# Module `Monad.List`

The list monad denotes a non-deterministic computation, i.e., a computation that can have more than one result or no results at all.

`module type S = sig ... end`
`module type S2 = sig ... end`
`include S with type 'a t = 'a list and type 'a m = 'a and type 'a e = 'a list`
```include Trans.S with type 'a t = 'a list with type 'a m = 'a with type 'a e = 'a list```
`type 'a t = 'a list`
`type 'a m = 'a`
`type 'a e = 'a list`
`val lift : 'a m -> 'a t`

`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`

`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`

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

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

`m >>= f` is `bind m f`

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

`m >>= f` is `map m ~f`

`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 Syntax.Let.S with type 'a t := 'a t`
`val let* : 'a t -> ( 'a -> 'b t ) -> 'b t`

`let* r = f x in b` is `f x >>= fun r -> b`

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

monoidal product

`val let+ : 'a t -> ( 'a -> 'b ) -> 'b t`

`let+ r = f x in b` is `f x >>| fun r -> b`

`val and+ : 'a t -> 'b t -> ('a * 'b) t`

monoidal product

`include Core_kernel.Monad.S with type 'a t := 'a t`
`val (>>=) : 'a t -> ( 'a -> 'b t ) -> 'b t`
`val (>>|) : 'a t -> ( 'a -> 'b ) -> 'b t`
`module Monad_infix : sig ... end`
`val bind : 'a t -> f:( 'a -> 'b t ) -> 'b t`
`val return : 'a -> 'a t`
`val map : 'a t -> f:( 'a -> 'b ) -> 'b t`
`val join : 'a t t -> 'a t`
`val ignore_m : 'a t -> unit t`
`val all : 'a t list -> 'a list t`
`val all_unit : unit t list -> unit t`
`module Let_syntax : sig ... end`
`module Let : Syntax.Let.S with type 'a t := 'a t`

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

`include Choice.S with type 'a t := 'a t`
`include Choice.Basic with type 'a t := 'a t`
`val pure : 'a -> 'a t`

`pure x` creates a computation that results in `x`.

`val accept : 'a -> 'a t`

`accept x` accepts `x` as a result of computation. (Same as `pure x`.

`val reject : unit -> 'a t`

`reject ()` rejects the rest of computation sequence, and terminate the computation with the `zero` result (Same as `zero ()`

`val guard : bool -> unit t`

`guard cond` ensures `cond` is `true` in the rest of computation. Otherwise the rest of the computation is rejected.

`val on : bool -> unit t -> unit t`

`on cond x` computes `x` only iff `cond` is `true`

`val unless : bool -> unit t -> unit t`

`unless cond x` computes `x` unless `cond` is `true`.

`include Plus.S with type 'a t := 'a t`
`val zero : unit -> 'a t`

`zero ()` constructs a zero element

`val plus : 'a t -> 'a t -> 'a t`

`plus x y` an associative operation.

`module T1 (M : Core_kernel.T1) : sig ... end`
```module Make (M : Monad) : S with type 'a m := 'a T1(M).m and type 'a t := 'a T1(M).t and type 'a e := 'a T1(M).e```

`Make(M)` composes the List monad with `M`

`module T2 (M : Core_kernel.T2) : sig ... end`
```module Make2 (M : Monad2) : S2 with type ('a, 'e) m := ( 'a, 'e ) T2(M).m and type ('a, 'e) t := ( 'a, 'e ) T2(M).t and type ('a, 'e) e := ( 'a, 'e ) T2(M).e```

`Make2(M)` composes the List monad with `M`