package alg_structs

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List defines applications that work across all possible combinations of the items in the respective lists. This is often used to model non-determinism.

E.g., to get all pairs that can be formed by selecting first and second elements from the respective lists:

# let x = List.NonDet.((fun x y -> (x, y)) <@> [1;2] <*> ['a';'b']);;

- : (int * char) list = [(1, 'a'); (1, 'b'); (2, 'a'); (2, 'b')]

include Seed with type 'a t = 'a Stdlib.List.t
include Functor.S with type 'a t = 'a Stdlib.List.t
include Functor.Seed with type 'a t = 'a Stdlib.List.t
type 'a t = 'a Stdlib.List.t

The principle type.

The type constructor t is the mapping of objects taking every type 'a to a type 'a t.

val map : f:('a -> 'b) -> 'a t -> 'b t

map ~f maps the function f : 'a -> 'b to a function 'f T : 'a T -> 'b T.

As an example, if T (x : u) : u t then map ~(f:u -> v) (T x) is T (f x) : v t. As a result, map is often thought of as applying f "in" T.

The function map is the mapping of arrows, taking every arrow 'a -> 'b to an arrow 'a t -> 'b t.

val (<@>) : ('a -> 'b) -> 'a t -> 'b t

Infix for map

val (|>>) : 'a t -> ('a -> 'b) -> 'b t

Mapped version of |> (which is flipped (<&>))

val return : 'a -> 'a t

return x is the minimal value of x in t

val apply : ('a -> 'b) t -> 'a t -> 'b t

apply (F f) (F x) is F (f x), i.e., f applied to x in t

val map2 : 'a t -> 'b t -> f:('a -> 'b -> 'c) -> 'c t

map2 ~f x y is return f <*> x <*> y, i.e., f "lifted" in to t and then applied to both x and y.

val (<*>) : ('a -> 'b) t -> 'a t -> 'b t

(F f) <*> (F x) is F (f x)

val (*>) : 'a t -> 'b t -> 'b t

a *> b sequences actions a and b but discards the value of a

val (<*) : 'a t -> 'b t -> 'a t

a <* b sequences actions a and b but discards the value of b

val both : 'a t -> 'b t -> ('a * 'b) t

both (F a) (F b) is F (a, b), i.e., it is the product of a and b in F

module Let_bind : sig ... end

Binding operators for use with the OCaml 4.08 extension. See the OCaml docs on binding operators for more information.


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