(* 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 "Real.real :: 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 "Real.real :: 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 #>
Z3_Replay_Methods.add_arith_abstracter abstract))
end;