Debug.SimpleExpr.Expr

Simple expressions base types and manipulations.

Expression manipulation

number :: Integer -> SimpleExpr

Initializes a single integer number expression.

Examples of usage

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

variable :: String -> SimpleExpr

Initializes a single symbolic variable expression.

Examples of usage

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

unaryFunc :: String -> SimpleExpr -> SimpleExpr

Inituialize unarry function

Examples of usage

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

binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr

Inituialize unarry function

Examples of usage

>>> 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

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

Examples of usage

>>> 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

Minimalistic simplification step.

Examples of usage

>>> 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

Expression F-algebra functional.

Constructors

NumberF Integer

VariableF String

BinaryFuncF String a a

SymbolicFuncF String [a]

Instances

Eq1 SimpleExprF

Defined in Debug.SimpleExpr.Expr

Methods

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

Functor SimpleExprF

Defined in Debug.SimpleExpr.Expr

Methods

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

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

Num SimpleExpr

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

Defined in Debug.SimpleExpr.Expr

Methods

showsPrec :: Int -> SimpleExpr -> ShowS

show :: SimpleExpr -> String

showList :: [SimpleExpr] -> ShowS

Additive SimpleExpr

Defined in Debug.SimpleExpr.Expr

Methods

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

zero :: SimpleExpr

Subtractive SimpleExpr

Defined in Debug.SimpleExpr.Expr

Methods

negate :: SimpleExpr -> SimpleExpr

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

ExpField SimpleExpr

Defined in Debug.SimpleExpr.Expr

Methods

exp :: SimpleExpr -> SimpleExpr

log :: SimpleExpr -> SimpleExpr

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

logBase :: SimpleExpr -> SimpleExpr -> SimpleExpr

sqrt :: SimpleExpr -> SimpleExpr

Field SimpleExpr

Defined in Debug.SimpleExpr.Expr

TrigField SimpleExpr

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

Defined in Debug.SimpleExpr.Expr

Methods

recip :: SimpleExpr -> SimpleExpr

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

Multiplicative SimpleExpr

Defined in Debug.SimpleExpr.Expr

Methods

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

one :: SimpleExpr

Distributive SimpleExpr

Defined in Debug.SimpleExpr.Expr

Eq a => Eq (SimpleExprF a)

Defined in Debug.SimpleExpr.Expr

Methods

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

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

FromIntegral (Fix SimpleExprF) Integer

Defined in Debug.SimpleExpr.Expr

Methods

fromIntegral :: Integer -> Fix SimpleExprF

FromIntegral (SimpleExprF a) Integer

Defined in Debug.SimpleExpr.Expr

Methods

fromIntegral :: Integer -> SimpleExprF a

type SimpleExpr = Fix SimpleExprF

Simple expression type, see tutorial

type Expr = ListOf SimpleExpr

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

Auxiliary functions

class ListOf inner outer

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

>>> 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

ListOf inner ()

Defined in Debug.SimpleExpr.Expr

Methods

content :: () -> [inner]

ListOf inner inner

Defined in Debug.SimpleExpr.Expr

Methods

content :: inner -> [inner]

ListOf inner outer => ListOf inner [outer]

Defined in Debug.SimpleExpr.Expr

Methods

content :: [outer] -> [inner]

(ListOf inner outer1, ListOf inner outer2) => ListOf inner (outer1, outer2)

Defined in Debug.SimpleExpr.Expr

Methods

content :: (outer1, outer2) -> [inner]

(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3) => ListOf inner (outer1, outer2, outer3)

Defined in Debug.SimpleExpr.Expr

Methods

content :: (outer1, outer2, outer3) -> [inner]

(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3, ListOf inner outer4) => ListOf inner (outer1, outer2, outer3, outer4)

Defined in Debug.SimpleExpr.Expr

Methods

content :: (outer1, outer2, outer3, outer4) -> [inner]

(ListOf inner outer1, ListOf inner outer2, ListOf inner outer3, ListOf inner outer4, ListOf inner outer5) => ListOf inner (outer1, outer2, outer3, outer4, outer5)

Defined in Debug.SimpleExpr.Expr

Methods

content :: (outer1, outer2, outer3, outer4, outer5) -> [inner]

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

Returns a list of entities the argument consists of.

dependencies :: SimpleExpr -> [SimpleExpr]

Returns the list of head dependencies of an expression.

Examples of usage

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

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

showWithBrackets :: SimpleExpr -> String

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