Generics.OneLiner

All functions without postfix are for instances of Generic, and functions with postfix 1 are for instances of Generic1 (with kind * -> *) which get an extra argument to specify how to deal with the parameter. Functions with postfix 01 are also for Generic1 but they get yet another argument that, like the Generic functions, allows handling of constant leaves. The function createA_ does not require any such instance, but must be given a constructor explicitly.

Producing values

create :: forall c t. (ADT t, Constraints t c) => (forall s. c s => [s]) -> [t]

Create a value (one for each constructor), given how to construct the components.

minBound = head $ create @Bounded [minBound]
maxBound = last $ create @Bounded [maxBound]

create is createA specialized to lists.

createA :: forall c t f. (ADT t, Constraints t c, Alternative f) => (forall s. c s => f s) -> f t

Create a value (one for each constructor), given how to construct the components, under an applicative effect.

Here's how to implement get from the binary package, first encoding the constructor in a byte:

get = getWord8 >>= \ix -> getCompose (createA @Binary (Compose [get])) !! fromEnum ix

createA is generic specialized to Joker.

ctorIndex :: ADT t => t -> Int

Get the index in the lists returned by create and createA of the constructor of the given value.

For example, this is the implementation of put that generates the binary data that the above implentation of get expects:

put t = putWord8 (toEnum (ctorIndex t)) <> gfoldMap @Binary put t

create1 :: forall c t a. (ADT1 t, Constraints1 t c) => (forall b s. c s => [b] -> [s b]) -> [a] -> [t a]

create1 is createA1 specialized to lists.

createA1 :: forall c t f a. (ADT1 t, Constraints1 t c, Alternative f) => (forall b s. c s => f b -> f (s b)) -> f a -> f (t a)

createA1 is generic1 specialized to Joker.

ctorIndex1 :: ADT1 t => t a -> Int

createA_ :: forall c t f. (FunConstraints c t, Applicative f) => (forall s. c s => f s) -> t -> f (FunResult t)

Create a value, given a constructor (or a function) and how to construct its components, under an applicative effect.

For example, this is the implementation of arbitrary for a type with a single constructor (e.g., quadruples (,,,)).

arbitrary = createA_ @Arbitrary arbitrary (,,,)

Traversing values

gmap :: forall c t. (ADT t, Constraints t c) => (forall s. c s => s -> s) -> t -> t

Map over a structure, updating each component.

gmap is generic specialized to (->).

gfoldMap :: forall c t m. (ADT t, Constraints t c, Monoid m) => (forall s. c s => s -> m) -> t -> m

Map each component of a structure to a monoid, and combine the results.

If you have a class Size, which measures the size of a structure, then this could be the default implementation:

size = succ . getSum . gfoldMap @Size (Sum . size)

gfoldMap is gtraverse specialized to Const.

gtraverse :: forall c t f. (ADT t, Constraints t c, Applicative f) => (forall s. c s => s -> f s) -> t -> f t

Map each component of a structure to an action, evaluate these actions from left to right, and collect the results.

gtraverse is generic specialized to Star.

gmap1 :: forall c t a b. (ADT1 t, Constraints1 t c) => (forall d e s. c s => (d -> e) -> s d -> s e) -> (a -> b) -> t a -> t b

fmap = gmap1 @Functor fmap

gmap1 is generic1 specialized to (->).

gfoldMap1 :: forall c t m a. (ADT1 t, Constraints1 t c, Monoid m) => (forall s b. c s => (b -> m) -> s b -> m) -> (a -> m) -> t a -> m

foldMap = gfoldMap1 @Foldable foldMap

gfoldMap1 is gtraverse1 specialized to Const.

gtraverse1 :: forall c t f a b. (ADT1 t, Constraints1 t c, Applicative f) => (forall d e s. c s => (d -> f e) -> s d -> f (s e)) -> (a -> f b) -> t a -> f (t b)

traverse = gtraverse1 @Traversable traverse

gtraverse1 is generic1 specialized to Star.

Combining values

mzipWith :: forall c t m. (ADT t, Constraints t c, Monoid m) => (forall s. c s => s -> s -> m) -> t -> t -> m

Combine two values by combining each component of the structures to a monoid, and combine the results. Returns mempty if the constructors don't match.

compare s t = compare (ctorIndex s) (ctorIndex t) <> mzipWith @Ord compare s t

mzipWith is zipWithA specialized to Compose Maybe (Const m)

mzipWith' :: forall c t m. (ADT t, Constraints t c, Monoid m) => m -> (forall s. c s => s -> s -> m) -> t -> t -> m

Variant of mzipWith where you can choose the value which is returned when the constructors don't match.

compare s t = mzipWith' @Ord (compare (ctorIndex s) (ctorIndex t)) compare s t

zipWithA :: forall c t f. (ADT t, Constraints t c, Alternative f) => (forall s. c s => s -> s -> f s) -> t -> t -> f t

Combine two values by combining each component of the structures with the given function, under an applicative effect. Returns empty if the constructors don't match.

zipWithA is generic specialized to Zip

mzipWith1 :: forall c t m a. (ADT1 t, Constraints1 t c, Monoid m) => (forall s b. c s => (b -> b -> m) -> s b -> s b -> m) -> (a -> a -> m) -> t a -> t a -> m

liftCompare = mzipWith1 @Ord1 liftCompare

mzipWith1 is zipWithA1 specialized to Compose Maybe (Const m)

mzipWith1' :: forall c t m a. (ADT1 t, Constraints1 t c, Monoid m) => m -> (forall s b. c s => (b -> b -> m) -> s b -> s b -> m) -> (a -> a -> m) -> t a -> t a -> m

Variant of mzipWith1 where you can choose the value which is returned when the constructors don't match.

zipWithA1 :: forall c t f a b. (ADT1 t, Constraints1 t c, Alternative f) => (forall d e s. c s => (d -> d -> f e) -> s d -> s d -> f (s e)) -> (a -> a -> f b) -> t a -> t a -> f (t b)

zipWithA1 is generic1 specialized to Zip

newtype Zip f a b

Constructors

Zip

Fields

• runZip :: a -> a -> f b

Instances

Functor f => Profunctor (Zip f)

Methods

dimap :: (a -> b) -> (c -> d) -> Zip f b c -> Zip f a d

lmap :: (a -> b) -> Zip f b c -> Zip f a c

rmap :: (b -> c) -> Zip f a b -> Zip f a c

(#.) :: Coercible * c b => (b -> c) -> Zip f a b -> Zip f a c

(.#) :: Coercible * b a => Zip f b c -> (a -> b) -> Zip f a c

Alternative f => GenericEmptyProfunctor (Zip f)

Methods

identity :: Zip f a a

zero :: Zip f (V1 k a) (V1 k a')

Alternative f => GenericSumProfunctor (Zip f)

Methods

plus :: Zip f (f a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((k :+: f) g a) ((k :+: f') g' a')

Applicative f => GenericProductProfunctor (Zip f)

Methods

mult :: Zip f (f a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((k :*: f) g a) ((k :*: f') g' a')

Applicative f => GenericUnitProfunctor (Zip f)

Methods

unit :: Zip f (U1 k a) (U1 k a')

Consuming values

consume :: forall c t f. (ADT t, Constraints t c, Decidable f) => (forall s. c s => f s) -> f t

Generate ways to consume values of type t. This is the contravariant version of createA.

consume is generic specialized to Clown.

consume1 :: forall c t f a. (ADT1 t, Constraints1 t c, Decidable f) => (forall b s. c s => f b -> f (s b)) -> f a -> f (t a)

consume1 is generic1 specialized to Clown.

Functions for records

These functions only work for single constructor data types.

nullaryOp :: forall c t. (ADTRecord t, Constraints t c) => (forall s. c s => s) -> t

Implement a nullary operator by calling the operator for each component.

mempty = nullaryOp @Monoid mempty
fromInteger i = nullaryOp @Num (fromInteger i)

nullaryOp is record specialized to Tagged.

unaryOp :: forall c t. (ADTRecord t, Constraints t c) => (forall s. c s => s -> s) -> t -> t

Implement a unary operator by calling the operator on the components. This is here for consistency, it is the same as record.

negate = unaryOp @Num negate

binaryOp :: forall c t. (ADTRecord t, Constraints t c) => (forall s. c s => s -> s -> s) -> t -> t -> t

Implement a binary operator by calling the operator on the components.

mappend = binaryOp @Monoid mappend
(+) = binaryOp @Num (+)

binaryOp is algebra specialized to pairs.

createA' :: forall c t f. (ADTRecord t, Constraints t c, Applicative f) => (forall s. c s => f s) -> f t

Create a value of a record type (with exactly one constructor), given how to construct the components, under an applicative effect.

Here's how to implement get from the binary package:

get = createA' (For :: For Binary) get

createA' is record specialized to Joker.

algebra :: forall c t f. (ADTRecord t, Constraints t c, Functor f) => (forall s. c s => f s -> s) -> f t -> t

Create an F-algebra, given an F-algebra for each of the components.

binaryOp f l r = algebra @c (\(Pair a b) -> f a b) (Pair l r)

algebra is record specialized to Costar.

dialgebra :: forall c t f g. (ADTRecord t, Constraints t c, Functor f, Applicative g) => (forall s. c s => f s -> g s) -> f t -> g t

dialgebra is record specialized to Biff (->).

createA1' :: forall c t f a. (ADTRecord1 t, Constraints1 t c, Applicative f) => (forall b s. c s => f b -> f (s b)) -> f a -> f (t a)

createA1' is record1 specialized to Joker.

gcotraverse1 :: forall c t f a b. (ADTRecord1 t, Constraints1 t c, Functor f) => (forall d e s. c s => (f d -> e) -> f (s d) -> s e) -> (f a -> b) -> f (t a) -> t b

cotraverse = gcotraverse1 @Distributive cotraverse

gcotraverse1 is record1 specialized to Costar.

Generic programming with profunctors

All the above functions have been implemented using these functions, using different profunctors.

record :: forall c p t. (ADTRecord t, Constraints t c, GenericRecordProfunctor p) => (forall s. c s => p s s) -> p t t

nonEmpty :: forall c p t. (ADTNonEmpty t, Constraints t c, GenericNonEmptyProfunctor p) => (forall s. c s => p s s) -> p t t

generic :: forall c p t. (ADT t, Constraints t c, GenericProfunctor p) => (forall s. c s => p s s) -> p t t

record1 :: forall c p t a b. (ADTRecord1 t, Constraints1 t c, GenericRecordProfunctor p) => (forall d e s. c s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

nonEmpty1 :: forall c p t a b. (ADTNonEmpty1 t, Constraints1 t c, GenericNonEmptyProfunctor p) => (forall d e s. c s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

generic1 :: forall c p t a b. (ADT1 t, Constraints1 t c, GenericProfunctor p) => (forall d e s. c s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

record01 :: forall c0 c1 p t a b. (ADTRecord1 t, Constraints01 t c0 c1, GenericRecordProfunctor p) => (forall s. c0 s => p s s) -> (forall d e s. c1 s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

nonEmpty01 :: forall c0 c1 p t a b. (ADTNonEmpty1 t, Constraints01 t c0 c1, GenericNonEmptyProfunctor p) => (forall s. c0 s => p s s) -> (forall d e s. c1 s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

generic01 :: forall c0 c1 p t a b. (ADT1 t, Constraints01 t c0 c1, GenericProfunctor p) => (forall s. c0 s => p s s) -> (forall d e s. c1 s => p d e -> p (s d) (s e)) -> p a b -> p (t a) (t b)

Classes

class (Profunctor p, GenericUnitProfunctor p, GenericProductProfunctor p) => GenericRecordProfunctor p

A generic function using a GenericRecordProfunctor works on any data type with exactly one constructor, a.k.a. records, with multiple fields (mult) or no fields (unit).

GenericRecordProfunctor is similar to ProductProfuctor from the product-profunctor package, but using types from GHC.Generics.

Instances

(Profunctor p, GenericUnitProfunctor p, GenericProductProfunctor p) => GenericRecordProfunctor p

class (GenericRecordProfunctor p, GenericSumProfunctor p) => GenericNonEmptyProfunctor p

A generic function using a GenericNonEmptyProfunctor works on any data type with at least one constructor.

Instances

(GenericRecordProfunctor p, GenericSumProfunctor p) => GenericNonEmptyProfunctor p

class (GenericNonEmptyProfunctor p, GenericEmptyProfunctor p) => GenericProfunctor p

A generic function using a GenericProfunctor works on any algebraic data type, including those with no constructors and constants.

Instances

(GenericNonEmptyProfunctor p, GenericEmptyProfunctor p) => GenericProfunctor p

class Profunctor p => GenericUnitProfunctor p where

Minimal complete definition

unit

Methods

unit :: p (U1 a) (U1 a')

Instances

Applicative f => GenericUnitProfunctor (Star f)

Methods

unit :: Star f (U1 k a) (U1 k a')

Functor f => GenericUnitProfunctor (Costar f)

Methods

unit :: Costar f (U1 k a) (U1 k a')

GenericUnitProfunctor (Tagged *)

Methods

unit :: Tagged * (U1 k a) (U1 k a')

GenericUnitProfunctor (Ctor *)

Methods

unit :: Ctor * (U1 k a) (U1 k a')

Applicative f => GenericUnitProfunctor (Zip f)

Methods

unit :: Zip f (U1 k a) (U1 k a')

GenericUnitProfunctor ((->) LiftedRep LiftedRep)

Methods

unit :: (LiftedRep -> LiftedRep) (U1 k a) (U1 k a')

Applicative f => GenericUnitProfunctor (Joker * * f)

Methods

unit :: Joker * * f (U1 k a) (U1 k a')

Divisible f => GenericUnitProfunctor (Clown * * f)

Methods

unit :: Clown * * f (U1 k a) (U1 k a')

(GenericUnitProfunctor p, GenericUnitProfunctor q) => GenericUnitProfunctor (Product * * p q)

Methods

unit :: Product * * p q (U1 k a) (U1 k a')

(Applicative f, GenericUnitProfunctor p) => GenericUnitProfunctor (Tannen * * * f p)

Methods

unit :: Tannen * * * f p (U1 k a) (U1 k a')

(Functor f, Applicative g, Profunctor p, GenericUnitProfunctor p) => GenericUnitProfunctor (Biff * * * * p f g)

Methods

unit :: Biff * * * * p f g (U1 k a) (U1 k a')

class Profunctor p => GenericProductProfunctor p where

Minimal complete definition

mult

Methods

mult :: p (f a) (f' a') -> p (g a) (g' a') -> p ((f :*: g) a) ((f' :*: g') a')

Instances

Applicative f => GenericProductProfunctor (Star f)

Methods

mult :: Star f (f a) (f' a') -> Star f (g a) (g' a') -> Star f ((k :*: f) g a) ((k :*: f') g' a')

Functor f => GenericProductProfunctor (Costar f)

Methods

mult :: Costar f (f a) (f' a') -> Costar f (g a) (g' a') -> Costar f ((k :*: f) g a) ((k :*: f') g' a')

GenericProductProfunctor (Tagged *)

Methods

mult :: Tagged * (f a) (f' a') -> Tagged * (g a) (g' a') -> Tagged * ((k :*: f) g a) ((k :*: f') g' a')

GenericProductProfunctor (Ctor *)

Methods

mult :: Ctor * (f a) (f' a') -> Ctor * (g a) (g' a') -> Ctor * ((k :*: f) g a) ((k :*: f') g' a')

Applicative f => GenericProductProfunctor (Zip f)

Methods

mult :: Zip f (f a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((k :*: f) g a) ((k :*: f') g' a')

GenericProductProfunctor ((->) LiftedRep LiftedRep)

Methods

mult :: (LiftedRep -> LiftedRep) (f a) (f' a') -> (LiftedRep -> LiftedRep) (g a) (g' a') -> (LiftedRep -> LiftedRep) ((k :*: f) g a) ((k :*: f') g' a')

Applicative f => GenericProductProfunctor (Joker * * f)

Methods

mult :: Joker * * f (f a) (f' a') -> Joker * * f (g a) (g' a') -> Joker * * f ((k :*: f) g a) ((k :*: f') g' a')

Divisible f => GenericProductProfunctor (Clown * * f)

Methods

mult :: Clown * * f (f a) (f' a') -> Clown * * f (g a) (g' a') -> Clown * * f ((k :*: f) g a) ((k :*: f') g' a')

(GenericProductProfunctor p, GenericProductProfunctor q) => GenericProductProfunctor (Product * * p q)

Methods

mult :: Product * * p q (f a) (f' a') -> Product * * p q (g a) (g' a') -> Product * * p q ((k :*: f) g a) ((k :*: f') g' a')

(Applicative f, GenericProductProfunctor p) => GenericProductProfunctor (Tannen * * * f p)

Methods

mult :: Tannen * * * f p (f a) (f' a') -> Tannen * * * f p (g a) (g' a') -> Tannen * * * f p ((k :*: f) g a) ((k :*: f') g' a')

(Functor f, Applicative g, Profunctor p, GenericProductProfunctor p) => GenericProductProfunctor (Biff * * * * p f g)

Methods

mult :: Biff * * * * p f g (f a) (f' a') -> Biff * * * * p f g (g a) (g' a') -> Biff * * * * p f g ((k :*: f) g a) ((k :*: f') g' a')

class Profunctor p => GenericSumProfunctor p where

Minimal complete definition

plus

Methods

plus :: p (f a) (f' a') -> p (g a) (g' a') -> p ((f :+: g) a) ((f' :+: g') a')

Instances

Applicative f => GenericSumProfunctor (Star f)

Methods

plus :: Star f (f a) (f' a') -> Star f (g a) (g' a') -> Star f ((k :+: f) g a) ((k :+: f') g' a')

GenericSumProfunctor (Ctor *)

Methods

plus :: Ctor * (f a) (f' a') -> Ctor * (g a) (g' a') -> Ctor * ((k :+: f) g a) ((k :+: f') g' a')

Alternative f => GenericSumProfunctor (Zip f)

Methods

plus :: Zip f (f a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((k :+: f) g a) ((k :+: f') g' a')

GenericSumProfunctor ((->) LiftedRep LiftedRep)

Methods

plus :: (LiftedRep -> LiftedRep) (f a) (f' a') -> (LiftedRep -> LiftedRep) (g a) (g' a') -> (LiftedRep -> LiftedRep) ((k :+: f) g a) ((k :+: f') g' a')

Alternative f => GenericSumProfunctor (Joker * * f)

Methods

plus :: Joker * * f (f a) (f' a') -> Joker * * f (g a) (g' a') -> Joker * * f ((k :+: f) g a) ((k :+: f') g' a')

Decidable f => GenericSumProfunctor (Clown * * f)

Methods

plus :: Clown * * f (f a) (f' a') -> Clown * * f (g a) (g' a') -> Clown * * f ((k :+: f) g a) ((k :+: f') g' a')

(GenericSumProfunctor p, GenericSumProfunctor q) => GenericSumProfunctor (Product * * p q)

Methods

plus :: Product * * p q (f a) (f' a') -> Product * * p q (g a) (g' a') -> Product * * p q ((k :+: f) g a) ((k :+: f') g' a')

(Applicative f, GenericSumProfunctor p) => GenericSumProfunctor (Tannen * * * f p)

Methods

plus :: Tannen * * * f p (f a) (f' a') -> Tannen * * * f p (g a) (g' a') -> Tannen * * * f p ((k :+: f) g a) ((k :+: f') g' a')

class Profunctor p => GenericEmptyProfunctor p where

Minimal complete definition

identity, zero

Methods

identity :: p a a

zero :: p (V1 a) (V1 a')

Instances

Applicative f => GenericEmptyProfunctor (Star f)

Methods

identity :: Star f a a

zero :: Star f (V1 k a) (V1 k a')

GenericEmptyProfunctor (Ctor *)

Methods

identity :: Ctor * a a

zero :: Ctor * (V1 k a) (V1 k a')

Alternative f => GenericEmptyProfunctor (Zip f)

Methods

identity :: Zip f a a

zero :: Zip f (V1 k a) (V1 k a')

GenericEmptyProfunctor ((->) LiftedRep LiftedRep)

Methods

identity :: (LiftedRep -> LiftedRep) a a

zero :: (LiftedRep -> LiftedRep) (V1 k a) (V1 k a')

Alternative f => GenericEmptyProfunctor (Joker * * f)

Methods

identity :: Joker * * f a a

zero :: Joker * * f (V1 k a) (V1 k a')

Decidable f => GenericEmptyProfunctor (Clown * * f)

Methods

identity :: Clown * * f a a

zero :: Clown * * f (V1 k a) (V1 k a')

(GenericEmptyProfunctor p, GenericEmptyProfunctor q) => GenericEmptyProfunctor (Product * * p q)

Methods

identity :: Product * * p q a a

zero :: Product * * p q (V1 k a) (V1 k a')

(Applicative f, GenericEmptyProfunctor p) => GenericEmptyProfunctor (Tannen * * * f p)

Methods

identity :: Tannen * * * f p a a

zero :: Tannen * * * f p (V1 k a) (V1 k a')

Types

type ADT t = (Generic t, ADT' (Rep t), Constraints t AnyType)

ADT is a constraint type synonym. The Generic instance can be derived, and any generic representation will be an instance of ADT' and AnyType.

type ADTNonEmpty t = (Generic t, ADTNonEmpty' (Rep t), Constraints t AnyType)

ADTNonEmpty is a constraint type synonym. An instance is an ADT with *at least* one constructor.

type ADTRecord t = (Generic t, ADTRecord' (Rep t), Constraints t AnyType)

ADTRecord is a constraint type synonym. An instance is an ADT with *exactly* one constructor.

type Constraints t c = Constraints' (Rep t) c AnyType

Constraints is a constraint type synonym, containing the constraint requirements for an instance for t of class c. It requires an instance of class c for each component of t.

type ADT1 t = (Generic1 t, ADT1' (Rep1 t), Constraints1 t AnyType)

type ADTNonEmpty1 t = (Generic1 t, ADTNonEmpty1' (Rep1 t), Constraints1 t AnyType)

type ADTRecord1 t = (Generic1 t, ADTRecord1' (Rep1 t), Constraints1 t AnyType)

type Constraints1 t c = Constraints' (Rep1 t) AnyType c

type Constraints01 t c0 c1 = Constraints' (Rep1 t) c0 c1

class FunConstraints c t

Automatically apply a lifted function to a polymorphic argument as many times as possible.

A constraint `FunConstraint c t` is equivalent to the conjunction of constraints `c s` for every argument type of t.

If r is not a function type:

c a :- FunConstraints c (a -> r)
(c a, c b) :- FunConstraints c (a -> b -> r)
(c a, c b, c d) :- FunConstraints c (a -> b -> d -> r)

Minimal complete definition

autoApply

Instances

(~) * (FunResult r) r => FunConstraints c r

Methods

autoApply :: Applicative f => (forall s. c s => f s) -> f r -> f (FunResult r)

(c a, FunConstraints c b) => FunConstraints c (a -> b)

Methods

autoApply :: Applicative f => (forall s. c s => f s) -> f (a -> b) -> f (FunResult (a -> b))

type family FunResult t where ...

The result type of a curried function.

If r is not a function type (i.e., does not unify with `_ -> _`):

FunResult (a -> r) ~ r
FunResult (a -> b -> r) ~ r
FunResult (a -> b -> c -> r) ~ r

Equations

FunResult (a -> b) = FunResult b

FunResult r = r

class AnyType (a :: k)

Any type is instance of AnyType, you can use it with @AnyType if you don't actually need a class constraint.

Instances

AnyType k a