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)
  deriving Generic

instance Functor Twice where
  fmap = gfmap

Unlike gsolomap, gfmap is safe to use in all contexts.

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
  deriving Generic

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 gsolomap id = id. Under the above conditions, that law and the types should uniquely determine the implementation, which 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 gsolomap f . gsolomap g, is a type error because the type in the middle cannot be inferred.

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)

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
  deriving Generic

mapThree :: (a -> a') -> (b -> b') -> (c -> c') -> Three a b c -> Three a' b' c'
mapThree f g h = gmultimap (f :+ g :+ h :+ ())

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)

Generic implementation of bimap from Bifunctor. See also GenericBifunctor.

Generic implementation of first from Bifunctor. See also GenericBifunctor.

Generic implementation of second from Bifunctor. See also GenericBifunctor.

Generic implementation of foldMap from Foldable.

Generic implementation of bifoldMap from Bifoldable.

Generic implementation of traverse from Traversable.

Generic implementation of bitraverse from Bitraversable.

Explicitly require a constraint, to force the instantiation of a quantified constraint.

Generic Functor. Constraint for gfmap.

Internal component of GFunctor.

This is an example of the "quantified constraints trick" to encode forall a b. GMap1 a b (Rep (f a)) (Rep (f b)) which doesn't actually work as-is.

Constraint for gbimap.

Internal component of GBifunctor.

Constraint for gfirst.

Internal component of GFirst.

Constraint for gsecond.

Generic Bifunctor.

Constraint for gtraverse.

Generic Traversable.

Constraint for gtraverse.

Generic Bitraversable.

Constraint for gfoldMap.

Generic Foldable. Constraint for GenericFunctor (deriving-via Foldable).

Constraint for gbifoldMap.

Generic Foldable. Constraint for GenericFunctor (deriving-via Foldable).

Constraint for gsolomap.

Constraint for solomap.

Constraint for gmultimap.

Constraint for multimap.

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)
  deriving Generic
  deriving (Functor, Foldable) via (GenericFunctor Twice)

newtype for DerivingVia of Bifunctor and Bifoldable instances.

Note: although GenericBifunctor has Functor and Foldable instances, it is recommended to use GenericFunctor instead for those two classes. They have to use a separate deriving clause from Bifunctor and Bifoldable anyway. Those instances exist because they are to become superclasses of Bifunctor and Bifoldable. The Foldable instance of GenericBifunctor is also less efficient than GenericFunctor unless the extra const mempty gets optimized away.

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
  deriving Generic
  deriving (Functor, Foldable) via (GenericFunctor (Tree a))
  deriving (Bifunctor, Bifoldable) via (GenericBifunctor Tree)

data CofreeF f a b = a :< f b
  deriving Generic
  deriving (Bifunctor, Bifoldable) via (GenericBifunctor (CofreeF f))

We use the same class to implement all of fmap, foldMap, traverse, instantiating m as Identity, 'Const (EndoM mm)' and 'Aps n' respectively. Those three cases differ in their instances for K1.

(the K stands for Kleisli, because the result is Kleisli m (f ()) (g ())

Danger! GFoldMap1 m arr f f MUST come from a quantified constraint (see use in gfoldMap).