signature STLC = sig

  datatype stp =
    TpBase of string (* base type *)
  | TpFun of stp * stp (* function type *)
  | TpTup of stp list (* tuple type *)

  datatype ttm =
    TtmBool of bool (* boolean constant *)
  | TtmInt of int (* integer constant *)
  | TtmStr of string (* string constant *)
  | TtmVar of string (* variable *)
  | TtmIf of ttm * ttm * ttm (* if-then-else term *)
  | TtmOp of string * ttm list (* built-in operator *)
  | TtmLam of string * stp * ttm (* lambda abstraction *)
  | TtmApp of ttm * ttm (* application *)
  | TtmLet of string * ttm * ttm (* let-binding *)
  | TtmLetrec of string * stp * ttm * ttm (* letrec-binding *)
  | TtmTup of ttm list (* tuple *)
  | TtmPro of ttm * int (* projection *)
  | TtmFix of ttm (* fixed point *)
  | TtmAsc of ttm * stp (* ascription *)

  val parseString: string -> ttm

  val typeCheck: ttm -> bool

  datatype utm = (* for untyped term via deBruijn indices *)
    UtmBool of bool
  | UtmInt of int
  | UtmStr of string
  | UtmVar of int
  | UtmIf of utm * utm * utm
  | UtmOp of string * utm list
  | UtmLam of utm
  | UtmApp of utm * utm
  | UtmLet of utm * utm
  | UtmLetrec of utm * utm
  | UtmTup of utm list
  | UtmPro of utm * int
  | UtmFix of utm

  val erase: ttm -> utm

  val evaluate: utm -> utm

end