module Y = 
    let permutation xxs =
        let rec ins (acc : _ list list) (x : _) (hh : _ list) (xs : _ list) = 
            match xs with 
            | [] -> (hh @ [x]) :: acc
            | h :: t ->  ins ((hh @ (x :: xs)) :: acc) x (h :: hh) t
        let rec loop (acc : _ list list) xs = 
            match xs with
            | x :: t -> 
                let acc = List.collect (fun a -> ins [] x [] a) acc 
                loop acc t
            | _ -> acc
        loop [[]] xxs
 
    let not_ontop     x (arr : _[]) = arr.[Array.length arr - 1] <> x
    let not_onbottom  x (arr : _[]) = arr.[0] <> x
    let level         x (arr : _[]) = Array.findIndex ((=)x) arr
    let not_near    a b (arr : _[]) = abs (level a arr - level b arr) <> 1
    let higher_than a b (arr : _[]) = level a arr < level b arr
 
    let solver rules mens = 
        for house' in permutation mens do
            let house = List.toArray house'
            if List.forall (fun rule -> rule house) rules
                then printfn "%A" house
 
open Y
 
type Someone = | Baker | Cooper | Fletcher | Miller | Smith
 
[<EntryPoint>]
let main argv = 
    let mens  = [ Baker; Cooper; Fletcher; Miller; Smith ]
    let rules = [ Baker    |> not_ontop    
                  Cooper   |> not_onbottom 
                  Fletcher |> not_ontop    
                  Fletcher |> not_onbottom 
                  Miller   |> higher_than  Cooper
                  Smith    |> not_near   Fletcher 
                  Fletcher |> not_near   Cooper
                ]
    Y.solver rules mens
    0

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