(* Title: HOL/Real/rat_arith0.ML
ID: $Id$
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) #>
(fn thy => (change_simpset_of thy (fn ss => ss addsimprocs [fast_rat_arith_simproc]); thy));
end;