Based on our grammar, the expression 10 - 4 + 3
can be parsed either as

(10 - 4)    +      3,

or as

10     -      (4 + 3)



type regex =
  | String of string
  | Plus of regex * regex
  | Concat of regex * regex
  | Star of regex

let rec matches str regex =
  match regex with
  | String(s) -> str = s
  | Plus(r1, r2) -> (matches str r1) || (matches str r2)
  | Concat(r1, r2) -> Split str in all possible ways into two strings, str = str1 . str2
                      Check if (matches str1 r1) and (matches str2 r2)
                      Return yes if such a split exists.
  | Star(r1) -> str = empty or (matches str r1)
                Problem: What about iteration?
                str = empty, or
                  split str in all possible ways into two strings, str = str1 . str2, with str1 non-empty
                  Check if (matches str1 r1) and (matches str2 regex)
                  Note: regex refers to the full regular expression originally passed as argument
                  Return yes if such a split exists.