Copyright	(c) 2014 Justus Sagemüller
License	GPL v3 (see COPYING)
Maintainer	(@) jsag $ hvl.no
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Functor.Constrained

Contents

Functors
[Co]product mapping

Description

Synopsis

class (Category r, Category t) => Functor (f :: Type -> Type) (r :: Type -> Type -> Type) (t :: Type -> Type -> Type) | f r -> t, f t -> r where
- fmap :: (Object r a, Object t (f a), Object r b, Object t (f b)) => r a b -> t (f a) (f b)
(<$>) :: (Functor f r (->), Object r a, Object r b) => r a b -> f a -> f b
constrainedFmap :: forall r t (o :: Type -> Constraint) a b f. (Category r, Category t, o a, o b, o (f a), o (f b)) => (r a b -> t (f a) (f b)) -> (o ⊢ r) a b -> (o ⊢ t) (f a) (f b)
class (CoCartesian r, Cartesian t, Functor f r t, Object t (f (ZeroObject r))) => SumToProduct (f :: Type -> Type) (r :: Type -> Type -> Type) (t :: Type -> Type -> Type) where
- sum2product :: (ObjectSum r a b, ObjectPair t (f a) (f b)) => t (f (a + b)) (f a, f b)
- mapEither :: (Object r a, ObjectSum r b c, Object t (f a), ObjectPair t (f b) (f c)) => r a (b + c) -> t (f a) (f b, f c)
- filter :: (Object r a, Object r Bool, Object t (f a)) => r a Bool -> t (f a) (f a)

Functors

class (Category r, Category t) => Functor (f :: Type -> Type) (r :: Type -> Type -> Type) (t :: Type -> Type -> Type) | f r -> t, f t -> r where Source #

Methods

fmap :: (Object r a, Object t (f a), Object r b, Object t (f b)) => r a b -> t (f a) (f b) Source #

Instances

Instances details

Functor Complex (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a, Object (Discrete :: Type -> Type -> Type) (Complex a), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (Complex b)) => Discrete a b -> Discrete (Complex a) (Complex b) Source #
Functor Complex (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a, Object (Coercion :: Type -> Type -> Type) (Complex a), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (Complex b)) => Coercion a b -> Coercion (Complex a) (Complex b) Source #
Functor IO (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a, Object (Discrete :: Type -> Type -> Type) (IO a), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (IO b)) => Discrete a b -> Discrete (IO a) (IO b) Source #
Functor IO (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a, Object (Coercion :: Type -> Type -> Type) (IO a), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (IO b)) => Coercion a b -> Coercion (IO a) (IO b) Source #
Functor Maybe (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a, Object (Discrete :: Type -> Type -> Type) (Maybe a), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (Maybe b)) => Discrete a b -> Discrete (Maybe a) (Maybe b) Source #
Functor Maybe (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a, Object (Coercion :: Type -> Type -> Type) (Maybe a), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (Maybe b)) => Coercion a b -> Coercion (Maybe a) (Maybe b) Source #
Functor [] (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a, Object (Discrete :: Type -> Type -> Type) [a], Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) [b]) => Discrete a b -> Discrete [a] [b] Source #
Functor [] (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a, Object (Coercion :: Type -> Type -> Type) [a], Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) [b]) => Coercion a b -> Coercion [a] [b] Source #
Functor [] k k => Functor [] (o ⊢ k) (o ⊢ k) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (o ⊢ k) a, Object (o ⊢ k) [a], Object (o ⊢ k) b, Object (o ⊢ k) [b]) => (o ⊢ k) a b -> (o ⊢ k) [a] [b] Source #
Functor f => Functor f (->) (->) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (->) a, Object (->) (f a), Object (->) b, Object (->) (f b)) => (a -> b) -> f a -> f b Source #
Functor (Either a) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a0, Object (Discrete :: Type -> Type -> Type) (Either a a0), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (Either a b)) => Discrete a0 b -> Discrete (Either a a0) (Either a b) Source #
Functor (Either a) (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a0, Object (Coercion :: Type -> Type -> Type) (Either a a0), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (Either a b)) => Coercion a0 b -> Coercion (Either a a0) (Either a b) Source #
Functor ((,) a) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a0, Object (Discrete :: Type -> Type -> Type) (a, a0), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (a, b)) => Discrete a0 b -> Discrete (a, a0) (a, b) Source #
Functor ((,) a) (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a0, Object (Coercion :: Type -> Type -> Type) (a, a0), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (a, b)) => Coercion a0 b -> Coercion (a, a0) (a, b) Source #
Functor ((->) a) (Discrete :: Type -> Type -> Type) (Discrete :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Discrete :: Type -> Type -> Type) a0, Object (Discrete :: Type -> Type -> Type) (a -> a0), Object (Discrete :: Type -> Type -> Type) b, Object (Discrete :: Type -> Type -> Type) (a -> b)) => Discrete a0 b -> Discrete (a -> a0) (a -> b) Source #
Functor ((->) a) (Coercion :: Type -> Type -> Type) (Coercion :: Type -> Type -> Type) Source #
Instance details Defined in Control.Functor.Constrained Methods fmap :: (Object (Coercion :: Type -> Type -> Type) a0, Object (Coercion :: Type -> Type -> Type) (a -> a0), Object (Coercion :: Type -> Type -> Type) b, Object (Coercion :: Type -> Type -> Type) (a -> b)) => Coercion a0 b -> Coercion (a -> a0) (a -> b) Source #

(<$>) :: (Functor f r (->), Object r a, Object r b) => r a b -> f a -> f b infixl 4 Source #

constrainedFmap :: forall r t (o :: Type -> Constraint) a b f. (Category r, Category t, o a, o b, o (f a), o (f b)) => (r a b -> t (f a) (f b)) -> (o ⊢ r) a b -> (o ⊢ t) (f a) (f b) Source #

[Co]product mapping

class (CoCartesian r, Cartesian t, Functor f r t, Object t (f (ZeroObject r))) => SumToProduct (f :: Type -> Type) (r :: Type -> Type -> Type) (t :: Type -> Type -> Type) where Source #

It is fairly common for functors (typically, container-like) to map Either to tuples in a natural way, thus "separating the variants". This is related to Foldable (with list and tuple monoids), but rather more effective.

Methods

sum2product :: (ObjectSum r a b, ObjectPair t (f a) (f b)) => t (f (a + b)) (f a, f b) Source #

  sum2product ≡ mapEither id

mapEither :: (Object r a, ObjectSum r b c, Object t (f a), ObjectPair t (f b) (f c)) => r a (b + c) -> t (f a) (f b, f c) Source #

  mapEither f ≡ sum2product . fmap f

filter :: (Object r a, Object r Bool, Object t (f a)) => r a Bool -> t (f a) (f a) Source #

Instances

Instances details

(o (), o Void, o [Void]) => SumToProduct [] (o ⊢ (->)) (o ⊢ (->)) Source #
Instance details Defined in Control.Functor.Constrained Methods sum2product :: (ObjectSum (o ⊢ (->)) a b, ObjectPair (o ⊢ (->)) [a] [b]) => (o ⊢ (->)) [a + b] ([a], [b]) Source # mapEither :: (Object (o ⊢ (->)) a, ObjectSum (o ⊢ (->)) b c, Object (o ⊢ (->)) [a], ObjectPair (o ⊢ (->)) [b] [c]) => (o ⊢ (->)) a (b + c) -> (o ⊢ (->)) [a] ([b], [c]) Source # filter :: (Object (o ⊢ (->)) a, Object (o ⊢ (->)) Bool, Object (o ⊢ (->)) [a]) => (o ⊢ (->)) a Bool -> (o ⊢ (->)) [a] [a] Source #
SumToProduct [] (->) (->) Source #
Instance details Defined in Control.Functor.Constrained Methods sum2product :: (ObjectSum (->) a b, ObjectPair (->) [a] [b]) => [a + b] -> ([a], [b]) Source # mapEither :: (Object (->) a, ObjectSum (->) b c, Object (->) [a], ObjectPair (->) [b] [c]) => (a -> (b + c)) -> [a] -> ([b], [c]) Source # filter :: (Object (->) a, Object (->) Bool, Object (->) [a]) => (a -> Bool) -> [a] -> [a] Source #