(* Title: HOL/Real/rat_arith0.ML ID: $Id: rat_arith.ML,v 1.10 2005/05/04 08:42:52 nipkow Exp $ Author: Lawrence C Paulson Copyright 2004 University of Cambridge Simprocs for common factor cancellation & Rational coefficient handling Instantiation of the generic linear arithmetic package for type rat. *) (****Instantiation of the generic linear arithmetic package for fields****) local val simprocs = field_cancel_numeral_factors val simps = [order_less_irrefl, neg_less_iff_less, True_implies_equals, inst "a" "(number_of ?v)" right_distrib, divide_1, divide_zero_left, times_divide_eq_right, times_divide_eq_left, minus_divide_left RS sym, minus_divide_right RS sym, of_int_0, of_int_1, of_int_add, of_int_minus, of_int_diff, of_int_mult, of_int_of_nat_eq]; in val fast_rat_arith_simproc = Simplifier.simproc (Theory.sign_of(the_context())) "fast_rat_arith" ["(m::rat) < n","(m::rat) <= n", "(m::rat) = n"] Fast_Arith.lin_arith_prover; val nat_inj_thms = [of_nat_le_iff RS iffD2, of_nat_less_iff RS iffD2, of_nat_eq_iff RS iffD2]; val int_inj_thms = [of_int_le_iff RS iffD2, of_int_less_iff RS iffD2, of_int_eq_iff RS iffD2]; val ratT = Type("Rational.rat", []); val rat_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 = int_inj_thms @ inj_thms, lessD = lessD, (*Can't change LA_Data_Ref.lessD: the rats are dense!*) neqE = neqE, simpset = simpset addsimps simps addsimprocs simprocs}), arith_inj_const("IntDef.of_nat", HOLogic.natT --> ratT), arith_inj_const("IntDef.of_int", HOLogic.intT --> ratT), Simplifier.change_simpset_of (op addsimprocs) [fast_rat_arith_simproc]]; end;