| 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-Inferred |
| Language | Haskell2010 |
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
- invmapProfunctor :: Profunctor p => (a -> b) -> (b -> a) -> p a a -> p b b
- invmapArrow :: Arrow arr => (a -> b) -> (b -> a) -> arr a a -> arr b b
-
newtype
WrappedContravariant
f a =
WrapContravariant
{
- unwrapContravariant :: f a
- newtype InvariantProfunctor p a = InvariantProfunctor (p a a)
- newtype InvariantArrow c a = InvariantArrow (c a 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) =
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
class Invariant f where Source #
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
Instances
invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b Source #
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 Source #
A generic implementation of
invmap
.
newtype WrappedFunctor f a Source #
Constructors
| WrapFunctor | |
|
Fields
|
|
Instances
invmapContravariant :: Contravariant f => (a -> b) -> (b -> a) -> f a -> f b Source #
Every
Contravariant
functor is also an
Invariant
functor.
invmapProfunctor :: Profunctor p => (a -> b) -> (b -> a) -> p a a -> p b b Source #
A
Profunctor
with the same input and output types can be seen as an
Invariant
functor.
invmapArrow :: Arrow arr => (a -> b) -> (b -> a) -> arr a a -> arr b b Source #
newtype WrappedContravariant f a Source #
Wrap a
Contravariant
functor to be used as a member of
Invariant
.
Constructors
| WrapContravariant | |
|
Fields
|
|
Instances
newtype InvariantProfunctor p a Source #
A
Profunctor
with the same input and output types can be seen as an
Invariant
functor.
Constructors
| InvariantProfunctor (p a a) |
Instances
| Profunctor p => Invariant ( InvariantProfunctor p) Source # | |
|
Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantProfunctor p a -> InvariantProfunctor p b Source # |
|
newtype InvariantArrow c a Source #
Constructors
| InvariantArrow (c a a) |
Instances
| Arrow c => Invariant ( InvariantArrow c) Source # | |
|
Defined in Data.Functor.Invariant Methods invmap :: (a -> b) -> (b -> a) -> InvariantArrow c a -> InvariantArrow c b Source # |
|
Invariant2
class Invariant2 f where Source #
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 Source # | |
| Invariant2 (,) Source # | |
|
Defined in Data.Functor.Invariant |
|
| Invariant2 Op Source # |
from the
|
| Invariant2 Arg Source # |
from Data.Semigroup |
| Invariant2 ( (,,) a) Source # | |
|
Defined in Data.Functor.Invariant |
|
| Arrow arr => Invariant2 ( WrappedArrow arr) Source # |
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 Source # |
|
| Invariant m => Invariant2 ( Kleisli m) Source # |
from Control.Arrow |
| Invariant2 ( Const :: Type -> Type -> Type ) Source # |
from Control.Applicative |
| Invariant2 ( Yoneda p) Source # |
from the
|
| Invariant2 ( Coyoneda p) Source # |
from the
|
| Invariant2 p => Invariant2 ( CofreeMapping p) Source # |
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 Source # |
|
| Invariant2 ( FreeMapping p) Source # |
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 Source # |
|
| Invariant2 p => Invariant2 ( CofreeTraversing p) Source # |
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 Source # |
|
| Invariant2 ( FreeTraversing p) Source # |
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 Source # |
|
| Invariant2 p => Invariant2 ( TambaraSum p) Source # |
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 Source # |
|
| Invariant2 ( PastroSum p) Source # |
from the
|
| Invariant2 ( CotambaraSum p) Source # |
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 Source # |
|
| Invariant2 ( CopastroSum p) Source # |
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 Source # |
|
| Invariant2 p => Invariant2 ( Closure p) Source # |
from the
|
| Invariant2 ( Environment p) Source # |
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 Source # |
|
| Invariant2 p => Invariant2 ( Tambara p) Source # |
from the
|
| Invariant2 ( Pastro p) Source # |
from the
|
| Invariant2 ( Cotambara p) Source # |
from the
|
| Invariant2 ( Copastro p) Source # |
from the
|
| Invariant2 ( Tagged :: Type -> Type -> Type ) Source # |
from the
|
| Invariant2 ( Constant :: Type -> Type -> Type ) Source # |
from the
|
| Invariant2 ((->) :: Type -> Type -> Type ) Source # | |
|
Defined in Data.Functor.Invariant |
|
| Invariant2 ( K1 i :: Type -> Type -> Type ) Source # |
from GHC.Generics |
| Invariant2 ( (,,,) a b) Source # | |
|
Defined in Data.Functor.Invariant |
|
| Invariant w => Invariant2 ( Cokleisli w) Source # |
from the
|
| Invariant f => Invariant2 ( Star f) Source # |
from the
|
| Invariant f => Invariant2 ( Costar f) Source # |
from the
|
| Invariant2 ( Forget r :: Type -> Type -> Type ) Source # |
from the
|
| Invariant2 ( (,,,,) a b c) Source # | |
|
Defined in Data.Functor.Invariant |
|
| Bifunctor p => Invariant2 ( WrappedBifunctor p) Source # |
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 Source # |
|
| Invariant g => Invariant2 ( Joker g :: Type -> Type -> Type ) Source # |
from the
|
| Invariant2 p => Invariant2 ( Flip p) Source # |
from the
|
| Invariant f => Invariant2 ( Clown f :: Type -> Type -> Type ) Source # |
from the
|
| Invariant2 p => Invariant2 ( Codensity p) Source # |
from the
|
| Arrow arr => Invariant2 ( WrappedArrow arr) Source # |
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 Source # |
|
| Profunctor p => Invariant2 ( WrappedProfunctor p) Source # | |
|
Defined in Data.Functor.Invariant Methods invmap2 :: (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> WrappedProfunctor p a b -> WrappedProfunctor p c d Source # |
|
| ( Invariant2 p, Invariant2 q) => Invariant2 ( Sum p q) Source # |
from the
|
| ( Invariant2 f, Invariant2 g) => Invariant2 ( Product f g) Source # |
from the
|
| ( Invariant f, Invariant2 p) => Invariant2 ( Tannen f p) Source # |
from the
|
| ( Invariant f, Invariant2 p) => Invariant2 ( Cayley f p) Source # |
from the
|
| ( Invariant2 p, Invariant2 q) => Invariant2 ( Ran p q) Source # |
from the
|
| ( Invariant2 p, Invariant2 q) => Invariant2 ( Procompose p q) Source # |
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 Source # |
|
| ( Invariant2 p, Invariant2 q) => Invariant2 ( Rift p q) Source # |
from the
|
| ( Invariant2 p, Invariant f, Invariant g) => Invariant2 ( Biff p f g) Source # |
from the
|
invmap2Bifunctor :: Bifunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d Source #
Every
Bifunctor
is also an
Invariant2
functor.
newtype WrappedBifunctor (p :: k -> k1 -> Type ) (a :: k) (b :: k1) Source #
Constructors
| WrapBifunctor | |
|
Fields
|
|
Instances
invmap2Profunctor :: Profunctor f => (a -> c) -> (c -> a) -> (b -> d) -> (d -> b) -> f a b -> f c d Source #
Every
Profunctor
is also an
Invariant2
functor.
newtype WrappedProfunctor p a b Source #
Wrap a
Profunctor
to be used as a member of
Invariant2
.
Constructors
| WrapProfunctor | |
|
Fields
|
|