| Copyright | (C) 2012-2017 Nicolas Frisby (C) 2015-2017 Ryan Scott |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Ryan Scott |
| Portability | Portable |
| Safe Haskell | Safe |
| Language | Haskell98 |
Data.Functor.Invariant
Contents
Description
Haskell98 invariant functors (also known as exponential functors).
For more information, see Edward Kmett's article "Rotten Bananas":
Synopsis
- class Invariant f where
- invmap :: (a -> b) -> (b -> a) -> f a -> f b
- invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b
- genericInvmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b
- newtype WrappedFunctor f a = WrapFunctor {
- unwrapFunctor :: f a
- invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b
- newtype WrappedContravariant f a = WrapContravariant {
- unwrapContravariant :: f a
- class Invariant2 f where
- invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
- invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
- newtype WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) :: forall k k1. (k -> k1 -> Type) -> k -> k1 -> Type = WrapBifunctor {
- unwrapBifunctor :: p a b
- invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d
- newtype WrappedProfunctor p a b = WrapProfunctor {
- unwrapProfunctor :: p a b
Invariant
Any * -> * type parametric in the argument permits an instance of
Invariant.
Instances should satisfy the following laws:
invmap id id = id invmap f2 f2' . invmap f1 f1' = invmap (f2 . f1) (f1' . f2')
Minimal complete definition
Nothing
Methods
invmap :: (a -> b) -> (b -> a) -> f a -> f b #
invmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b #
Instances
invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b #
GHC.Generics
With GHC 7.2 or later, Invariant instances can be defined easily using GHC
generics like so:
{-# LANGUAGE DeriveGeneric, FlexibleContexts #-}
import Data.Functor.Invariant
import GHC.Generics
data T f a = T (f a) deriving Generic1
instance Invariant f => Invariant (T f)
Be aware that generic Invariant instances cannot be derived for data types
that have function arguments in which the last type parameter appears in a
position other than the result type (e.g., data Fun a = Fun (a -> a)). For
these, you can derive them using the Data.Functor.Invariant.TH module.
genericInvmap :: (Generic1 f, Invariant (Rep1 f)) => (a -> b) -> (b -> a) -> f a -> f b #
A generic implementation of invmap.
newtype WrappedFunctor f a #
Constructors
| WrapFunctor | |
Fields
| |
Instances
invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b #
Every Contravariant functor is also an Invariant functor.
newtype WrappedContravariant f a #
Wrap a Contravariant functor to be used as a member of Invariant.
Constructors
| WrapContravariant | |
Fields
| |
Instances
Invariant2
class Invariant2 f where #
Any * -> * -> * type parametric in both arguments permits an instance of
Invariant2.
Instances should satisfy the following laws:
invmap2 id id id id = id invmap2 f2 f2' g2 g2' . invmap2 f1 f1' g1 g1' = invmap2 (f2 . f1) (f1' . f2') (g2 . g1) (g1' . g2')
Instances
| Invariant2 Either # | |
Defined in Data.Functor.Invariant | |
| Invariant2 (,) # | |
Defined in Data.Functor.Invariant | |
| Invariant2 Op # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 Arg # | from Data.Semigroup |
Defined in Data.Functor.Invariant | |
| Invariant2 ((,,) a) # | |
Defined in Data.Functor.Invariant | |
| Arrow arr => Invariant2 (WrappedArrow arr) # | from Control.Applicative |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d # | |
| Monad m => Invariant2 (Kleisli m) # | from Control.Arrow |
Defined in Data.Functor.Invariant | |
| Invariant2 (Const :: Type -> Type -> Type) # | from Control.Applicative |
Defined in Data.Functor.Invariant | |
| Invariant2 (Yoneda p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 p => Invariant2 (Codensity p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 p => Invariant2 (CofreeMapping p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeMapping p a b -> CofreeMapping p c d # | |
| Invariant2 (FreeMapping p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeMapping p a b -> FreeMapping p c d # | |
| Invariant2 p => Invariant2 (CofreeTraversing p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CofreeTraversing p a b -> CofreeTraversing p c d # | |
| Invariant2 (FreeTraversing p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> FreeTraversing p a b -> FreeTraversing p c d # | |
| Invariant2 p => Invariant2 (TambaraSum p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> TambaraSum p a b -> TambaraSum p c d # | |
| Invariant2 (PastroSum p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (CotambaraSum p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CotambaraSum p a b -> CotambaraSum p c d # | |
| Invariant2 (CopastroSum p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> CopastroSum p a b -> CopastroSum p c d # | |
| Invariant2 p => Invariant2 (Closure p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (Environment p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Environment p a b -> Environment p c d # | |
| Invariant2 p => Invariant2 (Tambara p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (Pastro p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (Cotambara p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant f => Invariant2 (Star f) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant f => Invariant2 (Costar f) # | from the |
Defined in Data.Functor.Invariant | |
| Arrow arr => Invariant2 (WrappedArrow arr) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedArrow arr a b -> WrappedArrow arr c d # | |
| Invariant2 (Forget r) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (Tagged :: Type -> Type -> Type) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 (Constant :: Type -> Type -> Type) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 ((->) :: Type -> Type -> Type) # | |
Defined in Data.Functor.Invariant | |
| Invariant2 (K1 i :: Type -> Type -> Type) # | from GHC.Generics |
Defined in Data.Functor.Invariant | |
| Invariant2 ((,,,) a b) # | |
Defined in Data.Functor.Invariant | |
| Comonad w => Invariant2 (Cokleisli w) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant f, Invariant2 p) => Invariant2 (Cayley f p) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant2 p, Invariant2 q) => Invariant2 (Ran p q) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant2 p, Invariant2 q) => Invariant2 (Procompose p q) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> Procompose p q a b -> Procompose p q c d # | |
| (Invariant2 p, Invariant2 q) => Invariant2 (Rift p q) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 ((,,,,) a b c) # | |
Defined in Data.Functor.Invariant | |
| Bifunctor p => Invariant2 (WrappedBifunctor p) # | from the |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedBifunctor p a b -> WrappedBifunctor p c d # | |
| Invariant g => Invariant2 (Joker g :: Type -> Type -> Type) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant2 p => Invariant2 (Flip p) # | from the |
Defined in Data.Functor.Invariant | |
| Invariant f => Invariant2 (Clown f :: Type -> Type -> Type) # | from the |
Defined in Data.Functor.Invariant | |
| Profunctor p => Invariant2 (WrappedProfunctor p) # | |
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d # | |
| (Invariant2 p, Invariant2 q) => Invariant2 (Sum p q) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant2 f, Invariant2 g) => Invariant2 (Product f g) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant f, Invariant2 p) => Invariant2 (Tannen f p) # | from the |
Defined in Data.Functor.Invariant | |
| (Invariant2 p, Invariant f, Invariant g) => Invariant2 (Biff p f g) # | from the |
Defined in Data.Functor.Invariant | |
invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d #
Every Bifunctor is also an Invariant2 functor.
newtype WrappedBifunctor (p :: k -> k1 -> Type) (a :: k) (b :: k1) :: forall k k1. (k -> k1 -> Type) -> k -> k1 -> Type #
Constructors
| WrapBifunctor | |
Fields
| |
Instances
invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d #
Every Profunctor is also an Invariant2 functor.
newtype WrappedProfunctor p a b #
Wrap a Profunctor to be used as a member of Invariant2.
Constructors
| WrapProfunctor | |
Fields
| |