File ‹Tools/SMT/z3_real.ML›

(*  Title:      HOL/Tools/SMT/z3_real.ML
    Author:     Sascha Boehme, TU Muenchen

Z3 setup for reals.
*)

structure Z3_Real: sig end =
struct

fun real_type_parser (SMTLIB.Sym "Real", []) = SOME \<^typ>‹Real.real›
  | real_type_parser _ = NONE

fun real_term_parser (SMTLIB.Dec (i, 0), []) = SOME (HOLogic.mk_number \<^typ>‹Real.real› i)
  | real_term_parser (SMTLIB.Sym "/", [t1, t2]) =
      SOME (\<^term>‹Rings.divide :: real => _› $ t1 $ t2)
  | real_term_parser (SMTLIB.Sym "to_real", [t]) = SOME (\<^term>‹Int.of_int :: int => _› $ t)
  | real_term_parser _ = NONE

fun abstract abs t =
  (case t of
    (c as \<^term>‹Rings.divide :: real => _›) $ t1 $ t2 =>
      abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
  | (c as \<^term>‹Int.of_int :: int => _›) $ t =>
      abs t #>> (fn u => SOME (c $ u))
  | _ => pair NONE)

val _ = Theory.setup (Context.theory_map (
  SMTLIB_Proof.add_type_parser real_type_parser #>
  SMTLIB_Proof.add_term_parser real_term_parser #>
  SMT_Replay_Methods.add_arith_abstracter abstract))

end;