F# syntax with sets and updating - algorithm

Question

In F# im trying to remove an occurence in the set if a condition is met, however it's not really working they way i'd like it to.

Answer 1

The trick to removing elements from a set is the function Set.filter, which takes a function as an argument - filter will feed in every value of the set to your function, and add it to a new set if the function returns true. An example implementation might be:
let filter f (original : Set<'T>) =
set [ for value in original do if f value then yield value ]
which has type filter : ('T -> bool) -> Set<'T> -> Set<'T>. An example of using it would be
filter (fun x -> x % 2 = 0) (set [ 1; 2; 3; 4; 5 ])
This filters the set for even numbers, so the return value would be set [ 2; 4 ].
I'm not entirely sure what problem you're having exactly, but here is a solution to the game Mastermind using Knuth's algorithm, albeit with a random starting guess, rather than his choice of "1122".
I thought it was quite a nice exercise, though writing the checkGuess function was the hardest part of it for me!
You can run a test by opening this in F# interactive by running the function playMastermind (), which will show you its guesses.
/// The colours that pegs are allowed to be.
type Peg = Blue | Red | Green | Yellow | Purple | Brown
/// A shared instance of the System.Random () class for all the random number
/// generators.
let private rnd = new System.Random ()
/// Make a random set of four peg colours.
let randomGuess () =
let randomPeg () =
match rnd.Next(1, 6) with
| 1 -> Blue
| 2 -> Red
| 3 -> Green
| 4 -> Yellow
| 5 -> Purple
| 6 -> Brown
| _ -> failwith "Random number generation failed."
[ randomPeg (); randomPeg (); randomPeg (); randomPeg () ]
/// Iterate over the colours to make all of the possible combinations.
let allPossibles =
let colours = [ Blue; Red; Green; Yellow; Purple; Brown]
set [ for a in colours do for b in colours do for c in colours do for d in colours -> [ a; b; c; d ] ]
/// Get the number of white and black pegs when comparing solution to guess.
let checkGuess solution guess =
/// Create a map of (colour -> count).
let toMap = List.countBy id >> Map.ofList
/// Compute how many pegs' colours are shared in the guesses.
let mapIntersect map1 map2 =
let overlap peg count =
match Map.tryFind peg map2 with
| None -> 0
| Some num -> min num count
Map.fold (fun acc peg count -> acc + overlap peg count) 0 map1
/// Simply compare to see if each peg is in the correct place.
let blacks = List.map2 (fun x y -> if x = y then 1 else 0) solution guess |> List.sum
// The number of pegs of the right colour but the wrong location is the
// same as the total number of pegs of the right colour subtract the ones
// that are also in the right place.
let whites = mapIntersect (toMap solution) (toMap guess) - blacks
whites, blacks
/// Get a random element of a set.
let randomSetElement set =
let arr = Set.toArray set
arr.[rnd.Next (Array.length arr)]
let playMastermind () =
// This creates a closure so we can check our guess against the solution,
// without storing the actual value of the solution.
let checkAnswer = checkGuess (randomGuess ())
let rec loop turnCount remaining =
if Set.count remaining = 1 then
let answer = Set.maxElement remaining
printfn "The answer is %A, which I calculated in %d turns." answer (turnCount - 1)
else
let guess = randomSetElement remaining
let (whites, blacks) = checkAnswer guess
printfn "On turn %d I guessed %A, which gave %d white pins and %d black pins." turnCount guess whites blacks
/// Remove all possibilities from the solution that wouldn't give the
/// same numbers of white and black pins and continue.
loop (turnCount + 1) (Set.filter (fun possible -> (whites, blacks) = checkGuess possible guess) remaining)
// Play the game!
loop 1 allPossibles

Answer 2

I'd make this a comment, but it's too long, so it needs to be an answer instead, even though it's not a complete answer to your problem.
One problem with your code, as it is now, is this section:
for candidate in candidateSet do
let scString = candidate.ToString()
let mutable secretList = []
for i = 0 to 3 do
let digit = (int scString.[i])-(int '0')
secretList <- secretList # [digit]
let tempCode = List.map (fun x -> numberToCodeColorPlus (x)) secretList
//Validate works and returns a peg set (b,w)..e.g. (0,0)
let secretCodePegs = validate guess tempCode
if secretCodePegs <> guessPegs then
candidateSet <- Set.remove candidate candidateSet
F#, like Python, uses indentation to denote blocks. So that let secretCodePegs = validate guess tempCode line is outside the for loop, not inside the for loop the way you clearly intended it to be. And the if secretCodePegs <> guessPegs then line that follows it, as far as F# is concerned, is part of a new block, and not part of the for loop any longer (because the let secretCodePegs = ... line ended the for loop). All you need to do is indent the let secretCodePegs = ... line by one level, and your code will work. In other words, that section should have looked like this:
for candidate in candidateSet do
let scString = candidate.ToString()
let mutable secretList = []
for i = 0 to 3 do
let digit = (int scString.[i])-(int '0')
secretList <- secretList # [digit]
let tempCode = List.map (fun x -> numberToCodeColorPlus (x)) secretList
//Validate works and returns a peg set (b,w)..e.g. (0,0)
let secretCodePegs = validate guess tempCode
if secretCodePegs <> guessPegs then
candidateSet <- Set.remove candidate candidateSet