Control.Invertible.BiArrow.Free

Documentation

data FreeA p a b

Constructors

PureP (a <-> b)

(p a x) :- (FreeA p x b) infixr 9

Instances

IsoProfunctor p => Category * (FreeA p)

Methods

id :: cat a a

(.) :: cat b c -> cat a b -> cat a c

(IsoProfunctor p, Groupoid * p) => Groupoid * (FreeA p)

Methods

inv :: k1 a b -> k1 b a

IsoProfunctor p => Semigroupoid * (FreeA p)

Methods

o :: c j k1 -> c i j -> c i k1

(IsoProfunctor p, Groupoid * p) => BiArrow (FreeA p)

Methods

(<->) :: (b -> c) -> (c -> b) -> FreeA p b c

invert :: FreeA p b c -> FreeA p c b

IsoProfunctor b => IsoProfunctor (FreeA b)

Methods

dimap :: (a <-> b) -> (c <-> d) -> FreeA b b c -> FreeA b a d

lmap :: (a <-> b) -> FreeA b b c -> FreeA b a c

rmap :: (b <-> c) -> FreeA b a b -> FreeA b a c

IsoStrong p => IsoStrong (FreeA p)

Methods

first' :: FreeA p a b -> FreeA p (a, c) (b, c)

second' :: FreeA p a b -> FreeA p (c, a) (c, b)

nil :: IsoProfunctor p => FreeA p a a

revinv :: (IsoProfunctor p, Groupoid p) => (forall x y. p x y -> p y x) -> FreeA p a b -> FreeA p b a

go :: IsoProfunctor p => (forall x y. p x y -> p y x) -> FreeA p x d -> FreeA p x c -> FreeA p d c