package monads

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package monads
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The Function Monad.

The function monad delays the computation until it is actually run. This is not the only monad that has such behavior, i.e., State, Cont, Lazy, and Reader monads are also delayed, but they all have other additional behaviors on top of the delaying the computation. The function monad can be seen as a Reader monad with unit environment, or as a Lazy monad without the memoization.

module type S = sig ... end
module type S2 = sig ... end
type 'a thunk

A function monad computation is a thunk that returns a value of type 'a.

include S with type 'a t = 'a thunk and type 'a m = 'a and type 'a e = 'a
include Trans.S with type 'a t = 'a thunk with type 'a m = 'a with type 'a e = 'a
type 'a t = 'a thunk
type 'a m = 'a
type 'a e = 'a
val lift : 'a m -> 'a t

lifts inner monad into the resulting monad

val run : 'a t -> 'a e

runs the computation

include Monad with type 'a t := 'a t
val void : 'a t -> unit t

void m computes m and discrards the result.

val sequence : unit t list -> unit t

sequence xs computes a sequence of computations xs in the left to right order.

val forever : 'a t -> 'b t

forever xs creates a computationt that never returns.

module Fn : sig ... end

Various function combinators lifted into the Kleisli category.

module Pair : sig ... end

The pair interface lifted into the monad.

module Triple : sig ... end

The triple interface lifted into a monad.

module Lift : sig ... end

Lifts functions into the monad.

module Exn : sig ... end

Interacting between monads and language exceptions

module Collection : sig ... end

Lifts collection interface into the monad.

module List : Collection.S with type 'a t := 'a list

The Monad.Collection.S interface for lists

module Seq : Collection.S with type 'a t := 'a Core_kernel.Sequence.t

The Monad.Collection.S interface for sequences

include Syntax.S with type 'a t := 'a t
val (>=>) : ('a -> 'b t) -> ('b -> 'c t) -> 'a -> 'c t

f >=> g is fun x -> f x >>= g

val (!!) : 'a -> 'a t

!!x is return x

val (!$) : ('a -> 'b) -> 'a t -> 'b t

!$f is Lift.unary f

val (!$$) : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t

!$$f is Lift.binary f

val (!$$$) : ('a -> 'b -> 'c -> 'd) -> 'a t -> 'b t -> 'c t -> 'd t

!$$$f is Lift.ternary f

val (!$$$$) : ('a -> 'b -> 'c -> 'd -> 'e) -> 'a t -> 'b t -> 'c t -> 'd t -> 'e t

!$$$$f is Lift.quaternary f

val (!$$$$$) : ('a -> 'b -> 'c -> 'd -> 'e -> 'f) -> 'a t -> 'b t -> 'c t -> 'd t -> 'e t -> 'f t

!$$$$$f is Lift.quinary f

include Core_kernel.Monad.S with type 'a t := 'a t
val (>>=) : 'a t -> ('a -> 'b t) -> 'b t

t >>= f returns a computation that sequences the computations represented by two monad elements. The resulting computation first does t to yield a value v, and then runs the computation returned by f v.

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

t >>| f is t >>= (fun a -> return (f a)).

module Monad_infix : sig ... end
val bind : 'a t -> f:('a -> 'b t) -> 'b t

bind t ~f = t >>= f

val return : 'a -> 'a t

return v returns the (trivial) computation that returns v.

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

map t ~f is t >>| f.

val join : 'a t t -> 'a t

join t is t >>= (fun t' -> t').

val ignore_m : 'a t -> unit t

ignore_m t is map t ~f:(fun _ -> ()). ignore_m used to be called ignore, but we decided that was a bad name, because it shadowed the widely used Caml.ignore. Some monads still do let ignore = ignore_m for historical reasons.

val all : 'a t list -> 'a list t
val all_unit : unit t list -> unit t

Like all, but ensures that every monadic value in the list produces a unit value, all of which are discarded rather than being collected into a list.

val all_ignore : unit t list -> unit t
  • deprecated [since 2018-02] Use [all_unit]
module Let_syntax : sig ... end

These are convenient to have in scope when programming with a monad:

module Syntax : Syntax.S with type 'a t := 'a t

Monadic operators, see Monad.Syntax.S for more.

module T1 (M : Monad) : sig ... end
module Make (M : Monad) : S with type 'a t := 'a T1(M).t and type 'a m := 'a T1(M).m and type 'a e := 'a T1(M).e
module T2 (M : Monad2) : sig ... end
module Make2 (M : Monad2) : S2 with type ('a, 'e) t := ('a, 'e) T2(M).t and type ('a, 'e) m := ('a, 'e) T2(M).m and type ('a, 'e) e := ('a, 'e) T2(M).e
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