(* Signature for creating expressions in x and y.
   CS 131
   Based on code by Kurt M. Dresner and Chris Stone
*)

signature EXPR =
sig
    type expr           (* type of expressions *)

    (* Expression creation *)
    (* All expressions should return values in the range [-1,1] when
       x and y also range over [-1,1]. *)

    val build_x      : expr          (* returns the expression for "x" *)
    val build_y      : expr          (* returns the expression for "y" *)

    val build_sinpi  : expr -> expr  (* creates   sine (PI * given expr) *)
    val build_cospi  : expr -> expr  (* creates   cosine (PI * given expr) *)

    val build_avg    : expr * expr -> expr  (* average of the two exprs. *)
    val build_times  : expr * expr -> expr  (* product of the two exprs. *)


    (* Expression evalation at the given (x,y) point *)
    val eval : expr -> real*real -> real

    (* Pretty-printer for expressions *)
    val ppexpr : expr -> unit

    (* A sample reasonably complicated expression *)
    val sampleExpr : expr
end