Data.Bijection

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

Documentation

data Bijection j a b

A type of bijective arrows

Constructors

Bi

Fields

• biTo :: a `j` b
• biFrom :: b `j` a

Instances

Arrow j => Arrow (Bijection j)

Defined in Data.Bijection

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 :: * -> * -> *)

Defined in Data.Bijection

Methods

id :: Bijection j a a

(.) :: Bijection j b c -> Bijection j a b -> Bijection j a c

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

Bijective functions

idb :: Arrow j => Bijection j a a

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 j a b -> Bijection j b a

Inverse bijection

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

Bijections on functors

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

Bijections on arrows.

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

Apply a function in an alternative (monomorphic) representation.