Data.Bijection

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

Documentation

A type of bijective arrows

Constructors

Bi
Fields biTo :: a `j` b biFrom :: b `j` a

Instances

Arrow j => Arrow (Bijection j) Source #
Methods arr :: (b -> c) -> Bijection j b c # first :: Bijection j b c -> Bijection j (b, d) (c, d) # second :: Bijection j b c -> Bijection j (d, b) (d, c) # (***) :: Bijection j b c -> Bijection j b' c' -> Bijection j (b, b') (c, c') # (&&&) :: Bijection j b c -> Bijection j b c' -> Bijection j b (c, c') #
Category * j => Category * (Bijection j) Source #
Methods id :: cat a a # (.) :: cat b c -> cat a b -> cat a c #

type (:<->:) a b = Bijection (->) a b infix 8 Source #

Bijective functions

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

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

Bijections on functors

(--->) :: Arrow j => Bijection j a b -> Bijection j c d -> (a `j` c) :<->: (b `j` d) infixr 2 Source #

Bijections on arrows.

inBi :: Arrow j => Bijection j a b -> (a `j` a) -> b `j` b Source #

Apply a function in an alternative (monomorphic) representation.