Copyright	(C) 2023 Alexey Tochin
License	BSD3 (see the file LICENSE)
Maintainer	Alexey Tochin <Alexey.Tochin@gmail.com>
Safe Haskell	Safe-Inferred
Language	Haskell2010
Extensions	Cpp ScopedTypeVariables ConstraintKinds InstanceSigs DeriveFunctor 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 :: Integer -> SimpleExpr
variable :: String -> SimpleExpr
unaryFunc :: String -> SimpleExpr -> SimpleExpr
binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr
simplify :: SimpleExpr -> SimpleExpr
simplifyStep :: (SimpleExpr -> SimpleExpr) -> SimpleExpr -> SimpleExpr
data SimpleExprF a
- = NumberF Integer
- | VariableF String
- | BinaryFuncF String a a
- | SymbolicFuncF String [a]
type SimpleExpr = Fix SimpleExprF
type Expr = ListOf SimpleExpr
class ListOf inner outer
content :: ListOf inner outer => outer -> [inner]
dependencies :: SimpleExpr -> [SimpleExpr]
showWithBrackets :: SimpleExpr -> String

Expression manipulation

number :: Integer -> 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

simplify :: 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"
>>> simplify $ (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)

Base types

data SimpleExprF a Source #

Expression F-algebra functional.

Constructors

NumberF Integer
VariableF String
BinaryFuncF String a a
SymbolicFuncF String [a]

Instances

Instances details

Eq1 SimpleExprF Source #
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 #
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 #
Instance details Defined in Debug.SimpleExpr.Expr Methods showsPrec :: Int -> SimpleExpr -> ShowS # show :: SimpleExpr -> String # showList :: [SimpleExpr] -> ShowS #
Additive SimpleExpr Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods (+) :: SimpleExpr -> SimpleExpr -> SimpleExpr # zero :: SimpleExpr #
Subtractive SimpleExpr Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods negate :: SimpleExpr -> SimpleExpr # (-) :: SimpleExpr -> SimpleExpr -> SimpleExpr #
ExpField SimpleExpr Source #
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 #
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 #
Instance details Defined in Debug.SimpleExpr.Expr Methods recip :: SimpleExpr -> SimpleExpr # (/) :: SimpleExpr -> SimpleExpr -> SimpleExpr #
Multiplicative SimpleExpr Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods (*) :: SimpleExpr -> SimpleExpr -> SimpleExpr # one :: SimpleExpr #
Eq a => Eq (SimpleExprF a) Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods (==) :: SimpleExprF a -> SimpleExprF a -> Bool # (/=) :: SimpleExprF a -> SimpleExprF a -> Bool #
FromIntegral (Fix SimpleExprF) Integer Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods fromIntegral :: Integer -> Fix SimpleExprF #
FromIntegral (SimpleExprF a) Integer Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods fromIntegral :: Integer -> SimpleExprF a #

type SimpleExpr = Fix SimpleExprF Source #

Simple expression type, see tutorial

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 #
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: () -> [inner] Source #
ListOf inner inner Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: inner -> [inner] Source #
ListOf inner outer => ListOf inner [outer] Source #
Instance details Defined in Debug.SimpleExpr.Expr Methods content :: [outer] -> [inner] Source #
(ListOf inner outer1, ListOf inner outer2) => ListOf inner (outer1, outer2) Source #
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 #
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 #
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 #
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.