type binop =
  | Plus
  | Minus
  | Times
  | Div
[@@deriving eq, ord, show]

type projection =
  | First
  | Second
[@@deriving eq, ord, show]

type t =
  | Var of Identifier.t
  | IntConst of int
  | Binop of t * binop * t
  | Pair of t * t
  | Proj of projection * t
  | Fun of Identifier.t * t
  | App of t * t
[@@deriving eq, ord, show]

let rec string_of_term = function
  | Var v -> "Var '" ^ v ^ "'"
  | IntConst n -> string_of_int n
  | Binop (a, b, c) ->
    "Binop ("
    ^ string_of_term a
    ^ " "
    ^ (match b with
       | Plus -> "+"
       | Minus -> "-"
       | Times -> "*"
       | Div -> "/")
    ^ " "
    ^ string_of_term c
    ^ ")"
  | Pair (a, b) -> "Pair (" ^ string_of_term a ^ ", " ^ string_of_term b ^ ")"
  | Proj (a, b) ->
    "Proj ("
    ^ (match a with
       | First -> "fst"
       | Second -> "snd")
    ^ ", "
    ^ string_of_term b
    ^ ")"
  | Fun (a, b) -> "Fun ('" ^ a ^ "', " ^ string_of_term b ^ ")"
  | App (a, b) -> "App (" ^ string_of_term a ^ ", " ^ string_of_term b ^ ")"
;;