LANGUAGE DataKinds #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE KindSignatures #-} {-# LANGUAGE RoleAnnotations #-} {-# LANGUAGE ScopedTypeVariables #-} -- (c) The University of Glasgow 2012 -- | Module for coercion axioms, used to represent type family instances -- and newtypes module GHC.Core.Coercion.Axiom ( BranchFlag, Branched, Unbranched, BranchIndex, Branches(..), manyBranches, unbranched, fromBranches, numBranches, mapAccumBranches, CoAxiom(..), CoAxBranch(..), toBranchedAxiom, toUnbranchedAxiom, coAxiomName, coAxiomArity, coAxiomBranches, coAxiomTyCon, isImplicitCoAxiom, coAxiomNumPats, coAxiomNthBranch, coAxiomSingleBranch_maybe, coAxiomRole, coAxiomSingleBranch, coAxBranchTyVars, coAxBranchCoVars, coAxBranchRoles, coAxBranchLHS, coAxBranchRHS, coAxBranchSpan, coAxBranchIncomps, placeHolderIncomps, Role(..), fsFromRole, CoAxiomRule(..), BuiltInFamRewrite(..), BuiltInFamInjectivity(..), TypeEqn, coAxiomRuleArgRoles, coAxiomRuleRole, coAxiomRuleBranch_maybe, isNewtypeAxiomRule_maybe, BuiltInSynFamily(..), trivialBuiltInFamily ) where import GHC.Prelude import Language.Haskell.Syntax.Basic (Role(..)) import {-# SOURCE #-} GHC.Core.TyCo.Rep ( Type ) import {-# SOURCE #-} GHC.Core.TyCo.Ppr ( pprType, pprTyVar ) import {-# SOURCE #-} GHC.Core.TyCon ( TyCon, isNewTyCon ) import GHC.Utils.Outputable import GHC.Data.FastString import GHC.Types.Name import GHC.Types.Unique import GHC.Types.Var import GHC.Utils.Misc import GHC.Utils.Binary import GHC.Utils.Panic import GHC.Data.Pair import GHC.Types.Basic import Data.Typeable ( Typeable ) import GHC.Types.SrcLoc import qualified Data.Data as Data import Data.Array import Data.List ( mapAccumL ) {- Note [Coercion axiom branches] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In order to allow closed type families, an axiom needs to contain an ordered list of alternatives, called branches. The kind of the coercion built from an axiom is determined by which index is used when building the coercion from the axiom. For example, consider the axiom derived from the following declaration: type family F a where F [Int] = Bool F [a] = Double F (a b) = Char This will give rise to this axiom: axF :: { F [Int] ~ Bool ; forall (a :: *). F [a] ~ Double ; forall (k :: *) (a :: k -> *) (b :: k). F (a b) ~ Char } The axiom is used with the AxiomCo constructor of Coercion. If we wish to have a coercion showing that F (Maybe Int) ~ Char, it will look like axF[2] <*> :: F (Maybe Int) ~ Char -- or, written using concrete-ish syntax -- AxiomRuleCo axF 2 [Refl *, Refl Maybe, Refl Int] Note that the index is 0-based. For type-checking, it is also necessary to check that no previous pattern can unify with the supplied arguments. After all, it is possible that some of the type arguments are lambda-bound type variables whose instantiation may cause an earlier match among the branches. We wish to prohibit this behavior, so the type checker rules out the choice of a branch where a previous branch can unify. See also [Apartness] in GHC.Core.FamInstEnv. For example, the following is malformed, where 'a' is a lambda-bound type variable: axF[2] <*> :: F (a Bool) ~ Char Why? Because a might be instantiated with [], meaning that branch 1 should apply, not branch 2. This is a vital consistency check; without it, we could derive Int ~ Bool, and that is a Bad Thing. Note [Branched axioms] ~~~~~~~~~~~~~~~~~~~~~~ Although a CoAxiom has the capacity to store many branches, in certain cases, we want only one. These cases are in data/newtype family instances, newtype coercions, and type family instances. Furthermore, these unbranched axioms are used in a variety of places throughout GHC, and it would difficult to generalize all of that code to deal with branched axioms, especially when the code can be sure of the fact that an axiom is indeed a singleton. At the same time, it seems dangerous to assume singlehood in various places through GHC. The solution to this is to label a CoAxiom with a phantom type variable declaring whether it is known to be a singleton or not. The branches are stored using a special datatype, declared below, that ensures that the type variable is accurate. ************************************************************************ * * Branches * * ************************************************************************ -} {- Note [BranchIndex] ~~~~~~~~~~~~~~~~~~~~ A CoAxiom has 1 or more branches. Each branch has contains a list of the free type variables in that branch, the LHS type patterns, and the RHS type for that branch. When we apply an axiom to a list of coercions, we must choose which branch of the axiom we wish to use, as the different branches may have different numbers of free type variables. (The number of type patterns is always the same among branches, but that doesn't quite concern us here.) -} type BranchIndex = Int -- Counting from zero -- The index of the branch in the list of branches -- See Note [BranchIndex] -- promoted data type data BranchFlag = Branched | Unbranched type Branched = 'Branched type Unbranched = 'Unbranched -- By using type synonyms for the promoted constructors, we avoid needing -- DataKinds and the promotion quote in client modules. This also means that -- we don't need to export the term-level constructors, which should never be used. newtype Branches (br :: BranchFlag) = MkBranches { unMkBranches :: Array BranchIndex CoAxBranch } type role Branches nominal manyBranches :: [CoAxBranch] -> Branches Branched manyBranches brs = assert (snd bnds >= fst bnds ) MkBranches (listArray bnds brs) where bnds = (0, length brs - 1) unbranched :: CoAxBranch -> Branches Unbranched unbranched br = MkBranches (listArray (0, 0) [br]) toBranched :: Branches br -> Branches Branched toBranched = MkBranches . unMkBranches toUnbranched :: Branches br -> Branches Unbranched toUnbranched (MkBranches arr) = assert (bounds arr == (0,0) ) MkBranches arr fromBranches :: Branches br -> [CoAxBranch] fromBranches = elems . unMkBranches branchesNth :: Branches br -> BranchIndex -> CoAxBranch branchesNth (MkBranches arr) n = arr ! n numBranches :: Branches br -> Int numBranches (MkBranches arr) = snd (bounds arr) + 1 -- | The @[CoAxBranch]@ passed into the mapping function is a list of -- all previous branches, reversed mapAccumBranches :: ([CoAxBranch] -> CoAxBranch -> CoAxBranch) -> Branches br -> Branches br mapAccumBranches f (MkBranches arr) = MkBranches (listArray (bounds arr) (snd $ mapAccumL go [] (elems arr))) where go :: [CoAxBranch] -> CoAxBranch -> ([CoAxBranch], CoAxBranch) go prev_branches cur_branch = ( cur_branch : prev_branches , f prev_branches cur_branch ) {- ************************************************************************ * * Coercion axioms * * ************************************************************************ Note [Storing compatibility] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ During axiom application, we need to be aware of which branches are compatible with which others. The full explanation is in Note [Compatibility] in GHc.Core.FamInstEnv. (The code is placed there to avoid a dependency from GHC.Core.Coercion.Axiom on the unification algorithm.) Although we could theoretically compute compatibility on the fly, this is silly, so we store it in a CoAxiom. Specifically, each branch refers to all other branches with which it is incompatible. This list might well be empty, and it will always be for the first branch of any axiom. CoAxBranches that do not (yet) belong to a CoAxiom should have a panic thunk stored in cab_incomps. The incompatibilities are properly a property of the axiom as a whole, and they are computed only when the final axiom is built. During serialization, the list is converted into a list of the indices of the branches. Note [CoAxioms are homogeneous] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ All axioms must be *homogeneous*, meaning that the kind of the LHS must match the kind of the RHS. In practice, this means: Given a CoAxiom { co_ax_tc = ax_tc }, for every branch CoAxBranch { cab_lhs = lhs, cab_rhs = rhs }: typeKind (mkTyConApp ax_tc lhs) `eqType` typeKind rhs This is checked in FamInstEnv.mkCoAxBranch. -} -- | A 'CoAxiom' is a \"coercion constructor\", i.e. a named equality axiom. -- If you edit this type, you may need to update the GHC formalism -- See Note [GHC Formalism] in GHC.Core.Lint data CoAxiom br = CoAxiom -- Type equality axiom. { co_ax_unique :: Unique -- Unique identifier , co_ax_name :: Name -- Name for pretty-printing , co_ax_role :: Role -- Role of the axiom's equality , co_ax_tc :: TyCon -- The head of the LHS patterns -- e.g. the newtype or family tycon , co_ax_branches :: Branches br -- The branches that form this axiom , co_ax_implicit :: Bool -- True <=> the axiom is "implicit" -- See Note [Implicit axioms] -- INVARIANT: co_ax_implicit == True implies length co_ax_branches == 1. } -- | A branch of a coercion axiom, which provides the evidence for -- unwrapping a newtype or a type-family reduction step using a single equation. data CoAxBranch = CoAxBranch { cab_loc :: SrcSpan -- ^ Location of the defining equation -- See Note [CoAxiom locations] , cab_tvs :: [TyVar] -- ^ Bound type variables; not necessarily fresh -- See Note [CoAxBranch type variables] , cab_eta_tvs :: [TyVar] -- ^ Eta-reduced tyvars -- cab_tvs and cab_lhs may be eta-reduced; see -- Note [Eta reduction for data families] , cab_cvs :: [CoVar] -- ^ Bound coercion variables -- Always empty, for now. -- See Note [Constraints in patterns] -- in GHC.Tc.TyCl , cab_roles :: [Role] -- ^ See Note [CoAxBranch roles] , cab_lhs :: [Type] -- ^ Type patterns to match against , cab_rhs :: Type -- ^ Right-hand side of the equality -- See Note [CoAxioms are homogeneous] , cab_incomps :: [CoAxBranch] -- ^ The previous incompatible branches -- See Note [Storing compatibility] } deriving Data.Data toBranchedAxiom :: CoAxiom br -> CoAxiom Branched toBranchedAxiom ax@(CoAxiom { co_ax_branches = branches }) = ax { co_ax_branches = toBranched branches } toUnbranchedAxiom :: CoAxiom br -> CoAxiom Unbranched toUnbranchedAxiom ax@(CoAxiom { co_ax_branches = branches }) = ax { co_ax_branches = toUnbranched branches } coAxiomNumPats :: CoAxiom br -> Int coAxiomNumPats = length . coAxBranchLHS . (flip coAxiomNthBranch 0) coAxiomArity :: CoAxiom br -> BranchIndex -> Arity coAxiomArity ax index = length tvs + length cvs where CoAxBranch { cab_tvs = tvs, cab_cvs = cvs } = coAxiomNthBranch ax index coAxiomName :: CoAxiom br -> Name coAxiomName = co_ax_name coAxiomRole :: CoAxiom br -> Role coAxiomRole = co_ax_role coAxiomBranches :: CoAxiom br -> Branches br coAxiomBranches = co_ax_branches coAxiomNthBranch :: CoAxiom br -> BranchIndex -> CoAxBranch coAxiomNthBranch (CoAxiom { co_ax_branches = bs }) index = branchesNth bs index coAxiomSingleBranch :: CoAxiom Unbranched -> CoAxBranch coAxiomSingleBranch (CoAxiom { co_ax_branches = MkBranches arr }) = arr ! 0 coAxiomSingleBranch_maybe :: CoAxiom br -> Maybe CoAxBranch coAxiomSingleBranch_maybe (CoAxiom { co_ax_branches = MkBranches arr }) | snd (bounds arr) == 0 = Just $ arr ! 0 | otherwise = Nothing coAxiomTyCon :: CoAxiom br -> TyCon coAxiomTyCon = co_ax_tc coAxBranchTyVars :: CoAxBranch -> [TyVar] coAxBranchTyVars = cab_tvs coAxBranchCoVars :: CoAxBranch -> [CoVar] coAxBranchCoVars = cab_cvs coAxBranchLHS :: CoAxBranch -> [Type] coAxBranchLHS = cab_lhs coAxBranchRHS :: CoAxBranch -> Type coAxBranchRHS = cab_rhs coAxBranchRoles :: CoAxBranch -> [Role] coAxBranchRoles = cab_roles coAxBranchSpan :: CoAxBranch -> SrcSpan coAxBranchSpan = cab_loc isImplicitCoAxiom :: CoAxiom br -> Bool isImplicitCoAxiom = co_ax_implicit coAxBranchIncomps :: CoAxBranch -> [CoAxBranch] coAxBranchIncomps = cab_incomps -- See Note [Compatibility] in GHC.Core.FamInstEnv placeHolderIncomps :: [CoAxBranch] placeHolderIncomps = panic "placeHolderIncomps" {- Note [CoAxBranch type variables] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In the case of a CoAxBranch of an associated type-family instance, we use the *same* type variables in cab_tvs (where possible) as the enclosing class or instance. Consider instance C Int [z] where type F Int [z] = ... -- Second param must be [z] In the CoAxBranch in the instance decl (F Int [z]) we use the same 'z', so that it's easy to check that that type is the same as that in the instance header. However, I believe that the cab_tvs of any CoAxBranch are distinct from the cab_tvs of other CoAxBranches in the same CoAxiom. This is important when checking for compatiblity and apartness; e.g. see GHC.Core.FamInstEnv.compatibleBranches. (The story seems a bit wobbly here, but it seems to work.) Note [CoAxBranch roles] ~~~~~~~~~~~~~~~~~~~~~~~ Consider this code: newtype Age = MkAge Int newtype Wrap a = MkWrap a convert :: Wrap Age -> Int convert (MkWrap (MkAge i)) = i We want this to compile to: NTCo:Wrap :: forall a. Wrap a ~R a NTCo:Age :: Age ~R Int convert = \x -> x |> (NTCo:Wrap[0] NTCo:Age[0]) But, note that NTCo:Age is at role R. Thus, we need to be able to pass coercions at role R into axioms. However, we don't *always* want to be able to do this, as it would be disastrous with type families. The solution is to annotate the arguments to the axiom with roles, much like we annotate tycon tyvars. Where do these roles get set? Newtype axioms inherit their roles from the newtype tycon; family axioms are all at role N. Note [CoAxiom locations] ~~~~~~~~~~~~~~~~~~~~~~~~ The source location of a CoAxiom is stored in two places in the datatype tree. * The first is in the location info buried in the Name of the CoAxiom. This span includes all of the branches of a branched CoAxiom. * The second is in the cab_loc fields of the CoAxBranches. In the case of a single branch, we can extract the source location of the branch from the name of the CoAxiom. In other cases, we need an explicit SrcSpan to correctly store the location of the equation giving rise to the FamInstBranch. Note [Implicit axioms] ~~~~~~~~~~~~~~~~~~~~~~ See also Note [Implicit TyThings] in GHC.Types.TyThing * A CoAxiom arising from data/type family instances is not "implicit". That is, it has its own IfaceAxiom declaration in an interface file * The CoAxiom arising from a newtype declaration *is* "implicit". That is, it does not have its own IfaceAxiom declaration in an interface file; instead the CoAxiom is generated by type-checking the newtype declaration Note [Eta reduction for data families] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider this data family T a b :: * newtype instance T Int a = MkT (IO a) deriving( Monad ) We'd like this to work. From the 'newtype instance' you might think we'd get: newtype TInt a = MkT (IO a) axiom ax1 a :: T Int a ~ TInt a -- The newtype-instance part axiom ax2 a :: TInt a ~ IO a -- The newtype part But now what can we do? We have this problem Given: d :: Monad IO Wanted: d' :: Monad (T Int) = d |> ???? What coercion can we use for the ??? Solution: eta-reduce both axioms, thus: axiom ax1 :: T Int ~ TInt axiom ax2 :: TInt ~ IO Now d' = d |> Monad (sym (ax2 ; ax1)) ----- Bottom line ------ For a CoAxBranch for a data family instance with representation TyCon rep_tc: - cab_tvs (of its CoAxiom) may be shorter than tyConTyVars of rep_tc. - cab_lhs may be shorter than tyConArity of the family tycon i.e. LHS is unsaturated - cab_rhs will be (rep_tc cab_tvs) i.e. RHS is un-saturated - This eta reduction happens for data instances as well as newtype instances. Here we want to eta-reduce the data family axiom. - This eta-reduction is done in GHC.Tc.TyCl.Instance.tcDataFamInstDecl. But for a /type/ family - cab_lhs has the exact arity of the family tycon There are certain situations (e.g., pretty-printing) where it is necessary to deal with eta-expanded data family instances. For these situations, the cab_eta_tvs field records the stuff that has been eta-reduced away. So if we have axiom forall a b. F [a->b] = D b a and cab_eta_tvs is [p,q], then the original user-written definition looked like axiom forall a b p q. F [a->b] p q = D b a p q (See #9692, #14179, and #15845 for examples of what can go wrong if we don't eta-expand when showing things to the user.) See also: * Note [Newtype eta] in GHC.Core.TyCon. This is notionally separate and deals with the axiom connecting a newtype with its representation type; but it too is eta-reduced. * Note [Implementing eta reduction for data families] in "GHC.Tc.TyCl.Instance". This describes the implementation details of this eta reduction happen. * Note [RoughMap and rm_empty] for how this complicates the RoughMap implementation slightly. -} {- ********************************************************************* * * Instances, especially pretty-printing * * ********************************************************************* -} instance Eq (CoAxiom br) where a == b = getUnique a == getUnique b a /= b = getUnique a /= getUnique b instance Uniquable (CoAxiom br) where getUnique = co_ax_unique instance NamedThing (CoAxiom br) where getName = co_ax_name instance Typeable br => Data.Data (CoAxiom br) where -- don't traverse? toConstr _ = abstractConstr "CoAxiom" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "CoAxiom" instance Outputable (CoAxiom br) where -- You may want GHC.Core.Coercion.pprCoAxiom instead ppr = ppr . getName instance Outputable CoAxBranch where -- This instance doesn't know the name of the type family -- If possible, use GHC.Core.Coercion.pprCoAxBranch instead ppr (CoAxBranch { cab_tvs = tvs, cab_cvs = cvs , cab_lhs = lhs_tys, cab_rhs = rhs, cab_incomps = incomps }) = text "CoAxBranch" <+> braces payload where payload = hang (text "forall" <+> pprWithCommas pprTyVar (tvs ++ cvs) <> dot) 2 (vcat [ text "" <+> sep (map pprType lhs_tys) , nest 2 (text "=" <+> ppr rhs) , ppUnless (null incomps) $ text "incomps:" <+> vcat (map ppr incomps) ]) {- ************************************************************************ * * Roles * * ************************************************************************ Roles are defined here to avoid circular dependencies. -} -- These names are slurped into the parser code. Changing these strings -- will change the **surface syntax** that GHC accepts! If you want to -- change only the pretty-printing, do some replumbing. See -- mkRoleAnnotDecl in GHC.Parser.PostProcess fsFromRole :: Role -> FastString fsFromRole Nominal = fsLit "nominal" fsFromRole Representational = fsLit "representational" fsFromRole Phantom = fsLit "phantom" instance Outputable Role where ppr = ftext . fsFromRole instance Binary Role where put_ bh Nominal = putByte bh 1 put_ bh Representational = putByte bh 2 put_ bh Phantom = putByte bh 3 get bh = do tag <- getByte bh case tag of 1 -> return Nominal 2 -> return Representational 3 -> return Phantom _ -> panic ("get Role " ++ show tag) {- ************************************************************************ * * CoAxiomRule Rules for building Evidence * * ************************************************************************ Note [CoAxiomRule] ~~~~~~~~~~~~~~~~~~ A CoAxiomRule is a built-in axiom, one that we assume to be true: CoAxiomRules come in four flavours: * BuiltInFamRew: provides evidence for, say (ax1) 3+4 ----> 7 (ax2) s+0 ----> s The evidence looks like AxiomCo ax1 [3,4] :: 3+4 ~ 7 AxiomCo ax2 [s] :: s+0 ~ s The arguments in the AxiomCo are the /instantiating types/, or more generally coercions (see Note [Coercion axioms applied to coercions] in GHC.Core.TyCo.Rep). * BuiltInFamInj: provides evidence for the injectivity of type families For example (ax3) g1: a+b ~ 0 ---> a~0 (ax4) g2: a+b ~ 0 ---> b~0 (ax5) g3: a+b1 ~ a~b2 ---> b1~b2 The argument to the AxiomCo is the full coercion (always just one). So then: AxiomCo ax3 [g1] :: a ~ 0 AxiomCo ax4 [g2] :: b ~ 0 AxiomCo ax5 [g3] :: b1 ~ b2 * BranchedAxiom: used for closed type families type family F a where F Int = Bool F Bool = Char F a = a -> Int We get one (CoAxiom Branched) for the entire family; when used in an AxiomCo we pair it with the BranchIndex to say which branch to pick. * UnbranchedAxiom: used for several purposes; - Newtypes - Data family instances - Open type family instances Note [Avoiding allocating lots of CoAxiomRules] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CoAxiomRule is a sum type of four alternatives, which is very nice. But there is a danger of allocating lots of (BuiltInFamRew bif) objects, every time we (say) need a type-family rewrite. To avoid this allocation, we cache the appropraite CoAxiomRule inside each BuiltInFamRewrite, BuiltInFamInjectivity making a little circular data structure. See the `bifrw_axr` field of BuiltInFamRewrite, and similarly the others. It's simple to do this, and saves a percent or two of allocation in programs that do a lot of type-family work. -} -- | CoAxiomRule describes a built-in axiom, one that we assume to be true -- See Note [CoAxiomRule] data CoAxiomRule = BuiltInFamRew BuiltInFamRewrite -- Built-in type-family rewrites -- e.g. 3+5 ~ 7 | BuiltInFamInj BuiltInFamInjectivity -- Built-in type-family deductions -- e.g. a+b~0 ==> a~0 -- Always unary | BranchedAxiom (CoAxiom Branched) BranchIndex -- Closed type family | UnbranchedAxiom (CoAxiom Unbranched) -- Open type family instance, -- data family instances -- and newtypes instance Eq CoAxiomRule where (BuiltInFamRew bif1) == (BuiltInFamRew bif2) = bifrw_name bif1 == bifrw_name bif2 (BuiltInFamInj bif1) == (BuiltInFamInj bif2) = bifinj_name bif1 == bifinj_name bif2 (UnbranchedAxiom ax1) == (UnbranchedAxiom ax2) = getUnique ax1 == getUnique ax2 (BranchedAxiom ax1 i1) == (BranchedAxiom ax2 i2) = getUnique ax1 == getUnique ax2 && i1 == i2 _ == _ = False coAxiomRuleRole :: CoAxiomRule -> Role coAxiomRuleRole (BuiltInFamRew {}) = Nominal coAxiomRuleRole (BuiltInFamInj {}) = Nominal coAxiomRuleRole (UnbranchedAxiom ax) = coAxiomRole ax coAxiomRuleRole (BranchedAxiom ax _) = coAxiomRole ax coAxiomRuleArgRoles :: CoAxiomRule -> [Role] coAxiomRuleArgRoles (BuiltInFamRew bif) = replicate (bifrw_arity bif) Nominal coAxiomRuleArgRoles (BuiltInFamInj {}) = [Nominal] coAxiomRuleArgRoles (UnbranchedAxiom ax) = coAxBranchRoles (coAxiomSingleBranch ax) coAxiomRuleArgRoles (BranchedAxiom ax i) = coAxBranchRoles (coAxiomNthBranch ax i) coAxiomRuleBranch_maybe :: CoAxiomRule -> Maybe (TyCon, Role, CoAxBranch) coAxiomRuleBranch_maybe (UnbranchedAxiom ax) = Just (co_ax_tc ax, co_ax_role ax, coAxiomSingleBranch ax) coAxiomRuleBranch_maybe (BranchedAxiom ax i) = Just (co_ax_tc ax, co_ax_role ax, coAxiomNthBranch ax i) coAxiomRuleBranch_maybe _ = Nothing isNewtypeAxiomRule_maybe :: CoAxiomRule -> Maybe (TyCon, CoAxBranch) isNewtypeAxiomRule_maybe (UnbranchedAxiom ax) | let tc = coAxiomTyCon ax, isNewTyCon tc = Just (tc, coAxiomSingleBranch ax) isNewtypeAxiomRule_maybe _ = Nothing instance Data.Data CoAxiomRule where -- don't traverse? toConstr _ = abstractConstr "CoAxiomRule" gunfold _ _ = error "gunfold" dataTypeOf _ = mkNoRepType "CoAxiomRule" instance Outputable CoAxiomRule where ppr (BuiltInFamRew bif) = ppr (bifrw_name bif) ppr (BuiltInFamInj bif) = ppr (bifinj_name bif) ppr (UnbranchedAxiom ax) = ppr (coAxiomName ax) ppr (BranchedAxiom ax i) = ppr (coAxiomName ax) <> brackets (int i) {- ********************************************************************* * * Built-in families * * ********************************************************************* -} -- | A more explicit representation for `t1 ~ t2`. type TypeEqn = Pair Type -- Type checking of built-in families data BuiltInSynFamily = BuiltInSynFamily { sfMatchFam :: [BuiltInFamRewrite] , sfInteract :: [BuiltInFamInjectivity] -- If given these type arguments and RHS, returns the equalities that -- are guaranteed to hold. That is, if -- (ar, Pair s1 s2) is an element of (sfInteract tys ty) -- then AxiomRule ar [co :: F tys ~ ty] :: s1~s2 } data BuiltInFamInjectivity -- Argument and result role are always Nominal = BIF_Interact { bifinj_name :: FastString , bifinj_axr :: CoAxiomRule -- Cached copy of (BuiltInFamINj this-bif) -- See Note [Avoiding allocating lots of CoAxiomRules] , bifinj_proves :: TypeEqn -> Maybe TypeEqn -- ^ Always unary: just one TypeEqn argument -- Returns @Nothing@ when it doesn't like the supplied argument. -- When this happens in a coercion that means that the coercion is -- ill-formed, and Core Lint checks for that. } data BuiltInFamRewrite -- Argument roles and result role are always Nominal = BIF_Rewrite { bifrw_name :: FastString , bifrw_axr :: CoAxiomRule -- Cached copy of (BuiltInFamRew this-bif) -- See Note [Avoiding allocating lots of CoAxiomRules] , bifrw_fam_tc :: TyCon -- Needed for tyConsOfType , bifrw_arity :: Arity -- Number of type arguments needed -- to instantiate this axiom , bifrw_match :: [Type] -> Maybe ([Type], Type) -- coaxrMatch: does this reduce on the given arguments? -- If it does, returns (types to instantiate the rule at, rhs type) -- That is: mkAxiomCo ax (zipWith mkReflCo coAxiomRuleArgRoles ts) -- :: F tys ~N rhs, , bifrw_proves :: [TypeEqn] -> Maybe TypeEqn } -- length(inst_tys) = bifrw_arity -- INVARIANT: bifrw_match and bifrw_proves are related as follows: -- If Just (inst_tys, res_ty) = bifrw_match ax arg_tys -- then * length arg_tys = tyConArity fam_tc -- * length inst_tys = bifrw_arity -- * bifrw_proves (map (return @Pair) inst_tys) = Just (return @Pair res_ty) -- Provides default implementations that do nothing. trivialBuiltInFamily :: BuiltInSynFamily trivialBuiltInFamily = BuiltInSynFamily { sfMatchFam = [], sfInteract = [] }