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.

Minimal complete definition

lambda

Methods

lambda :: LambdaTy src snk

Instances

Lambda IO OI

Methods

lambda :: LambdaTy IO OI

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

Methods

lambda :: LambdaTy f (f :->: Const * o)

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

Methods

lambda :: LambdaTy f (Flip (->) o :. f)

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

Methods

lambda :: LambdaTy f (f :. Flip (->) o)

Lambda Id (Flip (->) o)

Methods

lambda :: LambdaTy Id (Flip (->) o)

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

Methods

lambda :: LambdaTy (src :*: dom') (snk :*: ran')

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

Methods

lambda :: LambdaTy (Arrw j f g) (Arrw j 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

Methods

unlambda :: Endo (a -> b) -> (Endo a, Endo b)

fsrc :: Endo (a -> b) -> Endo a

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

Dual dissections

class Colambda f where

Like Copair, but for functions

Minimal complete definition

cores

Methods

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

Instances

Colambda Endo

Methods

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