Generics.OneLiner.Binary

These generic functions allow changing the types of the constant leaves. They require type classes with 2 parameters, the first for the input type and the second for the output type.

All functions without postfix are for instances of Generic, and functions with postfix 1 are for instances of Generic1 (with kind Type -> Type) 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.

Traversing values

gmap :: forall c t t'. (ADT t t', Constraints t t' c) => (forall s s'. c s s' => s -> s') -> t -> t'

Map over a structure, updating each component.

gmap is generic specialized to (->).

gtraverse :: forall c t t' f. (ADT t t', Constraints t t' c, Applicative f) => (forall s s'. c s 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.

glmap :: forall c t t'. (ADT t t', Constraints t t' c) => (forall s s'. c s s' => s -> s') -> t -> t'

Map over a structure linearly, updating each component.

glmap is generic specialized to the linear arrow.

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

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

gltraverse is generic specialized to linear Kleisli.

gmap1 :: forall c t t' a b. (ADT1 t t', Constraints1 t t' c) => (forall d e s s'. c s s' => (d -> e) -> s d -> s' e) -> (a -> b) -> t a -> t' b

gmap1 is generic1 specialized to (->).

gtraverse1 :: forall c t t' f a b. (ADT1 t t', Constraints1 t t' c, Applicative f) => (forall d e s s'. c s s' => (d -> f e) -> s d -> f (s' e)) -> (a -> f b) -> t a -> f (t' b)

gtraverse1 is generic1 specialized to Star.

glmap1 :: forall c t t' a b. (ADT1 t t', Constraints1 t t' c) => (forall d e s s'. c s s' => (d -> e) -> s d -> s' e) -> (a -> b) -> t a -> t' b

glmap1 is generic1 specialized to the linear arrow.

gltraverse1 :: forall c t t' f a b. (ADT1 t t', Constraints1 t t' c, Applicative f) => (forall d e s s'. c s s' => (d -> f e) -> s d -> f (s' e)) -> (a -> f b) -> t a -> f (t' b)

gltraverse1 is generic1 specialized to linear Kleisli.

gltraverse01 :: forall c t t' f a b. (ADT1 t t', Constraints01 t t' (D Movable) c, Applicative f) => (forall d e s s'. c s s' => (d -> f e) -> s d -> f (s' e)) -> (a -> f b) -> t a -> f (t' b)

gltraverse01 is generic01 specialized to linear Kleisli, requiring Movable for constants.

Combining values

zipWithA :: forall c t t' f. (ADT t t', Constraints t t' c, Alternative f) => (forall s s'. c s 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

zipWithA1 :: forall c t t' f a b. (ADT1 t t', Constraints1 t t' c, Alternative f) => (forall d e s s'. c s 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

Functions for records

These functions only work for single constructor data types.

unaryOp :: forall c t t'. (ADTRecord t t', Constraints t t' c) => (forall s s'. c s 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 t'. (ADTRecord t t', Constraints t t' c) => (forall s s'. c s 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.

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

dialgebra is record specialized to Biff (->).

gcotraverse1 :: forall c t t' f a b. (ADTRecord1 t t', Constraints1 t t' c, Functor f) => (forall d e s s'. c s s' => (f d -> e) -> f (s d) -> s' e) -> (f a -> b) -> f (t a) -> t' b

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 t'. (ADTRecord t t', Constraints t t' c, GenericRecordProfunctor p) => (forall s s'. c s s' => p s s') -> p t t'

nonEmpty :: forall c p t t'. (ADTNonEmpty t t', Constraints t t' c, GenericNonEmptyProfunctor p) => (forall s s'. c s s' => p s s') -> p t t'

generic :: forall c p t t'. (ADT t t', Constraints t t' c, GenericProfunctor p) => (forall s s'. c s s' => p s s') -> p t t'

record1 :: forall c p t t' a b. (ADTRecord1 t t', Constraints1 t t' c, GenericRecordProfunctor p) => (forall d e s s'. c s s' => p d e -> p (s d) (s' e)) -> p a b -> p (t a) (t' b)

nonEmpty1 :: forall c p t t' a b. (ADTNonEmpty1 t t', Constraints1 t t' c, GenericNonEmptyProfunctor p) => (forall d e s s'. c s s' => p d e -> p (s d) (s' e)) -> p a b -> p (t a) (t' b)

generic1 :: forall c p t t' a b. (ADT1 t t', Constraints1 t t' c, Generic1Profunctor p) => (forall d e s s'. c s s' => p d e -> p (s d) (s' e)) -> p a b -> p (t a) (t' b)

record01 :: forall c0 c1 p t t' a b. (ADTRecord1 t t', Constraints01 t t' c0 c1, GenericRecordProfunctor p) => (forall s s'. c0 s s' => p s s') -> (forall d e s s'. c1 s s' => p d e -> p (s d) (s' e)) -> p a b -> p (t a) (t' b)

nonEmpty01 :: forall c0 c1 p t t' a b. (ADTNonEmpty1 t t', Constraints01 t t' c0 c1, GenericNonEmptyProfunctor p) => (forall s s'. c0 s s' => p s s') -> (forall d e s s'. c1 s s' => p d e -> p (s d) (s' e)) -> p a b -> p (t a) (t' b)

generic01 :: forall c0 c1 p t t' a b. (ADT1 t t', Constraints01 t t' c0 c1, GenericProfunctor p) => (forall s s'. c0 s s' => p s s') -> (forall d e s s'. c1 s 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

Defined in Generics.OneLiner.Classes

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

Defined in Generics.OneLiner.Classes

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

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

Instances

(GenericNonEmptyProfunctor p, GenericEmptyProfunctor p) => GenericProfunctor p

Defined in Generics.OneLiner.Classes

class (GenericProfunctor p, GenericConstantProfunctor p) => Generic1Profunctor p

A generic function using a Generic1Profunctor works on any algebraic data type of kind Type -> Type, including those with no constructors and constants.

Instances

(GenericProfunctor p, GenericConstantProfunctor p) => Generic1Profunctor p

Defined in Generics.OneLiner.Classes

class Profunctor p => GenericUnitProfunctor p where

Methods

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

Instances

Applicative f => GenericUnitProfunctor (Kleisli f)

Defined in Generics.OneLiner.Classes

Methods

unit :: Kleisli f (U1 a) (U1 a')

GenericUnitProfunctor (Tagged :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

Applicative f => GenericUnitProfunctor (Zip f)

Defined in Generics.OneLiner.Classes

Methods

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

GenericUnitProfunctor (Ctor :: Type -> Type -> Type)

Defined in Generics.OneLiner.Internal

Methods

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

GenericUnitProfunctor (->)

Defined in Generics.OneLiner.Classes

Methods

unit :: U1 a -> U1 a'

Applicative f => GenericUnitProfunctor (Star f)

Defined in Generics.OneLiner.Classes

Methods

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

Functor f => GenericUnitProfunctor (Costar f)

Defined in Generics.OneLiner.Classes

Methods

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

GenericUnitProfunctor (FUN 'One :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

unit :: FUN 'One (U1 a) (U1 a')

Applicative f => GenericUnitProfunctor (Joker f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

Divisible f => GenericUnitProfunctor (Clown f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

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

class Profunctor p => GenericProductProfunctor p where

Methods

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

Instances

Applicative f => GenericProductProfunctor (Kleisli f)

Defined in Generics.OneLiner.Classes

Methods

mult :: Kleisli f (f0 a) (f' a') -> Kleisli f (g a) (g' a') -> Kleisli f ((f0 :*: g) a) ((f' :*: g') a')

GenericProductProfunctor (Tagged :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

Applicative f => GenericProductProfunctor (Zip f)

Defined in Generics.OneLiner.Classes

Methods

mult :: Zip f (f0 a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((f0 :*: g) a) ((f' :*: g') a')

GenericProductProfunctor (Ctor :: Type -> Type -> Type)

Defined in Generics.OneLiner.Internal

Methods

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

GenericProductProfunctor (->)

Defined in Generics.OneLiner.Classes

Methods

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

Applicative f => GenericProductProfunctor (Star f)

Defined in Generics.OneLiner.Classes

Methods

mult :: Star f (f0 a) (f' a') -> Star f (g a) (g' a') -> Star f ((f0 :*: g) a) ((f' :*: g') a')

Functor f => GenericProductProfunctor (Costar f)

Defined in Generics.OneLiner.Classes

Methods

mult :: Costar f (f0 a) (f' a') -> Costar f (g a) (g' a') -> Costar f ((f0 :*: g) a) ((f' :*: g') a')

GenericProductProfunctor (FUN 'One :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

mult :: FUN 'One (f a) (f' a') -> FUN 'One (g a) (g' a') -> FUN 'One ((f :*: g) a) ((f' :*: g') a')

Applicative f => GenericProductProfunctor (Joker f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

mult :: Joker f (f0 a) (f' a') -> Joker f (g a) (g' a') -> Joker f ((f0 :*: g) a) ((f' :*: g') a')

Divisible f => GenericProductProfunctor (Clown f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

mult :: Clown f (f0 a) (f' a') -> Clown f (g a) (g' a') -> Clown f ((f0 :*: g) a) ((f' :*: g') a')

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

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

mult :: Tannen f p (f0 a) (f' a') -> Tannen f p (g a) (g' a') -> Tannen f p ((f0 :*: g) a) ((f' :*: g') a')

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

Defined in Generics.OneLiner.Classes

Methods

mult :: Biff p f g (f0 a) (f' a') -> Biff p f g (g0 a) (g' a') -> Biff p f g ((f0 :*: g0) a) ((f' :*: g') a')

class Profunctor p => GenericSumProfunctor p where

Methods

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

Instances

Applicative f => GenericSumProfunctor (Kleisli f)

Defined in Generics.OneLiner.Classes

Methods

plus :: Kleisli f (f0 a) (f' a') -> Kleisli f (g a) (g' a') -> Kleisli f ((f0 :+: g) a) ((f' :+: g') a')

Alternative f => GenericSumProfunctor (Zip f)

Defined in Generics.OneLiner.Classes

Methods

plus :: Zip f (f0 a) (f' a') -> Zip f (g a) (g' a') -> Zip f ((f0 :+: g) a) ((f' :+: g') a')

GenericSumProfunctor (Ctor :: Type -> Type -> Type)

Defined in Generics.OneLiner.Internal

Methods

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

GenericSumProfunctor (->)

Defined in Generics.OneLiner.Classes

Methods

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

Applicative f => GenericSumProfunctor (Star f)

Defined in Generics.OneLiner.Classes

Methods

plus :: Star f (f0 a) (f' a') -> Star f (g a) (g' a') -> Star f ((f0 :+: g) a) ((f' :+: g') a')

GenericSumProfunctor (FUN 'One :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

plus :: FUN 'One (f a) (f' a') -> FUN 'One (g a) (g' a') -> FUN 'One ((f :+: g) a) ((f' :+: g') a')

Alternative f => GenericSumProfunctor (Joker f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

plus :: Joker f (f0 a) (f' a') -> Joker f (g a) (g' a') -> Joker f ((f0 :+: g) a) ((f' :+: g') a')

Decidable f => GenericSumProfunctor (Clown f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

plus :: Clown f (f0 a) (f' a') -> Clown f (g a) (g' a') -> Clown f ((f0 :+: g) a) ((f' :+: g') a')

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

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

plus :: Tannen f p (f0 a) (f' a') -> Tannen f p (g a) (g' a') -> Tannen f p ((f0 :+: g) a) ((f' :+: g') a')

class Profunctor p => GenericEmptyProfunctor p where

Methods

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

Instances

Applicative f => GenericEmptyProfunctor (Kleisli f)

Defined in Generics.OneLiner.Classes

Methods

zero :: Kleisli f (V1 a) (V1 a')

Functor f => GenericEmptyProfunctor (Zip f)

Defined in Generics.OneLiner.Classes

Methods

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

GenericEmptyProfunctor (Ctor :: Type -> Type -> Type)

Defined in Generics.OneLiner.Internal

Methods

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

GenericEmptyProfunctor (->)

Defined in Generics.OneLiner.Classes

Methods

zero :: V1 a -> V1 a'

Functor f => GenericEmptyProfunctor (Star f)

Defined in Generics.OneLiner.Classes

Methods

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

GenericEmptyProfunctor (FUN 'One :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

zero :: FUN 'One (V1 a) (V1 a')

Alternative f => GenericEmptyProfunctor (Joker f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

Decidable f => GenericEmptyProfunctor (Clown f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

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

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

Defined in Generics.OneLiner.Classes

Methods

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

class Profunctor p => GenericConstantProfunctor p where

Methods

identity :: p c c

Instances

Applicative f => GenericConstantProfunctor (Kleisli f)

Defined in Generics.OneLiner.Classes

Methods

identity :: Kleisli f c c

Alternative f => GenericConstantProfunctor (Zip f)

Defined in Generics.OneLiner.Classes

Methods

identity :: Zip f c c

GenericConstantProfunctor (Ctor :: Type -> Type -> Type)

Defined in Generics.OneLiner.Internal

Methods

identity :: Ctor c c

GenericConstantProfunctor (->)

Defined in Generics.OneLiner.Classes

Methods

identity :: c -> c

Applicative f => GenericConstantProfunctor (Star f)

Defined in Generics.OneLiner.Classes

Methods

identity :: Star f c c

GenericConstantProfunctor (FUN 'One :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

identity :: FUN 'One c c

Alternative f => GenericConstantProfunctor (Joker f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

identity :: Joker f c c

Decidable f => GenericConstantProfunctor (Clown f :: Type -> Type -> Type)

Defined in Generics.OneLiner.Classes

Methods

identity :: Clown f c c

(GenericConstantProfunctor p, GenericConstantProfunctor q) => GenericConstantProfunctor (Product p q)

Defined in Generics.OneLiner.Classes

Methods

identity :: Product p q c c

(Applicative f, GenericConstantProfunctor p) => GenericConstantProfunctor (Tannen f p)

Defined in Generics.OneLiner.Classes

Methods

identity :: Tannen f p c c

Types

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

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

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

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

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

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

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

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

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

Defined in Generics.OneLiner.Internal

Methods

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

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

Defined in Generics.OneLiner.Internal

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 b

Instances

AnyType (a :: k1) (b :: k2)

Defined in Generics.OneLiner.Internal