TypeCompose-0.5: Type composition classes & instances Source code Contents Index

Data.Bijection Portability TypeOperators Stability experimental Maintainer conal@conal.net

Description

Bijections. For a more general setting, see also [1] There and Back Again: Arrows for Invertible Programming, http://citeseer.ist.psu.edu/alimarine05there.html.

Synopsis

data Bijection (~>) a b = Bi { biTo :: a ~> b biFrom :: b ~> a } type :<->: a b = Bijection (->) a b idb :: Arrow ~> => Bijection ~> a a inverse :: Bijection ~> a b -> Bijection ~> b a bimap :: Functor f => (a :<->: b) -> f a :<->: f b (--->) :: Arrow ~> => Bijection ~> a b -> Bijection ~> c d -> (a ~> c) :<->: (b ~> d) inBi :: Arrow ~> => Bijection ~> a b -> (a ~> a) -> b ~> b

Documentation

data Bijection (~>) a b Source

A type of bijective arrows Constructors Bi biTo :: a ~> b biFrom :: b ~> a Instances Arrow ~> => Arrow (Bijection ~>)

type :<->: a b = Bijection (->) a b Source

Bijective functions

idb :: Arrow ~> => Bijection ~> a a Source

Bijective identity arrow. Warning: uses arr on (~>). If you have no arr, but you have a DeepArrow, you can instead use Bi idA idA.

inverse :: Bijection ~> a b -> Bijection ~> b a Source

Inverse bijection

bimap :: Functor f => (a :<->: b) -> f a :<->: f b Source

Bijections on functors

(--->) :: Arrow ~> => Bijection ~> a b -> Bijection ~> c d -> (a ~> c) :<->: (b ~> d) Source

Bijections on arrows.

inBi :: Arrow ~> => Bijection ~> a b -> (a ~> a) -> b ~> b Source

Apply a function in an alternative (monomorphic) representation.

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