Problem 3: Option types and nested matching

For winner.

The option type

OCaml has no null. "Maybe a value" gets its own type.

type 'a option =
  | None
  | Some of 'a

Think of it as a box. None is an empty box, Some x holds x. line_winner (Problem 2) already returns a player option: Some p when a line is won by p, None otherwise. winner has the same return type, answering for the whole board instead of one line.

Matching inside a match arm

Sometimes the natural way to combine several sub-results is a match whose branches themselves contain another match. Walking a list of attempts and asking each one "did you succeed?" is a good example.

let rec first_success attempts =
  match attempts with
  | [] -> None
  | attempt :: rest ->
    (match run attempt with
     | Some result -> Some result   (* this one worked - stop here *)
     | None -> first_success rest)  (* try the next one *)

Read the outer match as the usual list recursion: base case [], recursive case attempt :: rest. Inside the recursive case, a second match asks run about just this one attempt. If it succeeded, that's the overall answer. If not, recurse on the rest of the list. Parenthesizing the inner match keeps it scoped to that one arm.