Data.Lambda

Some function-like classes, having lambda-like construction. See LambdaTy for why lambda. See Data.Pair for similar classes.

Make function-like things

type LambdaTy src snk = forall a b. src a -> snk b -> snk (a -> b)

Type of lambda method. Think of src as the bound variable (or pattern) part of a lambda and snk as the expression part. They combine to form a function-typed expression. Instance template:

   instance (Applicative f, Lambda src snk)
     => Lambda (f :. src) (f :. snk) where
       lambda = apLambda

class Lambda src snk where

Type constructor class for function-like things having lambda-like construction.

Methods

lambda

Arguments

:: LambdaTy src snk

Form a function-like value

Instances

Lambda IO OI

Applicative f => Lambda f (:->: f (Const o))

Applicative f => Lambda f (:. (Flip (->) o) f)

Applicative f => Lambda f (:. f (Flip (->) o))

Lambda Id (Flip (->) o)

(Lambda src snk, Lambda dom' ran') => Lambda (:*: src dom') (:*: snk ran')

(Arrow ~>, Unlambda f f', Lambda g g') => Lambda (Arrw ~> f g) (Arrw ~> f' g')

Dissect function-like things

class Unlambda src snk | snk -> src where

Like Unpair, but for functions. Minimal instance definition: either (a) unlambda or (b) both of fsrc and fres.

Methods

unlambda :: snk (a -> b) -> (src a, snk b)

Deconstruct pair-like value

fsrc :: snk (a -> b) -> src a

First part of pair-like value

fres :: snk (a -> b) -> snk b

Second part of pair-like value

Instances

Unlambda Endo Endo

Dual dissections

class Colambda f where

Like Copair, but for functions

Methods

cores :: f b -> f (a -> b)

Instances

Colambda Endo