Copyright	(C) 2023 Alexey Tochin
License	BSD3 (see the file LICENSE)
Maintainer	Alexey Tochin <Alexey.Tochin@gmail.com>
Safe Haskell	None
Language	Haskell2010
Extensions	ScopedTypeVariables OverloadedStrings ConstraintKinds InstanceSigs DeriveFunctor DeriveGeneric TypeSynonymInstances FlexibleContexts FlexibleInstances ConstrainedClassMethods MultiParamTypeClasses RankNTypes ExplicitForAll

Debug.SimpleExpr.Expr

Contents

Expression manipulation
Base types
Auxiliary functions

Description

Simple expressions base types and manipulations.

Synopsis

number :: Natural -> SimpleExpr
variable :: String -> SimpleExpr
unaryFunc :: String -> SimpleExpr -> SimpleExpr
binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr
simplifyExpr :: SimpleExpr -> SimpleExpr
simplifyStep :: (SimpleExpr -> SimpleExpr) -> SimpleExpr -> SimpleExpr
simplify :: ExtandableMap SimpleExpr SimpleExpr a a => a -> a
data SimpleExprF a
- = NumberF Natural
- | VariableF String
- | SymbolicFuncF String [a]
type SimpleExpr = Fix SimpleExprF
type SE = SimpleExpr
type Expr = ListOf SimpleExpr
class ListOf inner outer
content :: ListOf inner outer => outer -> [inner]
dependencies :: SimpleExpr -> [SimpleExpr]
showWithBrackets :: SimpleExpr -> String

Expression manipulation

number :: Natural -> SimpleExpr Source #

Initializes a single integer number expression.

Examples of usage

Expand

>>> a = number 42
>>> a
42
>>> :t a
a :: SimpleExpr

variable :: String -> SimpleExpr Source #

Initializes a single symbolic variable expression.

Examples of usage

Expand

>>> x = variable "x"
>>> x
x
>>> :t x
x :: SimpleExpr

unaryFunc :: String -> SimpleExpr -> SimpleExpr Source #

Inituialize unarry function

Examples of usage

Expand

>>> x = variable "x"
>>> f = unaryFunc "f"
>>> f x
f(x)
>>> :t x
x :: SimpleExpr
>>> :t f
f :: SimpleExpr -> SimpleExpr

binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr Source #

Inituialize unarry function

Examples of usage

Expand

>>> x = variable "x"
>>> y = variable "y"
>>> (-*-) = binaryFunc "-*-"
>>> x -*- y
x-*-y
>>> :t x
x :: SimpleExpr
>>> :t (-*-)
(-*-) :: SimpleExpr -> SimpleExpr -> SimpleExpr
>>> :t x-*-y
x-*-y :: SimpleExpr

simplifyExpr :: SimpleExpr -> SimpleExpr Source #

Simplify expression using some primitive rules like '0 * x -> 0' specified in simplifyStep implementation.

Examples of usage

Expand

>>> import Prelude (($))
>>> import Debug.SimpleExpr (variable, simplify)
>>> import NumHask ((+), (-), (*))

>>> x = variable "x"
>>> simplifyExpr $ (x + 0) * 1 - x * (3 - 2)
0

simplifyStep :: (SimpleExpr -> SimpleExpr) -> SimpleExpr -> SimpleExpr Source #

Minimalistic simplification step.

Examples of usage

Expand

>>> import Prelude (($), id)
>>> import NumHask ((+), (*), (**))

>>> simplifyStep id (0 + (0 + (0 + 10)))
0+(0+10)

>>> simplifyStep id (1 * (0 + (10 ** 1)))
0+(10^1)

simplify :: ExtandableMap SimpleExpr SimpleExpr a a => a -> a Source #

Simplify expression using some primitive rules like '0 * x -> 0' specified in simplifyStep implementation.

Base types

data SimpleExprF a Source #

Expression F-algebra functional.

Constructors

NumberF Natural
VariableF String
SymbolicFuncF String [a]

Instances

Instances details

Eq1 SimpleExprF Source #

Equality comparison for SimpleExprF lifted over its parameter.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

liftEq :: (a -> b -> Bool) -> SimpleExprF a -> SimpleExprF b -> Bool #

Functor SimpleExprF Source #

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

fmap :: (a -> b) -> SimpleExprF a -> SimpleExprF b #

(<$) :: a -> SimpleExprF b -> SimpleExprF a #

Num SimpleExpr Source #

Numeric typeclass instance for SimpleExpr.

This instance enables standard numeric operations on symbolic expressions, allowing for more natural mathematical notation in symbolic computations.

Examples of usage

Expand

>>> import GHC.Num ((+))

The primary benefit of this instance is enabling direct use of numeric literals in symbolic expressions without explicit conversion. This allows you to write natural mathematical expressions:

>>> x = variable "x"
>>> x + 1
x+1

This concise notation is equivalent to the more verbose explicit form:

>>> x + (number 1)
x+1

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

(+) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

(-) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

(*) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

negate :: SimpleExpr -> SimpleExpr #

abs :: SimpleExpr -> SimpleExpr #

signum :: SimpleExpr -> SimpleExpr #

fromInteger :: Integer -> SimpleExpr #

Show SimpleExpr Source #

SimpleExpr instance of Show typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

showsPrec :: Int -> SimpleExpr -> ShowS #

show :: SimpleExpr -> String #

showList :: [SimpleExpr] -> ShowS #

Hashable1 SimpleExprF Source #

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> SimpleExprF a -> Int #

Additive SimpleExpr Source #

SimpleExpr instance of Additive typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

(+) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

zero :: SimpleExpr #

Subtractive SimpleExpr Source #

SimpleExpr instance of Subtractive typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

negate :: SimpleExpr -> SimpleExpr #

(-) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

ExpField SimpleExpr Source #

SimpleExpr instance of ExpField typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

exp :: SimpleExpr -> SimpleExpr #

log :: SimpleExpr -> SimpleExpr #

(**) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

logBase :: SimpleExpr -> SimpleExpr -> SimpleExpr #

sqrt :: SimpleExpr -> SimpleExpr #

TrigField SimpleExpr Source #

SimpleExpr instance of TrigField typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

pi :: SimpleExpr #

sin :: SimpleExpr -> SimpleExpr #

cos :: SimpleExpr -> SimpleExpr #

tan :: SimpleExpr -> SimpleExpr #

asin :: SimpleExpr -> SimpleExpr #

acos :: SimpleExpr -> SimpleExpr #

atan :: SimpleExpr -> SimpleExpr #

atan2 :: SimpleExpr -> SimpleExpr -> SimpleExpr #

sinh :: SimpleExpr -> SimpleExpr #

cosh :: SimpleExpr -> SimpleExpr #

tanh :: SimpleExpr -> SimpleExpr #

asinh :: SimpleExpr -> SimpleExpr #

acosh :: SimpleExpr -> SimpleExpr #

atanh :: SimpleExpr -> SimpleExpr #

Divisive SimpleExpr Source #

SimpleExpr instance of Divisive typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

recip :: SimpleExpr -> SimpleExpr #

(/) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

Multiplicative SimpleExpr Source #

SimpleExpr instance of Multiplicative typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

(*) :: SimpleExpr -> SimpleExpr -> SimpleExpr #

one :: SimpleExpr #

FromInteger SimpleExpr Source #

SimpleExpr instance of FromInteger typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

fromInteger :: Integer -> SimpleExpr #

Generic1 SimpleExprF Source #

Instance details

Defined in Debug.SimpleExpr.Expr

Associated Types

type Rep1 SimpleExprF

Instance details

Defined in Debug.SimpleExpr.Expr

type Rep1 SimpleExprF = D1 ('MetaData "SimpleExprF" "Debug.SimpleExpr.Expr" "simple-expr-0.2.0.0-inplace" 'False) (C1 ('MetaCons "NumberF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Natural)) :+: (C1 ('MetaCons "VariableF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)) :+: C1 ('MetaCons "SymbolicFuncF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))))

Methods

from1 :: SimpleExprF a -> Rep1 SimpleExprF a #

to1 :: Rep1 SimpleExprF a -> SimpleExprF a #

FromIntegral Natural n => FromIntegral SimpleExpr n Source #

SimpleExpr instance of FromIntegral typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

fromIntegral :: n -> SimpleExpr #

AlgebraicPower Integer SimpleExpr Source #

AlgebraicPower instance for raising SimpleExpr values to Integer exponents.

Instance details

Defined in Debug.SimpleExpr.Utils.Algebra

Methods

(^^) :: SimpleExpr -> Integer -> SimpleExpr Source #

Integral a => MultiplicativeAction a SimpleExpr Source #

SimpleExpr instance of MultiplicativeAction a.

Instance details

Defined in Debug.SimpleExpr.Utils.Algebra

Methods

(*|) :: a -> SimpleExpr -> SimpleExpr Source #

Eq a => Eq (SimpleExprF a) Source #

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

(==) :: SimpleExprF a -> SimpleExprF a -> Bool #

(/=) :: SimpleExprF a -> SimpleExprF a -> Bool #

Hashable a => Hashable (SimpleExprF a) Source #

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

hashWithSalt :: Int -> SimpleExprF a -> Int #

hash :: SimpleExprF a -> Int #

FromIntegral Natural n => FromIntegral (SimpleExprF a) n Source #

SimpleExprF instance of FromIntegral typeclass.

Instance details

Defined in Debug.SimpleExpr.Expr

Methods

fromIntegral :: n -> SimpleExprF a #

type Rep1 SimpleExprF Source #

Instance details

Defined in Debug.SimpleExpr.Expr

type Rep1 SimpleExprF = D1 ('MetaData "SimpleExprF" "Debug.SimpleExpr.Expr" "simple-expr-0.2.0.0-inplace" 'False) (C1 ('MetaCons "NumberF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Natural)) :+: (C1 ('MetaCons "VariableF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String)) :+: C1 ('MetaCons "SymbolicFuncF" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 String) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))))

type SimpleExpr = Fix SimpleExprF Source #

Simple expression type, see tutorial

type SE = SimpleExpr Source #

Short type alias for SimpleExpr.

type Expr = ListOf SimpleExpr Source #

Expression typeclass. It includes SimpleExpr as well as list and tuples of SimpleExpr etc.

Auxiliary functions

class ListOf inner outer Source #

Entity that is representable as a list of in general other entities. In particular, X is a list of single [X], see the example below.

Examples of usage

Expand

>>> data Atom = Atom String deriving Show
>>> type Particle = ListOf Atom

>>> content (Atom "He") :: [Atom]
[Atom "He"]

>>> content (Atom "H", Atom "H") :: [Atom]
[Atom "H",Atom "H"]

>>> content [Atom "H", Atom "O", Atom "H"] :: [Atom]
[Atom "H",Atom "O",Atom "H"]

Minimal complete definition

content

Instances

Instances details

ListOf inner () Source #	Base case instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: () -> [inner] Source #
ListOf inner inner Source #	Identity instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: inner -> [inner] Source #
ListOf inner outer => ListOf inner [outer] Source #	List `[]` instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: [outer] -> [inner] Source #
(ListOf inner outer1, ListOf inner outer2) => ListOf inner (outer1, outer2) Source #	Tuple instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: (outer1, outer2) -> [inner] Source #
(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3) => ListOf inner (outer1, outer2, outer3) Source #	Triple instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: (outer1, outer2, outer3) -> [inner] Source #
(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3, ListOf inner outer4) => ListOf inner (outer1, outer2, outer3, outer4) Source #	4-tuple instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: (outer1, outer2, outer3, outer4) -> [inner] Source #
(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3, ListOf inner outer4, ListOf inner outer5) => ListOf inner (outer1, outer2, outer3, outer4, outer5) Source #	5-tuple instance of `ListOf`.
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: (outer1, outer2, outer3, outer4, outer5) -> [inner] Source #

content :: ListOf inner outer => outer -> [inner] Source #

Returns a list of entities the argument consists of.

dependencies :: SimpleExpr -> [SimpleExpr] Source #

Returns the list of head dependencies of an expression.

Examples of usage

Expand

>>> import Prelude (($), id)
>>> import NumHask ((+), (*))

>>> dependencies (variable "x" + (variable "y" * variable "z"))
[x,y*z]

showWithBrackets :: SimpleExpr -> String Source #

Shows expression adding brackets if it is needed for a context.