(* Author: Carsten Schuermann *)
(* Booleans *)

signature BOOLEAN =
  sig
     datatype Exp
      = Val  of bool
      | And  of Exp * Exp
      | Or   of Exp * Exp
      | Not  of Exp 
      | Nand of Exp * Exp
      | Nor  of Exp * Exp

     val eval : Exp -> bool
  end


structure Boolean : BOOLEAN =
  struct
    datatype Exp
      = Val  of bool
      | And  of Exp * Exp
      | Or   of Exp * Exp
      | Not  of Exp 
      | Nand of Exp * Exp
      | Nor  of Exp * Exp

    fun eval (Val b) = b
      | eval (And (e1, e2)) = eval e1 andalso eval e2
      | eval (Or (e1, e2)) = eval e1 orelse eval e2
      | eval (Not e) = not (eval e)
      | eval (Nand (e1, e2)) = not ((eval e1) andalso (eval e2))
      | eval (Nor (e1, e2)) = not ((eval e1) orelse (eval e2))

  end