(* Title: HOL/Hyperreal/hypreal_arith.ML
ID: $Id$
Author: Tobias Nipkow, TU Muenchen
Copyright 1999 TU Muenchen
Simprocs for common factor cancellation & Rational coefficient handling
Instantiation of the generic linear arithmetic package for type hypreal.
*)
(*FIXME DELETE*)
val hypreal_mult_less_mono2 = thm"hypreal_mult_less_mono2";
val hypreal_mult_left_mono =
read_instantiate_sg(sign_of (the_context())) [("a","?a::hypreal")] mult_left_mono;
(****Instantiation of the generic linear arithmetic package****)
local
fun cvar(th,_ $ (_ $ _ $ var)) = cterm_of (#sign(rep_thm th)) var;
val hypreal_mult_mono_thms =
[(rotate_prems 1 hypreal_mult_less_mono2,
cvar(hypreal_mult_less_mono2, hd(prems_of hypreal_mult_less_mono2))),
(hypreal_mult_left_mono,
cvar(hypreal_mult_left_mono, hd(tl(prems_of hypreal_mult_left_mono))))]
val real_inj_thms = [hypreal_of_real_le_iff RS iffD2,
hypreal_of_real_less_iff RS iffD2,
hypreal_of_real_eq_iff RS iffD2];
in
val hyprealT = Type("Rational.hypreal", []);
val fast_hypreal_arith_simproc =
Simplifier.simproc (Theory.sign_of (the_context ()))
"fast_hypreal_arith"
["(m::hypreal) < n", "(m::hypreal) <= n", "(m::hypreal) = n"]
Fast_Arith.lin_arith_prover;
val hypreal_arith_setup =
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms @ hypreal_mult_mono_thms,
inj_thms = inj_thms @ real_inj_thms,
lessD = lessD, (*Can't change LA_Data_Ref.lessD: the hypreals are dense!*)
simpset = simpset}),
arith_inj_const ("HyperDef.hypreal_of_real", HOLogic.realT --> hyprealT),
arith_discrete ("HyperDef.hypreal",false),
Simplifier.change_simpset_of (op addsimprocs) [fast_hypreal_arith_simproc]];
end;