author | haftmann |
Thu, 29 Mar 2007 14:21:45 +0200 | |
changeset 22548 | 6ce4bddf3bcb |
parent 21243 | afffe1f72143 |
child 22803 | 5129e02f4df2 |
permissions | -rw-r--r-- |
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(* Title: HOL/Real/rat_arith.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson |
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Copyright 2004 University of Cambridge |
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Simprocs for common factor cancellation & Rational coefficient handling |
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Instantiation of the generic linear arithmetic package for type rat. |
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*) |
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local |
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val simprocs = field_cancel_numeral_factors |
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val simps = [@{thm order_less_irrefl}, @{thm neg_less_iff_less}, @{thm True_implies_equals}, |
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inst "a" "(number_of ?v)" @{thm right_distrib}, |
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@{thm divide_1}, @{thm divide_zero_left}, |
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@{thm times_divide_eq_right}, @{thm times_divide_eq_left}, |
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@{thm minus_divide_left} RS sym, @{thm minus_divide_right} RS sym, |
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of_int_0, of_int_1, of_int_add, of_int_minus, of_int_diff, |
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of_int_mult, of_int_of_nat_eq] |
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val nat_inj_thms = [of_nat_le_iff RS iffD2, |
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of_nat_eq_iff RS iffD2] |
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(* not needed because x < (y::nat) can be rewritten as Suc x <= y: |
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of_nat_less_iff RS iffD2 *) |
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val int_inj_thms = [of_int_le_iff RS iffD2, |
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of_int_eq_iff RS iffD2] |
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(* not needed because x < (y::int) can be rewritten as x + 1 <= y: |
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of_int_less_iff RS iffD2 *) |
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in |
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val fast_rat_arith_simproc = Simplifier.simproc @{theory} |
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"fast_rat_arith" ["(m::rat) < n","(m::rat) <= n", "(m::rat) = n"] |
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Fast_Arith.lin_arith_prover |
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val ratT = Type ("Rational.rat", []) |
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val rat_arith_setup = |
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Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} => |
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{add_mono_thms = add_mono_thms, |
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mult_mono_thms = mult_mono_thms, |
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inj_thms = int_inj_thms @ nat_inj_thms @ inj_thms, |
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lessD = lessD, (*Can't change LA_Data_Ref.lessD: the rats are dense!*) |
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neqE = neqE, |
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simpset = simpset addsimps simps |
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addsimprocs simprocs}) #> |
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arith_inj_const ("Nat.of_nat", HOLogic.natT --> ratT) #> |
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arith_inj_const ("IntDef.of_int", HOLogic.intT --> ratT) #> |
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(fn thy => (change_simpset_of thy (fn ss => ss addsimprocs [fast_rat_arith_simproc]); thy)) |
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end; |