How can I correctly return produced sequences in an F# recursive algorithm - functional-programming

Question

As a tutoring exercise I implemented the Knights Tour algorithm in CS and worked fine, after trying to port it to F# I cannot go past the part where I aggregate the resulting sequences of the Knight's path to return to the caller.
The code is this:
let offsets = [|(-2,-1);(-2,1);(-1,-2);(-1,2);(1,-2);(1,2);(2,-1);(2,1)|];
let squareToPair sqr =
(sqr % 8, sqr / 8)
let pairToSquare (col, row) =
row * 8 + col
// Memoizing function taken from Don Syme (http://blogs.msdn.com/b/dsyme/archive/2007/05/31/a-sample-of-the-memoization-pattern-in-f.aspx)
let memoize f =
let cache = ref Map.empty
fun x ->
match (!cache).TryFind(x) with
| Some res -> res
| None ->
let res = f x
cache := (!cache).Add(x,res)
res
let getNextMoves square =
let (col, row) = squareToPair square
offsets
|> Seq.map (fun (colOff, rowOff) -> (col + colOff, row + rowOff))
|> Seq.filter (fun (c, r) -> c >= 0 && c < 8 && r >= 0 && r < 8) // make sure we don't include squares out of the board
|> Seq.map (fun (c, r) -> pairToSquare (c, r))
let getNextMovesMemoized = memoize getNextMoves
let squareToBoard square =
1L <<< square
let squareToBoardMemoized = memoize squareToBoard
let getValidMoves square board =
getNextMovesMemoized square
|> Seq.filter (fun sqr -> ((squareToBoardMemoized sqr) &&& board) = 0L)
// gets all valid moves from a particular square and board state sorted by moves which have less next possible moves
let getValidMovesSorted square board =
getValidMoves square board
|> Seq.sortBy (fun sqr -> (getValidMoves sqr board) |> Seq.length )
let nextMoves = getValidMovesSorted
let sqrToBoard = squareToBoardMemoized
let findPath square =
let board = sqrToBoard square
let rec findPathRec brd sqr sequence = seq {
match brd with
| -1L -> yield sequence
| _ -> for m in nextMoves sqr do yield! findPathRec (brd ||| (sqrToBoard m)) m m::sequence
}
findPathRec board square [square]
let solution = findPath ((4,4) |> pairToSquare) |> Seq.take 1
I am getting the following error:
The type '(int64 -> seq<int>)' is not a type whose values can be enumerated with this syntax, i.e. is not compatible with either seq<_>, IEnumerable<_> or IEnumerable and does not have a GetEnumerator method (using external F# compiler)
I could probably be misunderstanding how this work, but I would expect the results of nextMoves to be seq<_>. Is there a better way of doing this? Am I missing something? Any recommended patterns?
Thanks in advance!

Answer 1

So the problem is that nextMoves has type
val nextMoves : (int -> int64 -> seq<int>)
because it is identical to getValidMovesSorted. You need to supply the board argument

Answer 2

nextMoves is just getValidMovesSorted which takes two arguments (square and board) - now in findPath you only provided one and I guess you wanted to write this
nextMoves sqr board
but then there are more issues in the rest of the code and it's really hard to figure out what you are trying to do
I think you wanted to do something like this:
let findPath square =
let board = sqrToBoard square
let rec findPathRec brd sqr (sequence : int list) =
match brd with
| -1L -> sequence
| _ ->
[
for m in nextMoves sqr board do
yield! findPathRec (brd ||| (sqrToBoard m)) m (m::sequence)
]
this will compile (but will result in an stack-overflow exception)