Documentation

class Category f => Function f whereSource

($*) :: Function f => f a b -> a -> bSource

class Function f => Increasing f Source

data Increasing' a b Source

type :>>= a b = Increasing' a bSource

uncheckedIncreasing :: (a -> b) -> Increasing' a bSource

class Increasing f => StrictlyIncreasing f Source

data StrictlyIncreasing' a b Source

type :>> a b = StrictlyIncreasing' a bSource

uncheckedStrictlyIncreasing :: (a -> b) -> StrictlyIncreasing' a bSource

class Function f => InjectionA f whereSource

data InjectionA' a b Source

uncheckedInjectionA :: (a -> b) -> (b -> Maybe a) -> InjectionA' a bSource

injectionA' :: InjectionA f => f a b -> InjectionA' a bSource

class InjectionA f => Injection f whereSource

data Injection' a b Source

uncheckedInjection :: (a -> b) -> (b -> a) -> Injection' a bSource

injection' :: Injection f => f a b -> Injection' a bSource

pairInjection :: (Injection f1, Injection f2) => f1 a1 b1 -> f2 a2 b2 -> Injection' (a1, a2) (b1, b2)Source

class InjectionA f => InjectionM f Source

data InjectionM' a b Source

uncheckedInjectionM :: (a -> b) -> (b -> Maybe a) -> InjectionM' a bSource

injectionM' :: InjectionM f => f a b -> InjectionM' a bSource

class (Injection f, InjectionM f) => Bijection f Source

data Bijection' a b Source

uncheckedBijection :: (a -> b) -> (b -> a) -> Bijection' a bSource

pairBijection :: (Bijection f1, Bijection f2) => f1 a1 b1 -> f2 a2 b2 -> Bijection' (a1, a2) (b1, b2)Source

inv :: Bijection f => f a b -> Bijection' b aSource

liftAB :: (Bijection g, Applicative f) => g a b -> Bijection' (f a) (f b)Source

class InjectionACofunctor f whereSource

class InjectionCofunctor f whereSource

class InjectionMCofunctor f whereSource

class ExpFunctor f whereSource

class IncreasingFunctor f whereSource

class StrictlyIncreasingFunctor f whereSource

class Cofunctor f whereSource

functorCofunctorComap :: (Functor f, Cofunctor c) => Compose f c b -> (a -> b) -> Compose f c aSource

class Comonoidal f whereSource

functorIacomap :: (Functor f, InjectionA g) => f b -> g a b -> f aSource

cofunctorIacomap :: (Cofunctor f, InjectionA g) => f b -> g a b -> f aSource

newtype RevFun b a Source

type :<- = RevFunSource

wrapU :: (Bijection og, Function i1g) => og o o' -> i1g i1 i1' -> (i1' -> o') -> i1 -> oSource

wrapB :: (Bijection og, Function i1g, Function i2g) => og o o' -> i1g i1 i1' -> i2g i2 i2' -> (i1' -> i2' -> o') -> i1 -> i2 -> oSource

liftItI :: Injection f => f a b -> (b -> b) -> a -> aSource

liftIItK :: Function f => f a a' -> (a' -> a' -> b) -> a -> a -> bSource

liftIItI :: Injection f => f a2 a' -> (a' -> a' -> a') -> a2 -> a2 -> a2Source

liftIKtI :: Injection f => f a1 a' -> (a' -> a -> a') -> a1 -> a -> a1Source

liftIItII :: Injection f => f a2 a' -> (a' -> a' -> (a', a')) -> a2 -> a2 -> (a2, a2)Source