Safe Haskell | None |
---|---|
Language | Haskell2010 |
Generic and generalized functors.
Synopsis
- gsolomap :: forall a b x y. (Generic x, Generic y, GSolomap a b x y) => (a -> b) -> x -> y
- solomap :: forall a b x y. Solomap a b x y => (a -> b) -> x -> y
- gmultimap :: forall arr x y. (Generic x, Generic y, GMultimap arr x y) => arr -> x -> y
- multimap :: forall arr x y. Multimap arr x y => arr -> x -> y
- data a :+ b = a :+ b
- newtype GenericFunctor f a = GenericFunctor (f a)
- newtype GenericBifunctor f a b = GenericBifunctor (f a b)
- gfmap :: forall f a b. GFunctor f => (a -> b) -> f a -> f b
- gfoldMap :: forall t m a. (GFoldMap m t, Monoid m) => (a -> m) -> t a -> m
- gtraverse :: forall t f a b. (GTraverse f t, Applicative f) => (a -> f b) -> t a -> f (t b)
- gbimap :: forall f a b c d. GBimap f => (a -> b) -> (c -> d) -> f a c -> f b d
- gfirst :: forall f a b c. GFirst f => (a -> b) -> f a c -> f b c
- gsecond :: forall f a c d. GSecond f => (c -> d) -> f a c -> f a d
- gbifoldMap :: forall t m a b. (GBifoldMap m t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
- gbitraverse :: forall t f a b c d. (GBitraverse f t, Applicative f) => (a -> f b) -> (c -> f d) -> t a c -> f (t b d)
- class (forall a. Generic (f a), forall a b. GFunctorRep a b f) => GFunctor f
- class (forall m. Monoid m => GFoldMap m t) => GFoldable t
- class (forall a. Generic (t a), forall a b. GFoldMapRep a b m t) => GFoldMap m t
- class (forall f. Applicative f => GBitraverse f t) => GTraversable t
- class (forall a. Generic (t a), forall a b. GTraverseRep a b f t) => GTraverse f t
- class (GBimap f, GFirst f, GSecond f) => GBifunctor f
- class (forall a c. Generic (f a c), forall a b c d. GBimapRep a b c d f) => GBimap f
- class (forall a c. Generic (f a c), forall a b c. GFirstRep a b c f) => GFirst f
- class (forall a c. Generic (f a c), forall a c d. GFunctorRep c d (f a)) => GSecond f
- class (forall m. Monoid m => GBifoldMap m t) => GBifoldable t
- class (forall a b. Generic (t a b), forall a b c d. GBifoldMapRep a b c d m t) => GBifoldMap m t
- class (forall f. Applicative f => GBitraverse f t) => GBitraversable t
- class (forall a b. Generic (t a b), forall a b c d. GBitraverseRep a b c d f t) => GBitraverse f t
- class GMultimap (a -> b) x y => GSolomap a b x y
- class Multimap (a -> b) x y => Solomap a b x y
- class GMap1 (Default Incoherent arr) (Rep x) (Rep y) => GMultimap arr x y
- class MultimapI (Default Incoherent arr) x y => Multimap arr x y
Derive functors
Unary functors
gsolomap :: forall a b x y. (Generic x, Generic y, GSolomap a b x y) => (a -> b) -> x -> y Source #
Generalized generic functor.
gsolomap
is a generalization of gfmap
(generic fmap
),
where the type parameter to be "mapped" does not have to be the last one.
gsolomap
is unsafe: misuse will break your programs.
Read the Usage section below for details.
Example
{-# LANGUAGE DeriveGeneric #-} import GHC.Generics (Generic
) import Generic.Functor (gsolomap
) data Result a r = Error a | Ok r -- Another name for Either derivingGeneric
mapError :: (a -> b) -> Result a r -> Result b r mapError =gsolomap
mapOk :: (r -> s) -> Result a r -> Result a s mapOk =gsolomap
mapBoth :: (a -> b) -> Result a a -> Result b b mapBoth =gsolomap
Usage
(This also applies to solomap
, gmultimap
, and multimap
.)
gsolomap
should only be used to define polymorphic "fmap
-like functions".
It works only in contexts where a
and b
are two distinct, non-unifiable
type variables. This is usually the case when they are bound by universal
quantification (forall a b. ...
), with no equality constraints on a
and
b
.
The one guarantee of gsolomap
is that
.
Under the above conditions, that law and the types should uniquely determine
the implementation, which gsolomap
id
= id
gsolomap
seeks automatically.
The unsafety is due to the use of incoherent instances as part of the
definition of GSolomap
. Functions are safe to specialize after GSolomap
(and Solomap
) constraints have been discharged.
Note also that the type parameters of gsolomap
must all be determined by
the context. For instance, composing two gsolomap
, as in
, is a type error because the type in the middle
cannot be inferred.gsolomap
f . gsolomap
g
solomap :: forall a b x y. Solomap a b x y => (a -> b) -> x -> y Source #
Generalized implicit functor.
Use this when x
and y
are applications of existing functors
(Functor
, Bifunctor
).
This is a different use case from gfmap
and gsolomap
, which make
functors out of freshly declared data
types.
solomap
is unsafe: misuse will break your programs.
See the Usage section of gsolomap
for details.
Example
map1 :: (a -> b) -> Either e (Maybe [IO a]) -> Either e (Maybe [IO b]) map1 =solomap
-- equivalent to: fmap . fmap . fmap . fmap map2 :: (a -> b) -> (e -> Either [a] r) -> (e -> Either [b] r) map2 =solomap
-- equivalent to: \f -> fmap (bimap (fmap f) id)
N-ary functors
gmultimap :: forall arr x y. (Generic x, Generic y, GMultimap arr x y) => arr -> x -> y Source #
Generic n-ary functor.
A generalization of gsolomap
to map over multiple parameters simultaneously.
gmultimap
takes a list of functions separated by (
and terminated by :+
)()
.
gmultimap
is unsafe: misuse will break your programs.
The type of every function in the list must be some (a -> b)
where a
and b
are distinct type variables.
See the Usage section of gsolomap
for details.
Example
{-# LANGUAGE DeriveGeneric #-} import GHC.Generics (Generic
) import Generic.Functor (gmultimap
) data Three a b c = One a | Two b | Three c derivingGeneric
mapThree :: (a -> a') -> (b -> b') -> (c -> c') -> Three a b c -> Three a' b' c' mapThree f g h =gmultimap
(f:+
g:+
h:+
())
multimap :: forall arr x y. Multimap arr x y => arr -> x -> y Source #
Implicit n-ary functor.
A generalization of solomap
to map over multiple parameters simultaneously.
multimap
takes a list of functions separated by (
and terminated by :+
)()
.
multimap
is unsafe: misuse will break your programs.
The type of every function in the list must be some (a -> b)
where a
and b
are distinct type variables.
See the Usage section of gsolomap
for details.
Example
type F a b c = Either a (b, c) map3 :: (a -> a') -> (b -> b') -> (c -> c') -> F a b c -> F a' b' c' map3 f g h =multimap
(f:+
g:+
h:+
()) -- equivalent to: \f g h -> bimap f (bimap g h)
Heterogeneous lists of arrows are constructed as lists separated by
(
and terminated by :+
)()
.
Example
Given f :: a -> a'
and g :: b -> b'
,
(f
is a list with the two elements :+
g :+
())f
and g
.
if f :: a -> a' g :: b -> b' then f:+
g:+
() :: (a -> a'):+
(b -> b'):+
()
Those lists are used by gmultimap
and multimap
.
bimap_ :: (a -> a') -> (b -> b') -> (Maybe a, [Either b a]) -> (Maybe a', [Either b' a']) bimap_ f g =multimap
(f:+
g:+
())
a :+ b infixr 1 |
Instances
CatLike cat => Multimap_ cat (S arr (Rule AnyId Incoherent :+ arr')) x x Source # | |
Defined in Generic.Functor.Internal.Implicit | |
Multimap_ cat (S arr (cat a b :+ arr')) a b Source # | |
Multimap_ cat (S arr arr') x y => Multimap_ cat (S arr (() :+ arr')) x y Source # | |
Multimap_ cat (S arr arr') x y => Multimap_ cat (S arr (NilArr :+ arr')) x y Source # | |
Multimap_ cat (S arr (arr0 :+ (arr1 :+ arr2))) x y => Multimap_ cat (S arr ((arr0 :+ arr1) :+ arr2)) x y Source # | |
Multimap_ cat (S arr arr') x y => Multimap_ cat (S arr (arr0 :+ arr')) x y Source # | |
(FunctorOf cat f, MultimapOf cat arr x y) => Multimap_ cat (S arr (Rule AnyFunctor Incoherent :+ arr')) (f x) (f y) Source # | |
Defined in Generic.Functor.Internal.Implicit multimap_ :: S arr (Rule AnyFunctor Incoherent :+ arr') -> cat (f x) (f y) Source # | |
(CoercibleKleisli f a b, CoercibleKleisli f arr arr') => CoercibleKleisli f (a :+ arr) (b :+ arr') Source # | |
Defined in Generic.Functor.Internal.Implicit | |
(BifunctorOf cat f, MultimapOf cat arr x1 y1, MultimapOf cat arr x2 y2) => Multimap_ cat (S arr (Rule AnyBifunctor Incoherent :+ arr')) (f x1 x2) (f y1 y2) Source # | |
Defined in Generic.Functor.Internal.Implicit multimap_ :: S arr (Rule AnyBifunctor Incoherent :+ arr') -> cat (f x1 x2) (f y1 y2) Source # | |
(MultimapOf ((->) :: Type -> Type -> Type) arr y1 x1, MultimapOf ((->) :: Type -> Type -> Type) arr x2 y2) => Multimap_ ((->) :: Type -> Type -> Type) (S arr (Rule AnyBifunctor Incoherent :+ arr')) (x1 -> x2) (y1 -> y2) Source # | |
Defined in Generic.Functor.Internal.Implicit multimap_ :: S arr (Rule AnyBifunctor Incoherent :+ arr') -> (x1 -> x2) -> (y1 -> y2) Source # | |
type WrapKleisli f (a :+ arr) Source # | |
Defined in Generic.Functor.Internal.Implicit |
Derive Functor, Bifunctor, Foldable, Traversable
DerivingVia
The type synonyms GenericFunctor
and GenericBifunctor
can be
used with the DerivingVia
extension to derive Functor
, Bifunctor
, and Foldable
.
Sadly, Traversable
cannot be derived-via.
newtype GenericFunctor f a Source #
newtype
for DerivingVia
of Functor
and Foldable
instances.
Note: the GHC extensions DeriveFunctor
, DeriveFoldable
, and DeriveTraversable
(which implies all three) already works out-of-the-box in most cases.
There are exceptions, such as the following example.
Example
{-# LANGUAGE DeriveGeneric, DerivingVia #-} import GHC.Generics (Generic
) import Generic.Functor (GenericFunctor
(..)) data Twice a = Twice (Either a a) derivingGeneric
deriving (Functor
,Foldable
) via (GenericFunctor
Twice)
GenericFunctor (f a) |
Instances
newtype GenericBifunctor f a b Source #
newtype
for DerivingVia
of Bifunctor
and Bifoldable
instances.
Note: deriving Bifunctor
for a generic type often requires Functor
instances for types mentioned in the fields.
Example
{-# LANGUAGE DeriveGeneric, DerivingVia #-} import Data.Bifoldable (Bifoldable
) import Data.Bifunctor (Bifunctor
) import GHC.Generics (Generic
) import Generic.Functor (GenericFunctor
(..),GenericBifunctor
(..)) data Tree a b = Node a (Tree a b) (Tree a b) | Leaf b derivingGeneric
deriving (Functor
,Foldable
) via (GenericFunctor
(Tree a)) deriving (Bifunctor
,Bifoldable
) via (GenericBifunctor
Tree) data CofreeF f a b = a :< f b derivingGeneric
deriving (Bifunctor
,Bifoldable
) via (GenericBifunctor
(CofreeF f))
GenericBifunctor (f a b) |
Instances
GBifoldable f => Bifoldable (GenericBifunctor f) Source # | |
Defined in Generic.Functor.Internal bifold :: Monoid m => GenericBifunctor f m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> GenericBifunctor f a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> GenericBifunctor f a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> GenericBifunctor f a b -> c # | |
GBifunctor f => Bifunctor (GenericBifunctor f) Source # | |
Defined in Generic.Functor.Internal bimap :: (a -> b) -> (c -> d) -> GenericBifunctor f a c -> GenericBifunctor f b d # first :: (a -> b) -> GenericBifunctor f a c -> GenericBifunctor f b c # second :: (b -> c) -> GenericBifunctor f a b -> GenericBifunctor f a c # |
Generic method definitions
gfmap :: forall f a b. GFunctor f => (a -> b) -> f a -> f b Source #
Generic implementation of fmap
. See also GenericFunctor
for DerivingVia
,
using gfmap
under the hood.
Example
{-# LANGUAGE DeriveGeneric #-} import GHC.Generics (Generic
) import Generic.Functor (gfmap
) data Twice a = Twice (Either a a) derivingGeneric
instanceFunctor
Twice wherefmap
=gfmap
gtraverse :: forall t f a b. (GTraverse f t, Applicative f) => (a -> f b) -> t a -> f (t b) Source #
Generic implementation of traverse
from Traversable
.
Bifunctors
gbimap :: forall f a b c d. GBimap f => (a -> b) -> (c -> d) -> f a c -> f b d Source #
Generic implementation of bimap
from Bifunctor
. See also GenericBifunctor
.
gfirst :: forall f a b c. GFirst f => (a -> b) -> f a c -> f b c Source #
Generic implementation of first
from Bifunctor
. See also GenericBifunctor
.
gsecond :: forall f a c d. GSecond f => (c -> d) -> f a c -> f a d Source #
Generic implementation of second
from Bifunctor
. See also GenericBifunctor
.
gbifoldMap :: forall t m a b. (GBifoldMap m t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m Source #
Generic implementation of bifoldMap
from Bifoldable
.
gbitraverse :: forall t f a b c d. (GBitraverse f t, Applicative f) => (a -> f b) -> (c -> f d) -> t a c -> f (t b d) Source #
Generic implementation of bitraverse
from Bitraversable
.
Auxiliary classes
Related to standard classes
class (forall a. Generic (f a), forall a b. GFunctorRep a b f) => GFunctor f Source #
Instances
(forall a. Generic (f a), forall a b. GFunctorRep a b f) => GFunctor f Source # | |
Defined in Generic.Functor.Internal |
class (forall m. Monoid m => GFoldMap m t) => GFoldable t Source #
Generic Foldable
. Constraint for GenericFunctor
(deriving-via Foldable
).
class (forall a. Generic (t a), forall a b. GFoldMapRep a b m t) => GFoldMap m t Source #
Constraint for gfoldMap
.
Instances
(forall a. Generic (t a), forall a b. GFoldMapRep a b m t) => GFoldMap m t Source # | |
Defined in Generic.Functor.Internal |
class (forall f. Applicative f => GBitraverse f t) => GTraversable t Source #
Generic Traversable
.
Instances
(forall (f :: Type -> Type). Applicative f => GBitraverse f t) => GTraversable t Source # | |
Defined in Generic.Functor.Internal |
class (forall a. Generic (t a), forall a b. GTraverseRep a b f t) => GTraverse f t Source #
Constraint for gtraverse
.
Instances
(forall a. Generic (t a), forall a b. GTraverseRep a b f t) => GTraverse f t Source # | |
Defined in Generic.Functor.Internal |
Bifunctors
class (GBimap f, GFirst f, GSecond f) => GBifunctor f Source #
Generic Bifunctor
.
Instances
(GBimap f, GFirst f, GSecond f) => GBifunctor f Source # | |
Defined in Generic.Functor.Internal |
class (forall a c. Generic (f a c), forall a b c d. GBimapRep a b c d f) => GBimap f Source #
Constraint for gbimap
.
class (forall a c. Generic (f a c), forall a b c. GFirstRep a b c f) => GFirst f Source #
Constraint for gfirst
.
class (forall a c. Generic (f a c), forall a c d. GFunctorRep c d (f a)) => GSecond f Source #
Constraint for gsecond
.
Instances
(forall a c. Generic (f a c), forall a c d. GFunctorRep c d (f a)) => GSecond f Source # | |
Defined in Generic.Functor.Internal |
class (forall m. Monoid m => GBifoldMap m t) => GBifoldable t Source #
Generic Foldable
. Constraint for GenericFunctor
(deriving-via Foldable
).
Instances
(forall m. Monoid m => GBifoldMap m t) => GBifoldable t Source # | |
Defined in Generic.Functor.Internal |
class (forall a b. Generic (t a b), forall a b c d. GBifoldMapRep a b c d m t) => GBifoldMap m t Source #
Constraint for gbifoldMap
.
Instances
(forall a b. Generic (t a b), forall a b c d. GBifoldMapRep a b c d m t) => GBifoldMap m t Source # | |
Defined in Generic.Functor.Internal |
class (forall f. Applicative f => GBitraverse f t) => GBitraversable t Source #
Generic Bitraversable
.
Instances
(forall (f :: Type -> Type). Applicative f => GBitraverse f t) => GBitraversable t Source # | |
Defined in Generic.Functor.Internal |
class (forall a b. Generic (t a b), forall a b c d. GBitraverseRep a b c d f t) => GBitraverse f t Source #
Constraint for gtraverse
.
Instances
(forall a b. Generic (t a b), forall a b c d. GBitraverseRep a b c d f t) => GBitraverse f t Source # | |
Defined in Generic.Functor.Internal |
Generalized functors
class GMultimap (a -> b) x y => GSolomap a b x y Source #
Constraint for gsolomap
.
Instances
GMultimap (a -> b) x y => GSolomap a b x y Source # | |
Defined in Generic.Functor.Internal |
class Multimap (a -> b) x y => Solomap a b x y Source #
Constraint for solomap
.
Instances
Multimap (a -> b) x y => Solomap a b x y Source # | |
Defined in Generic.Functor.Internal |
class GMap1 (Default Incoherent arr) (Rep x) (Rep y) => GMultimap arr x y Source #
Constraint for gmultimap
.
Instances
GMap1 (Default Incoherent arr) (Rep x) (Rep y) => GMultimap arr x y Source # | |
Defined in Generic.Functor.Internal |
class MultimapI (Default Incoherent arr) x y => Multimap arr x y Source #
Constraint for multimap
.
Instances
MultimapI (Default Incoherent arr) x y => Multimap arr x y Source # | |
Defined in Generic.Functor.Internal |