(* Title: HOL/Hyperreal/hypreal_arith.ML ID: $Id: hypreal_arith.ML,v 1.14 2005/09/15 23:34:53 huffman Exp $ 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. *) (****Instantiation of the generic linear arithmetic package****) local val real_inj_thms = [thm "star_of_le" RS iffD2, thm "star_of_less" RS iffD2, thm "star_of_eq" RS iffD2]; in val hyprealT = Type("StarDef.star", [HOLogic.realT]); 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, neqE, simpset} => {add_mono_thms = add_mono_thms, mult_mono_thms = mult_mono_thms, inj_thms = inj_thms @ real_inj_thms, lessD = lessD, (*Can't change LA_Data_Ref.lessD: the hypreals are dense!*) neqE = neqE, simpset = simpset}), arith_inj_const ("StarDef.star_of", HOLogic.realT --> hyprealT), Simplifier.change_simpset_of (op addsimprocs) [fast_hypreal_arith_simproc]]; end;