signature Real =
sig
(*
 * Types
 *)
   type real;

(*
 * Binary Operations (infix)
 *)
   val +  : real * real -> real
   and -  : real * real -> real
   and *  : real * real -> real
   and /  : real * real -> real

(*
 * Unary Operations
 *)
   and ~     : real -> real
   and ln    : real -> real
   and sin   : real -> real
   and cos   : real -> real
   and arctan: real -> real
   and abs   : real -> real
   and exp   : real -> real
(*
 * Predicates (infix)
 *)
   and <  : real * real -> bool
   and <= : real * real -> bool
   and >= : real * real -> bool
   and >  : real * real -> bool
end;


structure Real(* : Real *)=
struct
(*
 * Types
 *)
   type real = real;

(*
 * Binary Operations (infix)
 *)
   val op +  = op + : real * real -> real
   and op -  = op - : real * real -> real
   and op *  = op * : real * real -> real
   and op /  = op / : real * real -> real

(*
 * Unary Operations
 *)
   and ~      = ~      : real -> real
   and ln     = ln     : real -> real
   and sin    = sin    : real -> real
   and cos    = cos    : real -> real
   and arctan = arctan : real -> real
   and abs    = abs    : real -> real
   and exp    = exp    : real -> real
(*
 * Predicates (infix)
 *)
   and op <  = op <  : real * real -> bool
   and op <= = op <= : real * real -> bool
   and op >= = op >= : real * real -> bool
   and op >  = op >  : real * real -> bool
end;