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.

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.

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 is createA1 specialized to lists.

createA1 is generic1 specialized to Joker.

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 (,,,)

Map over a structure, updating each component.

gmap is generic specialized to (->).

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.

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.

fmap = gmap1 @Functor fmap

gmap1 is generic1 specialized to (->).

foldMap = gfoldMap1 @Foldable foldMap

gfoldMap1 is gtraverse1 specialized to Const.

traverse = gtraverse1 @Traversable traverse

gtraverse1 is generic1 specialized to Star.

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)

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

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

liftCompare = mzipWith1 @Ord1 liftCompare

mzipWith1 is zipWithA1 specialized to Compose Maybe (Const m)

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

zipWithA1 is generic1 specialized to Zip

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

consume is generic specialized to Clown.

consume1 is generic1 specialized to Clown.

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.

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

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

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

binaryOp is algebra specialized to pairs.

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.

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 is record specialized to Biff (->).

createA1' is record1 specialized to Joker.

cotraverse = gcotraverse1 @Distributive cotraverse

gcotraverse1 is record1 specialized to Costar.

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.

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

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

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)

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

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