author | paulson |
Tue, 27 Jan 2004 15:39:51 +0100 | |
changeset 14365 | 3d4df8c166ae |
child 14368 | 2763da611ad9 |
permissions | -rw-r--r-- |
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(* Title: HOL/Real/rat_arith0.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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(*FIXME DELETE*) |
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val rat_mult_strict_left_mono = |
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read_instantiate_sg(sign_of (the_context())) [("a","?a::rat")] mult_strict_left_mono; |
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val rat_mult_left_mono = |
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read_instantiate_sg(sign_of (the_context())) [("a","?a::rat")] mult_left_mono; |
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val rat_number_of_def = thm "rat_number_of_def"; |
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val diff_rat_def = thm "diff_rat_def"; |
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|
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val rat_of_int_zero = thm "rat_of_int_zero"; |
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val rat_of_int_one = thm "rat_of_int_one"; |
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val rat_of_int_add_distrib = thm "rat_of_int_add_distrib"; |
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val rat_of_int_minus_distrib = thm "rat_of_int_minus_distrib"; |
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val rat_of_int_diff_distrib = thm "rat_of_int_diff_distrib"; |
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val rat_of_int_mult_distrib = thm "rat_of_int_mult_distrib"; |
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val rat_inject = thm "rat_inject"; |
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val rat_of_int_zero_cancel = thm "rat_of_int_zero_cancel"; |
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val rat_of_int_less_iff = thm "rat_of_int_less_iff"; |
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val rat_of_int_le_iff = thm "rat_of_int_le_iff"; |
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|
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val number_of_rat = thm "number_of_rat"; |
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val rat_numeral_0_eq_0 = thm "rat_numeral_0_eq_0"; |
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val rat_numeral_1_eq_1 = thm "rat_numeral_1_eq_1"; |
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val add_rat_number_of = thm "add_rat_number_of"; |
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val minus_rat_number_of = thm "minus_rat_number_of"; |
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val diff_rat_number_of = thm "diff_rat_number_of"; |
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val mult_rat_number_of = thm "mult_rat_number_of"; |
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val rat_mult_2 = thm "rat_mult_2"; |
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val rat_mult_2_right = thm "rat_mult_2_right"; |
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val eq_rat_number_of = thm "eq_rat_number_of"; |
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val less_rat_number_of = thm "less_rat_number_of"; |
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val rat_minus_1_eq_m1 = thm "rat_minus_1_eq_m1"; |
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val rat_mult_minus1 = thm "rat_mult_minus1"; |
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val rat_mult_minus1_right = thm "rat_mult_minus1_right"; |
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val rat_add_number_of_left = thm "rat_add_number_of_left"; |
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val rat_mult_number_of_left = thm "rat_mult_number_of_left"; |
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val rat_add_number_of_diff1 = thm "rat_add_number_of_diff1"; |
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val rat_add_number_of_diff2 = thm "rat_add_number_of_diff2"; |
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|
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val rat_add_0_left = thm "rat_add_0_left"; |
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val rat_add_0_right = thm "rat_add_0_right"; |
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val rat_mult_1_left = thm "rat_mult_1_left"; |
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val rat_mult_1_right = thm "rat_mult_1_right"; |
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|
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(*Maps 0 to Numeral0 and 1 to Numeral1 and -(Numeral1) to -1*) |
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val rat_numeral_ss = |
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HOL_ss addsimps [rat_numeral_0_eq_0 RS sym, rat_numeral_1_eq_1 RS sym, |
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rat_minus_1_eq_m1]; |
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|
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fun rename_numerals th = |
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asm_full_simplify rat_numeral_ss (Thm.transfer (the_context ()) th); |
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structure Rat_Numeral_Simprocs = |
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struct |
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|
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(*Maps 0 to Numeral0 and 1 to Numeral1 so that arithmetic in simprocs |
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isn't complicated by the abstract 0 and 1.*) |
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val numeral_syms = [rat_numeral_0_eq_0 RS sym, rat_numeral_1_eq_1 RS sym]; |
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|
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(*Utilities*) |
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|
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val ratT = Type("Rational.rat", []); |
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|
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fun mk_numeral n = HOLogic.number_of_const ratT $ HOLogic.mk_bin n; |
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|
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(*Decodes a binary rat constant, or 0, 1*) |
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val dest_numeral = Int_Numeral_Simprocs.dest_numeral; |
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val find_first_numeral = Int_Numeral_Simprocs.find_first_numeral; |
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|
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val zero = mk_numeral 0; |
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val mk_plus = HOLogic.mk_binop "op +"; |
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|
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val uminus_const = Const ("uminus", ratT --> ratT); |
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|
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(*Thus mk_sum[t] yields t+0; longer sums don't have a trailing zero*) |
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fun mk_sum [] = zero |
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| mk_sum [t,u] = mk_plus (t, u) |
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| mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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|
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(*this version ALWAYS includes a trailing zero*) |
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fun long_mk_sum [] = zero |
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| long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
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|
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val dest_plus = HOLogic.dest_bin "op +" ratT; |
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|
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(*decompose additions AND subtractions as a sum*) |
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fun dest_summing (pos, Const ("op +", _) $ t $ u, ts) = |
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dest_summing (pos, t, dest_summing (pos, u, ts)) |
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| dest_summing (pos, Const ("op -", _) $ t $ u, ts) = |
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dest_summing (pos, t, dest_summing (not pos, u, ts)) |
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| dest_summing (pos, t, ts) = |
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if pos then t::ts else uminus_const$t :: ts; |
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|
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fun dest_sum t = dest_summing (true, t, []); |
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|
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val mk_diff = HOLogic.mk_binop "op -"; |
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val dest_diff = HOLogic.dest_bin "op -" ratT; |
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|
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val one = mk_numeral 1; |
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val mk_times = HOLogic.mk_binop "op *"; |
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|
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fun mk_prod [] = one |
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| mk_prod [t] = t |
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| mk_prod (t :: ts) = if t = one then mk_prod ts |
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else mk_times (t, mk_prod ts); |
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parents:
diff
changeset
|
119 |
|
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diff
changeset
|
120 |
val dest_times = HOLogic.dest_bin "op *" ratT; |
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parents:
diff
changeset
|
121 |
|
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parents:
diff
changeset
|
122 |
fun dest_prod t = |
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parents:
diff
changeset
|
123 |
let val (t,u) = dest_times t |
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parents:
diff
changeset
|
124 |
in dest_prod t @ dest_prod u end |
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parents:
diff
changeset
|
125 |
handle TERM _ => [t]; |
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parents:
diff
changeset
|
126 |
|
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parents:
diff
changeset
|
127 |
(*DON'T do the obvious simplifications; that would create special cases*) |
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parents:
diff
changeset
|
128 |
fun mk_coeff (k, ts) = mk_times (mk_numeral k, ts); |
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parents:
diff
changeset
|
129 |
|
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parents:
diff
changeset
|
130 |
(*Express t as a product of (possibly) a numeral with other sorted terms*) |
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parents:
diff
changeset
|
131 |
fun dest_coeff sign (Const ("uminus", _) $ t) = dest_coeff (~sign) t |
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parents:
diff
changeset
|
132 |
| dest_coeff sign t = |
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parents:
diff
changeset
|
133 |
let val ts = sort Term.term_ord (dest_prod t) |
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parents:
diff
changeset
|
134 |
val (n, ts') = find_first_numeral [] ts |
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parents:
diff
changeset
|
135 |
handle TERM _ => (1, ts) |
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parents:
diff
changeset
|
136 |
in (sign*n, mk_prod ts') end; |
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parents:
diff
changeset
|
137 |
|
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parents:
diff
changeset
|
138 |
(*Find first coefficient-term THAT MATCHES u*) |
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parents:
diff
changeset
|
139 |
fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
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parents:
diff
changeset
|
140 |
| find_first_coeff past u (t::terms) = |
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parents:
diff
changeset
|
141 |
let val (n,u') = dest_coeff 1 t |
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parents:
diff
changeset
|
142 |
in if u aconv u' then (n, rev past @ terms) |
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parents:
diff
changeset
|
143 |
else find_first_coeff (t::past) u terms |
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parents:
diff
changeset
|
144 |
end |
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parents:
diff
changeset
|
145 |
handle TERM _ => find_first_coeff (t::past) u terms; |
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parents:
diff
changeset
|
146 |
|
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parents:
diff
changeset
|
147 |
|
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parents:
diff
changeset
|
148 |
(*Simplify Numeral0+n, n+Numeral0, Numeral1*n, n*Numeral1*) |
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parents:
diff
changeset
|
149 |
val add_0s = map rename_numerals [rat_add_0_left, rat_add_0_right]; |
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parents:
diff
changeset
|
150 |
val mult_1s = map rename_numerals [rat_mult_1_left, rat_mult_1_right] @ |
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parents:
diff
changeset
|
151 |
[rat_mult_minus1, rat_mult_minus1_right]; |
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parents:
diff
changeset
|
152 |
|
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parents:
diff
changeset
|
153 |
(*To perform binary arithmetic*) |
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parents:
diff
changeset
|
154 |
val bin_simps = |
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parents:
diff
changeset
|
155 |
[rat_numeral_0_eq_0 RS sym, rat_numeral_1_eq_1 RS sym, |
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parents:
diff
changeset
|
156 |
add_rat_number_of, rat_add_number_of_left, minus_rat_number_of, |
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parents:
diff
changeset
|
157 |
diff_rat_number_of, mult_rat_number_of, rat_mult_number_of_left] @ |
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paulson
parents:
diff
changeset
|
158 |
bin_arith_simps @ bin_rel_simps; |
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paulson
parents:
diff
changeset
|
159 |
|
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paulson
parents:
diff
changeset
|
160 |
(*Binary arithmetic BUT NOT ADDITION since it may collapse adjacent terms |
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parents:
diff
changeset
|
161 |
during re-arrangement*) |
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parents:
diff
changeset
|
162 |
val non_add_bin_simps = |
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parents:
diff
changeset
|
163 |
bin_simps \\ [rat_add_number_of_left, add_rat_number_of]; |
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paulson
parents:
diff
changeset
|
164 |
|
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paulson
parents:
diff
changeset
|
165 |
(*To evaluate binary negations of coefficients*) |
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parents:
diff
changeset
|
166 |
val rat_minus_simps = NCons_simps @ |
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parents:
diff
changeset
|
167 |
[rat_minus_1_eq_m1, minus_rat_number_of, |
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paulson
parents:
diff
changeset
|
168 |
bin_minus_1, bin_minus_0, bin_minus_Pls, bin_minus_Min, |
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paulson
parents:
diff
changeset
|
169 |
bin_pred_1, bin_pred_0, bin_pred_Pls, bin_pred_Min]; |
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paulson
parents:
diff
changeset
|
170 |
|
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paulson
parents:
diff
changeset
|
171 |
(*To let us treat subtraction as addition*) |
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paulson
parents:
diff
changeset
|
172 |
val diff_simps = [diff_rat_def, minus_add_distrib, minus_minus]; |
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paulson
parents:
diff
changeset
|
173 |
|
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paulson
parents:
diff
changeset
|
174 |
(*to extract again any uncancelled minuses*) |
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paulson
parents:
diff
changeset
|
175 |
val rat_minus_from_mult_simps = |
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paulson
parents:
diff
changeset
|
176 |
[minus_minus, minus_mult_left RS sym, minus_mult_right RS sym]; |
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paulson
parents:
diff
changeset
|
177 |
|
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paulson
parents:
diff
changeset
|
178 |
(*combine unary minus with numeric literals, however nested within a product*) |
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paulson
parents:
diff
changeset
|
179 |
val rat_mult_minus_simps = |
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paulson
parents:
diff
changeset
|
180 |
[mult_assoc, minus_mult_left, minus_mult_commute]; |
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paulson
parents:
diff
changeset
|
181 |
|
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paulson
parents:
diff
changeset
|
182 |
(*Apply the given rewrite (if present) just once*) |
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paulson
parents:
diff
changeset
|
183 |
fun trans_tac None = all_tac |
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parents:
diff
changeset
|
184 |
| trans_tac (Some th) = ALLGOALS (rtac (th RS trans)); |
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paulson
parents:
diff
changeset
|
185 |
|
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paulson
parents:
diff
changeset
|
186 |
(*Final simplification: cancel + and * *) |
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paulson
parents:
diff
changeset
|
187 |
val simplify_meta_eq = |
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paulson
parents:
diff
changeset
|
188 |
Int_Numeral_Simprocs.simplify_meta_eq |
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paulson
parents:
diff
changeset
|
189 |
[add_0, add_0_right, |
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paulson
parents:
diff
changeset
|
190 |
mult_zero_left, mult_zero_right, mult_1, mult_1_right]; |
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paulson
parents:
diff
changeset
|
191 |
|
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paulson
parents:
diff
changeset
|
192 |
fun prep_simproc (name, pats, proc) = |
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paulson
parents:
diff
changeset
|
193 |
Simplifier.simproc (Theory.sign_of (the_context ())) name pats proc; |
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paulson
parents:
diff
changeset
|
194 |
|
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paulson
parents:
diff
changeset
|
195 |
structure CancelNumeralsCommon = |
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parents:
diff
changeset
|
196 |
struct |
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paulson
parents:
diff
changeset
|
197 |
val mk_sum = mk_sum |
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paulson
parents:
diff
changeset
|
198 |
val dest_sum = dest_sum |
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paulson
parents:
diff
changeset
|
199 |
val mk_coeff = mk_coeff |
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paulson
parents:
diff
changeset
|
200 |
val dest_coeff = dest_coeff 1 |
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paulson
parents:
diff
changeset
|
201 |
val find_first_coeff = find_first_coeff [] |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
202 |
val trans_tac = trans_tac |
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paulson
parents:
diff
changeset
|
203 |
val norm_tac = |
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paulson
parents:
diff
changeset
|
204 |
ALLGOALS (simp_tac (HOL_ss addsimps add_0s@mult_1s@diff_simps@ |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
205 |
rat_minus_simps@add_ac)) |
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paulson
parents:
diff
changeset
|
206 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps non_add_bin_simps@rat_mult_minus_simps)) |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
207 |
THEN ALLGOALS |
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paulson
parents:
diff
changeset
|
208 |
(simp_tac (HOL_ss addsimps rat_minus_from_mult_simps@ |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
209 |
add_ac@mult_ac)) |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
210 |
val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
211 |
val simplify_meta_eq = simplify_meta_eq |
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paulson
parents:
diff
changeset
|
212 |
end; |
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paulson
parents:
diff
changeset
|
213 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
214 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
215 |
structure EqCancelNumerals = CancelNumeralsFun |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
216 |
(open CancelNumeralsCommon |
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paulson
parents:
diff
changeset
|
217 |
val prove_conv = Bin_Simprocs.prove_conv |
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paulson
parents:
diff
changeset
|
218 |
val mk_bal = HOLogic.mk_eq |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
219 |
val dest_bal = HOLogic.dest_bin "op =" ratT |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
220 |
val bal_add1 = eq_add_iff1 RS trans |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
221 |
val bal_add2 = eq_add_iff2 RS trans |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
222 |
); |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
223 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
224 |
structure LessCancelNumerals = CancelNumeralsFun |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
225 |
(open CancelNumeralsCommon |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
226 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
227 |
val mk_bal = HOLogic.mk_binrel "op <" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
228 |
val dest_bal = HOLogic.dest_bin "op <" ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
229 |
val bal_add1 = less_add_iff1 RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
230 |
val bal_add2 = less_add_iff2 RS trans |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
231 |
); |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
232 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
233 |
structure LeCancelNumerals = CancelNumeralsFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
234 |
(open CancelNumeralsCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
235 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
236 |
val mk_bal = HOLogic.mk_binrel "op <=" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
237 |
val dest_bal = HOLogic.dest_bin "op <=" ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
238 |
val bal_add1 = le_add_iff1 RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
239 |
val bal_add2 = le_add_iff2 RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
240 |
); |
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paulson
parents:
diff
changeset
|
241 |
|
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paulson
parents:
diff
changeset
|
242 |
val cancel_numerals = |
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paulson
parents:
diff
changeset
|
243 |
map prep_simproc |
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paulson
parents:
diff
changeset
|
244 |
[("rateq_cancel_numerals", |
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paulson
parents:
diff
changeset
|
245 |
["(l::rat) + m = n", "(l::rat) = m + n", |
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paulson
parents:
diff
changeset
|
246 |
"(l::rat) - m = n", "(l::rat) = m - n", |
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paulson
parents:
diff
changeset
|
247 |
"(l::rat) * m = n", "(l::rat) = m * n"], |
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paulson
parents:
diff
changeset
|
248 |
EqCancelNumerals.proc), |
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paulson
parents:
diff
changeset
|
249 |
("ratless_cancel_numerals", |
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paulson
parents:
diff
changeset
|
250 |
["(l::rat) + m < n", "(l::rat) < m + n", |
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paulson
parents:
diff
changeset
|
251 |
"(l::rat) - m < n", "(l::rat) < m - n", |
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paulson
parents:
diff
changeset
|
252 |
"(l::rat) * m < n", "(l::rat) < m * n"], |
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paulson
parents:
diff
changeset
|
253 |
LessCancelNumerals.proc), |
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paulson
parents:
diff
changeset
|
254 |
("ratle_cancel_numerals", |
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paulson
parents:
diff
changeset
|
255 |
["(l::rat) + m <= n", "(l::rat) <= m + n", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
256 |
"(l::rat) - m <= n", "(l::rat) <= m - n", |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
257 |
"(l::rat) * m <= n", "(l::rat) <= m * n"], |
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paulson
parents:
diff
changeset
|
258 |
LeCancelNumerals.proc)]; |
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paulson
parents:
diff
changeset
|
259 |
|
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paulson
parents:
diff
changeset
|
260 |
|
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paulson
parents:
diff
changeset
|
261 |
structure CombineNumeralsData = |
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paulson
parents:
diff
changeset
|
262 |
struct |
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paulson
parents:
diff
changeset
|
263 |
val add = op + : int*int -> int |
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paulson
parents:
diff
changeset
|
264 |
val mk_sum = long_mk_sum (*to work for e.g. 2*x + 3*x *) |
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paulson
parents:
diff
changeset
|
265 |
val dest_sum = dest_sum |
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paulson
parents:
diff
changeset
|
266 |
val mk_coeff = mk_coeff |
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paulson
parents:
diff
changeset
|
267 |
val dest_coeff = dest_coeff 1 |
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paulson
parents:
diff
changeset
|
268 |
val left_distrib = combine_common_factor RS trans |
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paulson
parents:
diff
changeset
|
269 |
val prove_conv = Bin_Simprocs.prove_conv_nohyps |
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paulson
parents:
diff
changeset
|
270 |
val trans_tac = trans_tac |
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paulson
parents:
diff
changeset
|
271 |
val norm_tac = |
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paulson
parents:
diff
changeset
|
272 |
ALLGOALS (simp_tac (HOL_ss addsimps numeral_syms@add_0s@mult_1s@ |
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paulson
parents:
diff
changeset
|
273 |
diff_simps@rat_minus_simps@add_ac)) |
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paulson
parents:
diff
changeset
|
274 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps non_add_bin_simps@rat_mult_minus_simps)) |
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paulson
parents:
diff
changeset
|
275 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps rat_minus_from_mult_simps@ |
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paulson
parents:
diff
changeset
|
276 |
add_ac@mult_ac)) |
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paulson
parents:
diff
changeset
|
277 |
val numeral_simp_tac = ALLGOALS |
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paulson
parents:
diff
changeset
|
278 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
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paulson
parents:
diff
changeset
|
279 |
val simplify_meta_eq = |
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paulson
parents:
diff
changeset
|
280 |
Int_Numeral_Simprocs.simplify_meta_eq (add_0s@mult_1s) |
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paulson
parents:
diff
changeset
|
281 |
end; |
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paulson
parents:
diff
changeset
|
282 |
|
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paulson
parents:
diff
changeset
|
283 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
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paulson
parents:
diff
changeset
|
284 |
|
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paulson
parents:
diff
changeset
|
285 |
val combine_numerals = |
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paulson
parents:
diff
changeset
|
286 |
prep_simproc ("rat_combine_numerals", ["(i::rat) + j", "(i::rat) - j"], CombineNumerals.proc); |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
287 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
288 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
289 |
(** Declarations for ExtractCommonTerm **) |
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paulson
parents:
diff
changeset
|
290 |
|
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paulson
parents:
diff
changeset
|
291 |
(*this version ALWAYS includes a trailing one*) |
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paulson
parents:
diff
changeset
|
292 |
fun long_mk_prod [] = one |
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paulson
parents:
diff
changeset
|
293 |
| long_mk_prod (t :: ts) = mk_times (t, mk_prod ts); |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
294 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
295 |
(*Find first term that matches u*) |
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paulson
parents:
diff
changeset
|
296 |
fun find_first past u [] = raise TERM("find_first", []) |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
297 |
| find_first past u (t::terms) = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
298 |
if u aconv t then (rev past @ terms) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
299 |
else find_first (t::past) u terms |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
300 |
handle TERM _ => find_first (t::past) u terms; |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
301 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
302 |
(*Final simplification: cancel + and * *) |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
303 |
fun cancel_simplify_meta_eq cancel_th th = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
304 |
Int_Numeral_Simprocs.simplify_meta_eq |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
305 |
[rat_mult_1_left, rat_mult_1_right] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
306 |
(([th, cancel_th]) MRS trans); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
307 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
308 |
(*** Making constant folding work for 0 and 1 too ***) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
309 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
310 |
structure RatAbstractNumeralsData = |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
311 |
struct |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
312 |
val dest_eq = HOLogic.dest_eq o HOLogic.dest_Trueprop o concl_of |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
313 |
val is_numeral = Bin_Simprocs.is_numeral |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
314 |
val numeral_0_eq_0 = rat_numeral_0_eq_0 |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
315 |
val numeral_1_eq_1 = rat_numeral_1_eq_1 |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
316 |
val prove_conv = Bin_Simprocs.prove_conv_nohyps_novars |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
317 |
fun norm_tac simps = ALLGOALS (simp_tac (HOL_ss addsimps simps)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
318 |
val simplify_meta_eq = Bin_Simprocs.simplify_meta_eq |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
319 |
end |
3d4df8c166ae
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paulson
parents:
diff
changeset
|
320 |
|
3d4df8c166ae
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paulson
parents:
diff
changeset
|
321 |
structure RatAbstractNumerals = AbstractNumeralsFun (RatAbstractNumeralsData) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
322 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
323 |
(*For addition, we already have rules for the operand 0. |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
324 |
Multiplication is omitted because there are already special rules for |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
325 |
both 0 and 1 as operands. Unary minus is trivial, just have - 1 = -1. |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
326 |
For the others, having three patterns is a compromise between just having |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
327 |
one (many spurious calls) and having nine (just too many!) *) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
328 |
val eval_numerals = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
329 |
map prep_simproc |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
330 |
[("rat_add_eval_numerals", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
331 |
["(m::rat) + 1", "(m::rat) + number_of v"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
332 |
RatAbstractNumerals.proc add_rat_number_of), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
333 |
("rat_diff_eval_numerals", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
334 |
["(m::rat) - 1", "(m::rat) - number_of v"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
335 |
RatAbstractNumerals.proc diff_rat_number_of), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
336 |
("rat_eq_eval_numerals", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
337 |
["(m::rat) = 0", "(m::rat) = 1", "(m::rat) = number_of v"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
338 |
RatAbstractNumerals.proc eq_rat_number_of), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
339 |
("rat_less_eval_numerals", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
340 |
["(m::rat) < 0", "(m::rat) < 1", "(m::rat) < number_of v"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
341 |
RatAbstractNumerals.proc less_rat_number_of), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
342 |
("rat_le_eval_numerals", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
343 |
["(m::rat) <= 0", "(m::rat) <= 1", "(m::rat) <= number_of v"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
344 |
RatAbstractNumerals.proc le_number_of_eq_not_less)] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
345 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
346 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
347 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
348 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
349 |
Addsimprocs Rat_Numeral_Simprocs.eval_numerals; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
350 |
Addsimprocs Rat_Numeral_Simprocs.cancel_numerals; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
351 |
Addsimprocs [Rat_Numeral_Simprocs.combine_numerals]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
352 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
353 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
354 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
355 |
(** Constant folding for rat plus and times **) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
356 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
357 |
(*We do not need |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
358 |
structure Rat_Plus_Assoc = Assoc_Fold (Rat_Plus_Assoc_Data); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
359 |
because combine_numerals does the same thing*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
360 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
361 |
structure Rat_Times_Assoc_Data : ASSOC_FOLD_DATA = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
362 |
struct |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
363 |
val ss = HOL_ss |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
364 |
val eq_reflection = eq_reflection |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
365 |
val sg_ref = Sign.self_ref (Theory.sign_of (the_context ())) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
366 |
val T = Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
367 |
val plus = Const ("op *", [Rat_Numeral_Simprocs.ratT,Rat_Numeral_Simprocs.ratT] ---> Rat_Numeral_Simprocs.ratT) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
368 |
val add_ac = mult_ac |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
369 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
370 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
371 |
structure Rat_Times_Assoc = Assoc_Fold (Rat_Times_Assoc_Data); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
372 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
373 |
Addsimprocs [Rat_Times_Assoc.conv]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
374 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
375 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
376 |
(****Common factor cancellation****) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
377 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
378 |
(*To quote from Provers/Arith/cancel_numeral_factor.ML: |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
379 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
380 |
This simproc Cancels common coefficients in balanced expressions: |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
381 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
382 |
u*#m ~~ u'*#m' == #n*u ~~ #n'*u' |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
383 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
384 |
where ~~ is an appropriate balancing operation (e.g. =, <=, <, div, /) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
385 |
and d = gcd(m,m') and n=m/d and n'=m'/d. |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
386 |
*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
387 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
388 |
local |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
389 |
open Rat_Numeral_Simprocs |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
390 |
in |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
391 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
392 |
val rel_rat_number_of = [eq_rat_number_of, less_rat_number_of, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
393 |
le_number_of_eq_not_less] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
394 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
395 |
structure CancelNumeralFactorCommon = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
396 |
struct |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
397 |
val mk_coeff = mk_coeff |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
398 |
val dest_coeff = dest_coeff 1 |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
399 |
val trans_tac = trans_tac |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
400 |
val norm_tac = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
401 |
ALLGOALS (simp_tac (HOL_ss addsimps rat_minus_from_mult_simps @ mult_1s)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
402 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps bin_simps@rat_mult_minus_simps)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
403 |
THEN ALLGOALS (simp_tac (HOL_ss addsimps mult_ac)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
404 |
val numeral_simp_tac = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
405 |
ALLGOALS (simp_tac (HOL_ss addsimps rel_rat_number_of@bin_simps)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
406 |
val simplify_meta_eq = simplify_meta_eq |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
407 |
end |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
408 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
409 |
structure DivCancelNumeralFactor = CancelNumeralFactorFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
410 |
(open CancelNumeralFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
411 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
412 |
val mk_bal = HOLogic.mk_binop "HOL.divide" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
413 |
val dest_bal = HOLogic.dest_bin "HOL.divide" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
414 |
val cancel = mult_divide_cancel_left RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
415 |
val neg_exchanges = false |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
416 |
) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
417 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
418 |
structure EqCancelNumeralFactor = CancelNumeralFactorFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
419 |
(open CancelNumeralFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
420 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
421 |
val mk_bal = HOLogic.mk_eq |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
422 |
val dest_bal = HOLogic.dest_bin "op =" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
423 |
val cancel = mult_cancel_left RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
424 |
val neg_exchanges = false |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
425 |
) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
426 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
427 |
structure LessCancelNumeralFactor = CancelNumeralFactorFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
428 |
(open CancelNumeralFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
429 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
430 |
val mk_bal = HOLogic.mk_binrel "op <" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
431 |
val dest_bal = HOLogic.dest_bin "op <" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
432 |
val cancel = mult_less_cancel_left RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
433 |
val neg_exchanges = true |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
434 |
) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
435 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
436 |
structure LeCancelNumeralFactor = CancelNumeralFactorFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
437 |
(open CancelNumeralFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
438 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
439 |
val mk_bal = HOLogic.mk_binrel "op <=" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
440 |
val dest_bal = HOLogic.dest_bin "op <=" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
441 |
val cancel = mult_le_cancel_left RS trans |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
442 |
val neg_exchanges = true |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
443 |
) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
444 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
445 |
val rat_cancel_numeral_factors_relations = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
446 |
map prep_simproc |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
447 |
[("rateq_cancel_numeral_factor", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
448 |
["(l::rat) * m = n", "(l::rat) = m * n"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
449 |
EqCancelNumeralFactor.proc), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
450 |
("ratless_cancel_numeral_factor", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
451 |
["(l::rat) * m < n", "(l::rat) < m * n"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
452 |
LessCancelNumeralFactor.proc), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
453 |
("ratle_cancel_numeral_factor", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
454 |
["(l::rat) * m <= n", "(l::rat) <= m * n"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
455 |
LeCancelNumeralFactor.proc)] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
456 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
457 |
val rat_cancel_numeral_factors_divide = prep_simproc |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
458 |
("ratdiv_cancel_numeral_factor", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
459 |
["((l::rat) * m) / n", "(l::rat) / (m * n)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
460 |
"((number_of v)::rat) / (number_of w)"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
461 |
DivCancelNumeralFactor.proc) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
462 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
463 |
val rat_cancel_numeral_factors = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
464 |
rat_cancel_numeral_factors_relations @ |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
465 |
[rat_cancel_numeral_factors_divide] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
466 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
467 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
468 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
469 |
Addsimprocs rat_cancel_numeral_factors; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
470 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
471 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
472 |
(*examples: |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
473 |
print_depth 22; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
474 |
set timing; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
475 |
set trace_simp; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
476 |
fun test s = (Goal s; by (Simp_tac 1)); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
477 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
478 |
test "0 <= (y::rat) * -2"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
479 |
test "9*x = 12 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
480 |
test "(9*x) / (12 * (y::rat)) = z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
481 |
test "9*x < 12 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
482 |
test "9*x <= 12 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
483 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
484 |
test "-99*x = 132 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
485 |
test "(-99*x) / (132 * (y::rat)) = z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
486 |
test "-99*x < 132 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
487 |
test "-99*x <= 132 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
488 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
489 |
test "999*x = -396 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
490 |
test "(999*x) / (-396 * (y::rat)) = z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
491 |
test "999*x < -396 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
492 |
test "999*x <= -396 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
493 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
494 |
test "(- ((2::rat) * x) <= 2 * y)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
495 |
test "-99*x = -81 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
496 |
test "(-99*x) / (-81 * (y::rat)) = z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
497 |
test "-99*x <= -81 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
498 |
test "-99*x < -81 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
499 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
500 |
test "-2 * x = -1 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
501 |
test "-2 * x = -(y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
502 |
test "(-2 * x) / (-1 * (y::rat)) = z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
503 |
test "-2 * x < -(y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
504 |
test "-2 * x <= -1 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
505 |
test "-x < -23 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
506 |
test "-x <= -23 * (y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
507 |
*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
508 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
509 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
510 |
(** Declarations for ExtractCommonTerm **) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
511 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
512 |
local |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
513 |
open Rat_Numeral_Simprocs |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
514 |
in |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
515 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
516 |
structure CancelFactorCommon = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
517 |
struct |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
518 |
val mk_sum = long_mk_prod |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
519 |
val dest_sum = dest_prod |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
520 |
val mk_coeff = mk_coeff |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
521 |
val dest_coeff = dest_coeff |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
522 |
val find_first = find_first [] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
523 |
val trans_tac = trans_tac |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
524 |
val norm_tac = ALLGOALS (simp_tac (HOL_ss addsimps mult_1s@mult_ac)) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
525 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
526 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
527 |
structure EqCancelFactor = ExtractCommonTermFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
528 |
(open CancelFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
529 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
530 |
val mk_bal = HOLogic.mk_eq |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
531 |
val dest_bal = HOLogic.dest_bin "op =" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
532 |
val simplify_meta_eq = cancel_simplify_meta_eq mult_cancel_left |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
533 |
); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
534 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
535 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
536 |
structure DivideCancelFactor = ExtractCommonTermFun |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
537 |
(open CancelFactorCommon |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
538 |
val prove_conv = Bin_Simprocs.prove_conv |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
539 |
val mk_bal = HOLogic.mk_binop "HOL.divide" |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
540 |
val dest_bal = HOLogic.dest_bin "HOL.divide" Rat_Numeral_Simprocs.ratT |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
541 |
val simplify_meta_eq = cancel_simplify_meta_eq mult_divide_cancel_eq_if |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
542 |
); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
543 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
544 |
val rat_cancel_factor = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
545 |
map prep_simproc |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
546 |
[("rat_eq_cancel_factor", ["(l::rat) * m = n", "(l::rat) = m * n"], EqCancelFactor.proc), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
547 |
("rat_divide_cancel_factor", ["((l::rat) * m) / n", "(l::rat) / (m * n)"], |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
548 |
DivideCancelFactor.proc)]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
549 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
550 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
551 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
552 |
Addsimprocs rat_cancel_factor; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
553 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
554 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
555 |
(*examples: |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
556 |
print_depth 22; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
557 |
set timing; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
558 |
set trace_simp; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
559 |
fun test s = (Goal s; by (Asm_simp_tac 1)); |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
560 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
561 |
test "x*k = k*(y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
562 |
test "k = k*(y::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
563 |
test "a*(b*c) = (b::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
564 |
test "a*(b*c) = d*(b::rat)*(x*a)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
565 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
566 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
567 |
test "(x*k) / (k*(y::rat)) = (uu::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
568 |
test "(k) / (k*(y::rat)) = (uu::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
569 |
test "(a*(b*c)) / ((b::rat)) = (uu::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
570 |
test "(a*(b*c)) / (d*(b::rat)*(x*a)) = (uu::rat)"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
571 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
572 |
(*FIXME: what do we do about this?*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
573 |
test "a*(b*c)/(y*z) = d*(b::rat)*(x*a)/z"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
574 |
*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
575 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
576 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
577 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
578 |
(****Instantiation of the generic linear arithmetic package****) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
579 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
580 |
val add_zero_left = thm"Ring_and_Field.add_0"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
581 |
val add_zero_right = thm"Ring_and_Field.add_0_right"; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
582 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
583 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
584 |
local |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
585 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
586 |
(* reduce contradictory <= to False *) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
587 |
val add_rules = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
588 |
[order_less_irrefl, rat_numeral_0_eq_0, rat_numeral_1_eq_1, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
589 |
rat_minus_1_eq_m1, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
590 |
add_rat_number_of, minus_rat_number_of, diff_rat_number_of, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
591 |
mult_rat_number_of, eq_rat_number_of, less_rat_number_of, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
592 |
le_number_of_eq_not_less, diff_minus, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
593 |
minus_add_distrib, minus_minus, mult_assoc, minus_zero, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
594 |
add_zero_left, add_zero_right, left_minus, right_minus, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
595 |
mult_zero_left, mult_zero_right, mult_1, mult_1_right, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
596 |
minus_mult_left RS sym, minus_mult_right RS sym]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
597 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
598 |
val simprocs = [Rat_Times_Assoc.conv, Rat_Numeral_Simprocs.combine_numerals, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
599 |
rat_cancel_numeral_factors_divide]@ |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
600 |
Rat_Numeral_Simprocs.cancel_numerals @ |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
601 |
Rat_Numeral_Simprocs.eval_numerals; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
602 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
603 |
val mono_ss = simpset() addsimps |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
604 |
[add_mono,add_strict_mono,add_less_le_mono,add_le_less_mono]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
605 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
606 |
val add_mono_thms_rat = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
607 |
map (fn s => prove_goal (the_context ()) s |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
608 |
(fn prems => [cut_facts_tac prems 1, asm_simp_tac mono_ss 1])) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
609 |
["(i <= j) & (k <= l) ==> i + k <= j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
610 |
"(i = j) & (k <= l) ==> i + k <= j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
611 |
"(i <= j) & (k = l) ==> i + k <= j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
612 |
"(i = j) & (k = l) ==> i + k = j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
613 |
"(i < j) & (k = l) ==> i + k < j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
614 |
"(i = j) & (k < l) ==> i + k < j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
615 |
"(i < j) & (k <= l) ==> i + k < j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
616 |
"(i <= j) & (k < l) ==> i + k < j + (l::rat)", |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
617 |
"(i < j) & (k < l) ==> i + k < j + (l::rat)"]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
618 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
619 |
fun cvar(th,_ $ (_ $ _ $ var)) = cterm_of (#sign(rep_thm th)) var; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
620 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
621 |
val rat_mult_mono_thms = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
622 |
[(rat_mult_strict_left_mono, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
623 |
cvar(rat_mult_strict_left_mono, hd(tl(prems_of rat_mult_strict_left_mono)))), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
624 |
(rat_mult_left_mono, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
625 |
cvar(rat_mult_left_mono, hd(tl(prems_of rat_mult_left_mono))))] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
626 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
627 |
(* reduce contradictory <= to False *) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
628 |
val simps = [True_implies_equals, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
629 |
inst "a" "(number_of ?v)::rat" right_distrib, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
630 |
divide_1,times_divide_eq_right,times_divide_eq_left, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
631 |
rat_of_int_zero, rat_of_int_one, rat_of_int_add_distrib, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
632 |
rat_of_int_minus_distrib, rat_of_int_diff_distrib, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
633 |
rat_of_int_mult_distrib, number_of_rat RS sym]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
634 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
635 |
in |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
636 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
637 |
val fast_rat_arith_simproc = Simplifier.simproc (Theory.sign_of (the_context ())) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
638 |
"fast_rat_arith" ["(m::rat) < n","(m::rat) <= n", "(m::rat) = n"] |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
639 |
Fast_Arith.lin_arith_prover; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
640 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
641 |
val int_inj_thms = [rat_of_int_le_iff RS iffD2, rat_of_int_less_iff RS iffD2, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
642 |
rat_inject RS iffD2]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
643 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
644 |
val rat_arith_setup = |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
645 |
[Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset} => |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
646 |
{add_mono_thms = add_mono_thms @ add_mono_thms_rat, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
647 |
mult_mono_thms = mult_mono_thms @ rat_mult_mono_thms, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
648 |
inj_thms = (***int_inj_thms @*???**) inj_thms, |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
649 |
lessD = lessD, (*Can't change LA_Data_Ref.lessD: the rats are dense!*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
650 |
simpset = simpset addsimps add_rules |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
651 |
addsimps simps |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
652 |
addsimprocs simprocs}), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
653 |
(*??? |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
654 |
arith_inj_const ("Rational.rat", HOLogic.intT --> Rat_Numeral_Simprocs.ratT), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
655 |
???*) |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
656 |
arith_discrete ("Rational.rat",false), |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
657 |
Simplifier.change_simpset_of (op addsimprocs) [fast_rat_arith_simproc]]; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
658 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
659 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
660 |
end; |
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
661 |
|
3d4df8c166ae
replacing HOL/Real/PRat, PNat by the rational number development
paulson
parents:
diff
changeset
|
662 |