Cartesian Product of Lists

Computes the Cartesian product of a list of lists. See also corresponding example for a sequence of sequences.

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// Cartesian product of a list of lists.
let rec cartList nll = 
  let f0 n nll =  
    match nll with
    | [] -> [[n]]
    | _ -> List.map (fun nl->n::nl) nll
  match nll with
  | [] -> []
  | h::t -> List.collect (fun n->f0 n (cartList t)) h
 
 
// Test.

let choices = 
  [
    ["crispy";"thick";"deep-dish";];
    ["pepperoni";"sausage";];
    ["onions";"peppers";];
    ["mozzarella";"provolone";"parmesan"];
  ] 
 
let pizzas = cartList choices

pizzas |> Seq.iter (printfn "%A")

val cartList : nll:'a list list -> 'a list list

Full name: Script.cartList

val nll : 'a list list

val f0 : ('b -> 'b list list -> 'b list list)

val n : 'b

val nll : 'b list list

Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
  interface IEnumerable
  interface IEnumerable<'T>
  member Head : 'T
  member IsEmpty : bool
  member Item : index:int -> 'T with get
  member Length : int
  member Tail : 'T list
  static member Cons : head:'T * tail:'T list -> 'T list
  static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>

val map : mapping:('T -> 'U) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.map

val nl : 'b list

val h : 'a list

val t : 'a list list

val collect : mapping:('T -> 'U list) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.collect

val n : 'a

val choices : string list list

Full name: Script.choices

val pizzas : string list list

Full name: Script.pizzas

module Seq

from Microsoft.FSharp.Collections

val iter : action:('T -> unit) -> source:seq<'T> -> unit

Full name: Microsoft.FSharp.Collections.Seq.iter

val printfn : format:Printf.TextWriterFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.printfn

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More information

Link:	http://fssnip.net/1e
Posted:	14 years ago
Author:	Neil Carrier
Tags:	cartesian product , list