Types

Types

Type	Equivalent to	Notes
type Lens s t a b = ∀f. Functor f => (a -> f b) -> s -> f t	s -> (a, b -> t)
type Traversal s t a b = ∀f. Applicative f => (a -> f b) -> s -> f t	s -> ∃n. (a^n, b^n -> t)	X
type Getter s a = ∀f. Gettable f => (a -> f a) -> s -> f s	s -> a
type Setter s t a b = ∀f. Settable f => (a -> f b) -> s -> f t	(a -> b) -> s -> t
type Fold s a = ∀f. (Gettable f, Applicative f) => (a -> f a) -> s -> f s	s -> [a]
type Iso s t a b = ∀f k. (Isomorphic k, Functor f) => k (a -> f b) (s -> f t)	(s -> a, b -> t)
Indexed
type IndexedLens i s t a b = ∀f k. (Indexed i k, Functor f) => k (a -> f b) (s -> f t)	s -> ((i, a), b -> t)
type IndexedTraversal i s t a b = ∀f k. (Indexed i k, Applicative f) => k (a -> f b) (s -> f t)	s -> ∃n. ((i, a)^n, b^n -> t) +	X
type IndexedGetter i s a = ∀f k. (Indexed i k, Gettable f) => k (a -> f a) (s -> f s)	s -> (i, a)
type IndexedSetter i s t a b = ∀f k. (Indexed i k, Settable f) => k (a -> f b) (s -> f t)	((i, a) -> b) -> s -> t
type IndexedFold i s a = ∀f. (Indexed i k, Gettable f, Applicative f) => k (a -> f a) (s -> f s)	s -> [(i, a)]
Monadic
type Action m s a = ∀f. Effective m r f => (a -> f a) -> s-> f s	s -> m a
type MonadicFold m s a = ∀f. (Effective m r f, Applicative f) => (a -> f a) -> s -> f s	s -> m [a]
Hypothetical
type PartialLens s t a b = ∀f. Pointed f => (a -> f b) -> s -> f t	s -> Either t (a, b -> t)
type NonEmptyTraversal s t a b = ∀f. Apply f => (a -> f b) -> s -> f t	s -> ∃n. (a^(n+1), b^(n+1) -> t)	X

• a^n means "a list of n values of type a".