Applicative functors "allow sequencing of functorial computations" (wikipedia) with the limitation that "values computed by subcomputations cannot affect what subsequent computations will take place" (Core docs).
Assume that we've implemented Applicative for some parametertic type 'p t. Take two values F x : 'a t and F y : 'b t and a computation represented by a function F f : ('a -> 'b -> 'c) t. We can then use the applicative's namesake function S.apply to sequence this computation "within" type t:
apply (apply f x) y : 'c t
The "sequencing" of the computation (via application) is even more apparent when we use the infix notation for apply:
f <*> x <*> y
See Implementations for illustrative examples.
module type Seed = sig ... endThe Seed needed to generate an implementation of Applicative
module type S = sig ... endLaw notes the laws that should be obeyed by any instantiation of Applicative in the form of predicates that should be true for any arguments of the appropriate type.
Module functors for creating implementations of Applicative
Implementations for common data structures. See the documentation for each implementation module for an illustrative example.
Option provides sequencing of partial computations. E.g,
List defines applications that work across all possible combinations of the items in the respective lists. This is often used to model non-determinism.