Solve Sudoku with Solver Foundation and F#

SolverFoundationSudoku

//update the paths below to correctly reference the external resources
#r @"C:\ws\ReferenceAssemblies\Solver30\Microsoft.Solver.Foundation.dll"
#load @"C:\Users\Fai\Documents\Microsoft Solver Foundation\Samples\FSharp\SfsMeasures\SfsWrapper.fs"
;;
open Microsoft.SolverFoundation.Services
open Microsoft.SolverFoundation.SfsWrapper
;;
let sudokuPuzzle = 
    //9x9 matrix as list of 81 cells
    //use 0 for blank cell
    [0; 5; 0;  4; 8; 1;  0; 9; 0;
     8; 0; 0;  0; 0; 0;  0; 0; 2;
     0; 0; 1;  0; 0; 0;  7; 0; 0;

     3; 2; 0;  9; 0; 5;  0; 1; 6;
     0; 0; 0;  0; 3; 0;  0; 0; 0;
     6; 8; 0;  2; 0; 7;  0; 3; 5;

     0; 0; 3;  0; 0; 0;  4; 0; 0;
     5; 0; 0;  0; 0; 0;  0; 0; 1;
     0; 7; 0;  3; 2; 4;  0; 6; 0]

//create model
let ctx = SolverContext.GetContext()
ctx.ClearModel()
let mdl = SfsModel(ctx)

//map puzzle cells to model terms
let p2 = 
    sudokuPuzzle |> List.map(fun cell ->
    match cell with
    | 0 -> mdl.CreateIntRangeVariable(1, 9) :> SfsIntTerm<1> //variable term if 0
    | x when x >= 1 && x <= 9 -> mdl.CreateIntConstant(cell) //constant term otherwise
    | _ -> failwith "cell values should be 0 to 9")

//we bin each cell 3 ways; the row, col and group it belongs to
let binnedCells = p2 |> List.mapi (fun i cell ->
    let row = i / 9 
    let col = i % 9
    let group = (row / 3, col / 3)
    (row, col, group, cell))

//function to add 'all different' constraints for each group
//(the grouping function is provided as input)
let addConstraints groupByFunction aList =
    //function to extract just the cell term from a tuple
    let f2 = fun (row,col,group,cell:SfsIntTerm<1>) -> cell 
    aList
    |> Seq.groupBy groupByFunction 
    |> Seq.map (fun (_,xs) -> xs |> Seq.map f2 |> Seq.toArray |> mdl.AllDifferent) 
    |> Seq.toArray 
    |> mdl.AddConstraints

//for each row, col and group we add the 'all different' constraints
let rowConstraints =   binnedCells |> addConstraints (fun (row,_,_,_) -> row)
let colConstrains =    binnedCells |> addConstraints (fun (_,col,_,_) -> col)
let groupConstraints = binnedCells |> addConstraints (fun (_,_,group,_) -> group)
;;
let sol = mdl.Solve(SolverDirectives.ConstraintProgramming)
if sol.Quality = SolverQuality.Feasible then
    printfn "Solution found:"
    printfn "%A" p2
else
    printfn "No solution found"