author | wenzelm |
Tue, 31 Jul 2007 19:40:24 +0200 | |
changeset 24093 | 5d0ecd0c8f3c |
parent 23346 | 1517207ec8b9 |
child 24196 | f1dbfd7e3223 |
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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@{thm of_int_0}, @{thm of_int_1}, @{thm of_int_add}, |
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@{thm of_int_minus}, @{thm of_int_diff}, |
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@{thm of_int_mult}, @{thm of_int_of_nat_eq}] |
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val nat_inj_thms = [@{thm of_nat_le_iff} RS iffD2, |
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@{thm 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 = [@{thm of_int_le_iff} RS iffD2, |
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@{thm 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 ratT = Type ("Rational.rat", []) |
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val rat_arith_setup = |
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LinArith.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 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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end; |