Projecting a list of lists efficiently in F#

Question

I have to do projection of a list of lists which returns all combinations with each element from each list. For example:

projection([[1]; [2; 3]]) = [[1; 2]         


        

Answer 1

This function is Haskell's sequence (although sequence is more generic). Translating to F#:

let sequence lss =
    let k l ls = [ for x in l do for xs in ls -> x::xs ]
    List.foldBack k lss [[]]

in interactive:

> test projection 10;;
Real: 00:00:12.240, CPU: 00:00:12.807, GC gen0: 163, gen1: 155, gen2: 4
val it : int = 3628800
> test sequence 10;;
Real: 00:00:06.038, CPU: 00:00:06.021, GC gen0: 75, gen1: 74, gen2: 0
val it : int = 3628800

General idea: avoid explicit recursion in favor to standard combinators (fold, map etc.)