author | paulson |
Wed, 14 Jun 2000 18:19:20 +0200 | |
changeset 9068 | 202fdf72cf23 |
parent 9043 | ca761fe227d8 |
child 9080 | 67ca888af420 |
permissions | -rw-r--r-- |
7292 | 1 |
(* Title: HOL/RealBin.ML |
2 |
ID: $Id$ |
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1999 University of Cambridge |
|
5 |
||
6 |
Binary arithmetic for the reals (integer literals only) |
|
7 |
*) |
|
8 |
||
9 |
(** real_of_int (coercion from int to real) **) |
|
10 |
||
11 |
Goal "real_of_int (number_of w) = number_of w"; |
|
12 |
by (simp_tac (simpset() addsimps [real_number_of_def]) 1); |
|
13 |
qed "real_number_of"; |
|
14 |
Addsimps [real_number_of]; |
|
15 |
||
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
16 |
Goalw [real_number_of_def] "(0::real) = #0"; |
7292 | 17 |
by (simp_tac (simpset() addsimps [real_of_int_zero RS sym]) 1); |
18 |
qed "zero_eq_numeral_0"; |
|
19 |
||
20 |
Goalw [real_number_of_def] "1r = #1"; |
|
21 |
by (simp_tac (simpset() addsimps [real_of_int_one RS sym]) 1); |
|
22 |
qed "one_eq_numeral_1"; |
|
23 |
||
24 |
(** Addition **) |
|
25 |
||
26 |
Goal "(number_of v :: real) + number_of v' = number_of (bin_add v v')"; |
|
27 |
by (simp_tac |
|
28 |
(simpset_of Int.thy addsimps [real_number_of_def, |
|
29 |
real_of_int_add, number_of_add]) 1); |
|
30 |
qed "add_real_number_of"; |
|
31 |
||
32 |
Addsimps [add_real_number_of]; |
|
33 |
||
34 |
||
35 |
(** Subtraction **) |
|
36 |
||
37 |
Goalw [real_number_of_def] "- (number_of w :: real) = number_of (bin_minus w)"; |
|
38 |
by (simp_tac |
|
39 |
(simpset_of Int.thy addsimps [number_of_minus, real_of_int_minus]) 1); |
|
40 |
qed "minus_real_number_of"; |
|
41 |
||
42 |
Goalw [real_number_of_def] |
|
43 |
"(number_of v :: real) - number_of w = number_of (bin_add v (bin_minus w))"; |
|
44 |
by (simp_tac |
|
45 |
(simpset_of Int.thy addsimps [diff_number_of_eq, real_of_int_diff]) 1); |
|
46 |
qed "diff_real_number_of"; |
|
47 |
||
48 |
Addsimps [minus_real_number_of, diff_real_number_of]; |
|
49 |
||
50 |
||
51 |
(** Multiplication **) |
|
52 |
||
53 |
Goal "(number_of v :: real) * number_of v' = number_of (bin_mult v v')"; |
|
54 |
by (simp_tac |
|
55 |
(simpset_of Int.thy addsimps [real_number_of_def, |
|
56 |
real_of_int_mult, number_of_mult]) 1); |
|
57 |
qed "mult_real_number_of"; |
|
58 |
||
59 |
Addsimps [mult_real_number_of]; |
|
60 |
||
7588
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
61 |
Goal "(#2::real) = #1 + #1"; |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
62 |
by (Simp_tac 1); |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
63 |
val lemma = result(); |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
64 |
|
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
65 |
(*For specialist use: NOT as default simprules*) |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
66 |
Goal "#2 * z = (z+z::real)"; |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
67 |
by (simp_tac (simpset_of RealDef.thy |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
68 |
addsimps [lemma, real_add_mult_distrib, |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
69 |
one_eq_numeral_1 RS sym]) 1); |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
70 |
qed "real_mult_2"; |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
71 |
|
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
72 |
Goal "z * #2 = (z+z::real)"; |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
73 |
by (stac real_mult_commute 1 THEN rtac real_mult_2 1); |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
74 |
qed "real_mult_2_right"; |
26384af93359
Tidying to exploit the new arith_tac. RealBin no longer imports RealPow or
paulson
parents:
7583
diff
changeset
|
75 |
|
7292 | 76 |
|
77 |
(*** Comparisons ***) |
|
78 |
||
79 |
(** Equals (=) **) |
|
80 |
||
81 |
Goal "((number_of v :: real) = number_of v') = \ |
|
82 |
\ iszero (number_of (bin_add v (bin_minus v')))"; |
|
83 |
by (simp_tac |
|
84 |
(simpset_of Int.thy addsimps [real_number_of_def, |
|
85 |
real_of_int_eq_iff, eq_number_of_eq]) 1); |
|
86 |
qed "eq_real_number_of"; |
|
87 |
||
88 |
Addsimps [eq_real_number_of]; |
|
89 |
||
90 |
(** Less-than (<) **) |
|
91 |
||
92 |
(*"neg" is used in rewrite rules for binary comparisons*) |
|
93 |
Goal "((number_of v :: real) < number_of v') = \ |
|
94 |
\ neg (number_of (bin_add v (bin_minus v')))"; |
|
95 |
by (simp_tac |
|
96 |
(simpset_of Int.thy addsimps [real_number_of_def, real_of_int_less_iff, |
|
97 |
less_number_of_eq_neg]) 1); |
|
98 |
qed "less_real_number_of"; |
|
99 |
||
100 |
Addsimps [less_real_number_of]; |
|
101 |
||
102 |
||
103 |
(** Less-than-or-equals (<=) **) |
|
104 |
||
105 |
Goal "(number_of x <= (number_of y::real)) = \ |
|
106 |
\ (~ number_of y < (number_of x::real))"; |
|
107 |
by (rtac (linorder_not_less RS sym) 1); |
|
108 |
qed "le_real_number_of_eq_not_less"; |
|
109 |
||
110 |
Addsimps [le_real_number_of_eq_not_less]; |
|
111 |
||
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
112 |
(*** New versions of existing theorems involving 0, 1r ***) |
7292 | 113 |
|
114 |
Goal "- #1 = (#-1::real)"; |
|
115 |
by (Simp_tac 1); |
|
116 |
qed "minus_numeral_one"; |
|
117 |
||
118 |
||
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
119 |
(*Maps 0 to #0 and 1r to #1 and -1r to #-1*) |
7292 | 120 |
val real_numeral_ss = |
121 |
HOL_ss addsimps [zero_eq_numeral_0, one_eq_numeral_1, |
|
122 |
minus_numeral_one]; |
|
123 |
||
9068
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
124 |
fun rename_numerals thy th = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
125 |
asm_full_simplify real_numeral_ss (change_theory thy th); |
7292 | 126 |
|
127 |
||
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
128 |
(*Now insert some identities previously stated for 0 and 1r*) |
7292 | 129 |
|
130 |
(** RealDef & Real **) |
|
131 |
||
132 |
Addsimps (map (rename_numerals thy) |
|
133 |
[real_minus_zero, real_minus_zero_iff, |
|
134 |
real_add_zero_left, real_add_zero_right, |
|
135 |
real_diff_0, real_diff_0_right, |
|
136 |
real_mult_0_right, real_mult_0, real_mult_1_right, real_mult_1, |
|
137 |
real_mult_minus_1_right, real_mult_minus_1, real_rinv_1, |
|
138 |
real_minus_zero_less_iff]); |
|
139 |
||
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
140 |
AddIffs (map (rename_numerals thy) [real_mult_is_0, real_0_is_mult]); |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
141 |
|
9068
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
142 |
bind_thm ("real_0_less_mult_iff", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
143 |
rename_numerals thy real_zero_less_mult_iff); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
144 |
bind_thm ("real_0_le_mult_iff", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
145 |
rename_numerals thy real_zero_le_mult_iff); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
146 |
bind_thm ("real_mult_less_0_iff", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
147 |
rename_numerals thy real_mult_less_zero_iff); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
148 |
bind_thm ("real_mult_le_0_iff", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
149 |
rename_numerals thy real_mult_le_zero_iff); |
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
150 |
|
7292 | 151 |
|
152 |
(*Perhaps add some theorems that aren't in the default simpset, as |
|
153 |
done in Integ/NatBin.ML*) |
|
154 |
||
7583
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
155 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
156 |
(* Author: Tobias Nipkow, TU Muenchen |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
157 |
Copyright 1999 TU Muenchen |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
158 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
159 |
Instantiate linear arithmetic decision procedure for the reals. |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
160 |
FIXME: multiplication with constants (eg #2 * x) does not work yet. |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
161 |
Solution: there should be a simproc for combining coefficients. |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
162 |
*) |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
163 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
164 |
let |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
165 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
166 |
(* reduce contradictory <= to False *) |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
167 |
val simps = [order_less_irrefl,zero_eq_numeral_0,one_eq_numeral_1, |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
168 |
add_real_number_of,minus_real_number_of,diff_real_number_of, |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
169 |
mult_real_number_of,eq_real_number_of,less_real_number_of, |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
170 |
le_real_number_of_eq_not_less]; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
171 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
172 |
val simprocs = [Real_Cancel.sum_conv, Real_Cancel.rel_conv]; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
173 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
174 |
val add_mono_thms = |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
175 |
map (fn s => prove_goal thy s |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
176 |
(fn prems => [cut_facts_tac prems 1, |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
177 |
asm_simp_tac (simpset() addsimps |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
178 |
[real_add_le_mono,real_add_less_mono, |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
179 |
real_add_less_le_mono,real_add_le_less_mono]) 1])) |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
180 |
["(i <= j) & (k <= l) ==> i + k <= j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
181 |
"(i = j) & (k <= l) ==> i + k <= j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
182 |
"(i <= j) & (k = l) ==> i + k <= j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
183 |
"(i = j) & (k = l) ==> i + k = j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
184 |
"(i < j) & (k = l) ==> i + k < j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
185 |
"(i = j) & (k < l) ==> i + k < j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
186 |
"(i < j) & (k <= l) ==> i + k < j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
187 |
"(i <= j) & (k < l) ==> i + k < j + (l::real)", |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
188 |
"(i < j) & (k < l) ==> i + k < j + (l::real)"]; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
189 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
190 |
in |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
191 |
LA_Data_Ref.add_mono_thms := !LA_Data_Ref.add_mono_thms @ add_mono_thms; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
192 |
LA_Data_Ref.ss_ref := !LA_Data_Ref.ss_ref addsimps simps |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
193 |
addsimprocs simprocs; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
194 |
LA_Data_Ref.discrete := !LA_Data_Ref.discrete @ [("RealDef.real",false)] |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
195 |
end; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
196 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
197 |
let |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
198 |
val real_arith_simproc_pats = |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
199 |
map (fn s => Thm.read_cterm (Theory.sign_of thy) (s, HOLogic.boolT)) |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
200 |
["(m::real) < n","(m::real) <= n", "(m::real) = n"]; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
201 |
|
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
202 |
val fast_real_arith_simproc = mk_simproc |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
203 |
"fast_real_arith" real_arith_simproc_pats Fast_Arith.lin_arith_prover; |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
204 |
in |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
205 |
Addsimprocs [fast_real_arith_simproc] |
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
206 |
end; |
9013
9dd0274f76af
Updated files to remove 0r and 1r from theorems in descendant theories
fleuriot
parents:
8838
diff
changeset
|
207 |
|
7583
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
208 |
|
9013
9dd0274f76af
Updated files to remove 0r and 1r from theorems in descendant theories
fleuriot
parents:
8838
diff
changeset
|
209 |
Addsimps [zero_eq_numeral_0,one_eq_numeral_1]; |
7583
d1b40e0464b1
Restructured lin.arith.package and fixed a proof in RComplete.
nipkow
parents:
7292
diff
changeset
|
210 |
|
9013
9dd0274f76af
Updated files to remove 0r and 1r from theorems in descendant theories
fleuriot
parents:
8838
diff
changeset
|
211 |
|
9043
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
212 |
(** Simplification of arithmetic when nested to the right **) |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
213 |
|
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
214 |
Goal "number_of v + (number_of w + z) = (number_of(bin_add v w) + z::real)"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
215 |
by Auto_tac; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
216 |
qed "real_add_number_of_left"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
217 |
|
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
218 |
Goal "number_of v * (number_of w * z) = (number_of(bin_mult v w) * z::real)"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
219 |
by (simp_tac (simpset() addsimps [real_mult_assoc RS sym]) 1); |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
220 |
qed "real_mult_number_of_left"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
221 |
|
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
222 |
Goalw [real_diff_def] |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
223 |
"number_of v + (number_of w - c) = number_of(bin_add v w) - (c::real)"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
224 |
by (rtac real_add_number_of_left 1); |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
225 |
qed "real_add_number_of_diff1"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
226 |
|
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
227 |
Goal "number_of v + (c - number_of w) = \ |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
228 |
\ number_of (bin_add v (bin_minus w)) + (c::real)"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
229 |
by (stac (diff_real_number_of RS sym) 1); |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
230 |
by Auto_tac; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
231 |
qed "real_add_number_of_diff2"; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
232 |
|
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
233 |
Addsimps [real_add_number_of_left, real_mult_number_of_left, |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
234 |
real_add_number_of_diff1, real_add_number_of_diff2]; |
ca761fe227d8
First round of changes, towards installation of simprocs
paulson
parents:
9013
diff
changeset
|
235 |
|
9068
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
236 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
237 |
(*"neg" is used in rewrite rules for binary comparisons*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
238 |
Goal "real_of_nat (number_of v :: nat) = \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
239 |
\ (if neg (number_of v) then #0 \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
240 |
\ else (number_of v :: real))"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
241 |
by (simp_tac |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
242 |
(simpset_of Int.thy addsimps [nat_number_of_def, real_of_nat_real_of_int, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
243 |
real_of_nat_neg_int, real_number_of, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
244 |
zero_eq_numeral_0]) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
245 |
qed "real_of_nat_number_of"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
246 |
Addsimps [real_of_nat_number_of]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
247 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
248 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
249 |
(**** Simprocs for numeric literals ****) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
250 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
251 |
(** Combining of literal coefficients in sums of products **) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
252 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
253 |
Goal "(x < y) = (x-y < (#0::real))"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
254 |
by Auto_tac; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
255 |
qed "real_less_iff_diff_less_0"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
256 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
257 |
Goal "(x = y) = (x-y = (#0::real))"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
258 |
by Auto_tac; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
259 |
qed "real_eq_iff_diff_eq_0"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
260 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
261 |
Goal "(x <= y) = (x-y <= (#0::real))"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
262 |
by Auto_tac; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
263 |
qed "real_le_iff_diff_le_0"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
264 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
265 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
266 |
(** For combine_numerals **) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
267 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
268 |
Goal "i*u + (j*u + k) = (i+j)*u + (k::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
269 |
by (asm_simp_tac (simpset() addsimps [real_add_mult_distrib]) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
270 |
qed "left_real_add_mult_distrib"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
271 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
272 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
273 |
(** For cancel_numerals **) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
274 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
275 |
val rel_iff_rel_0_rls = map (inst "y" "?u+?v") |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
276 |
[real_less_iff_diff_less_0, real_eq_iff_diff_eq_0, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
277 |
real_le_iff_diff_le_0] @ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
278 |
map (inst "y" "n") |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
279 |
[real_less_iff_diff_less_0, real_eq_iff_diff_eq_0, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
280 |
real_le_iff_diff_le_0]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
281 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
282 |
Goal "!!i::real. (i*u + m = j*u + n) = ((i-j)*u + m = n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
283 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
284 |
real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
285 |
qed "real_eq_add_iff1"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
286 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
287 |
Goal "!!i::real. (i*u + m = j*u + n) = (m = (j-i)*u + n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
288 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
289 |
real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
290 |
qed "real_eq_add_iff2"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
291 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
292 |
Goal "!!i::real. (i*u + m < j*u + n) = ((i-j)*u + m < n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
293 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
294 |
real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
295 |
qed "real_less_add_iff1"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
296 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
297 |
Goal "!!i::real. (i*u + m < j*u + n) = (m < (j-i)*u + n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
298 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
299 |
real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
300 |
qed "real_less_add_iff2"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
301 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
302 |
Goal "!!i::real. (i*u + m <= j*u + n) = ((i-j)*u + m <= n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
303 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
304 |
real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
305 |
qed "real_le_add_iff1"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
306 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
307 |
Goal "!!i::real. (i*u + m <= j*u + n) = (m <= (j-i)*u + n)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
308 |
by (asm_simp_tac (simpset() addsimps [real_diff_def, real_add_mult_distrib] |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
309 |
@real_add_ac@rel_iff_rel_0_rls) 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
310 |
qed "real_le_add_iff2"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
311 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
312 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
313 |
structure Real_Numeral_Simprocs = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
314 |
struct |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
315 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
316 |
(*Utilities*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
317 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
318 |
fun mk_numeral n = HOLogic.number_of_const HOLogic.realT $ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
319 |
NumeralSyntax.mk_bin n; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
320 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
321 |
(*Decodes a binary real constant*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
322 |
fun dest_numeral (Const("Numeral.number_of", _) $ w) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
323 |
(NumeralSyntax.dest_bin w |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
324 |
handle Match => raise TERM("Real_Numeral_Simprocs.dest_numeral:1", [w])) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
325 |
| dest_numeral t = raise TERM("Real_Numeral_Simprocs.dest_numeral:2", [t]); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
326 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
327 |
fun find_first_numeral past (t::terms) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
328 |
((dest_numeral t, rev past @ terms) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
329 |
handle TERM _ => find_first_numeral (t::past) terms) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
330 |
| find_first_numeral past [] = raise TERM("find_first_numeral", []); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
331 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
332 |
val zero = mk_numeral 0; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
333 |
val mk_plus = HOLogic.mk_binop "op +"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
334 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
335 |
val uminus_const = Const ("uminus", HOLogic.realT --> HOLogic.realT); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
336 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
337 |
(*Thus mk_sum[t] yields t+#0; longer sums don't have a trailing zero*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
338 |
fun mk_sum [] = zero |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
339 |
| mk_sum [t,u] = mk_plus (t, u) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
340 |
| mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
341 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
342 |
(*this version ALWAYS includes a trailing zero*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
343 |
fun long_mk_sum [] = zero |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
344 |
| long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
345 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
346 |
val dest_plus = HOLogic.dest_bin "op +" HOLogic.realT; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
347 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
348 |
(*decompose additions AND subtractions as a sum*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
349 |
fun dest_summing (pos, Const ("op +", _) $ t $ u, ts) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
350 |
dest_summing (pos, t, dest_summing (pos, u, ts)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
351 |
| dest_summing (pos, Const ("op -", _) $ t $ u, ts) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
352 |
dest_summing (pos, t, dest_summing (not pos, u, ts)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
353 |
| dest_summing (pos, t, ts) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
354 |
if pos then t::ts else uminus_const$t :: ts; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
355 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
356 |
fun dest_sum t = dest_summing (true, t, []); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
357 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
358 |
val mk_diff = HOLogic.mk_binop "op -"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
359 |
val dest_diff = HOLogic.dest_bin "op -" HOLogic.realT; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
360 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
361 |
val one = mk_numeral 1; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
362 |
val mk_times = HOLogic.mk_binop "op *"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
363 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
364 |
fun mk_prod [] = one |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
365 |
| mk_prod [t] = t |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
366 |
| mk_prod (t :: ts) = if t = one then mk_prod ts |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
367 |
else mk_times (t, mk_prod ts); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
368 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
369 |
val dest_times = HOLogic.dest_bin "op *" HOLogic.realT; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
370 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
371 |
fun dest_prod t = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
372 |
let val (t,u) = dest_times t |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
373 |
in dest_prod t @ dest_prod u end |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
374 |
handle TERM _ => [t]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
375 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
376 |
(*DON'T do the obvious simplifications; that would create special cases*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
377 |
fun mk_coeff (k, ts) = mk_times (mk_numeral k, ts); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
378 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
379 |
(*Express t as a product of (possibly) a numeral with other sorted terms*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
380 |
fun dest_coeff sign (Const ("uminus", _) $ t) = dest_coeff (~sign) t |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
381 |
| dest_coeff sign t = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
382 |
let val ts = sort Term.term_ord (dest_prod t) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
383 |
val (n, ts') = find_first_numeral [] ts |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
384 |
handle TERM _ => (1, ts) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
385 |
in (sign*n, mk_prod ts') end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
386 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
387 |
(*Find first coefficient-term THAT MATCHES u*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
388 |
fun find_first_coeff past u [] = raise TERM("find_first_coeff", []) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
389 |
| find_first_coeff past u (t::terms) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
390 |
let val (n,u') = dest_coeff 1 t |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
391 |
in if u aconv u' then (n, rev past @ terms) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
392 |
else find_first_coeff (t::past) u terms |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
393 |
end |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
394 |
handle TERM _ => find_first_coeff (t::past) u terms; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
395 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
396 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
397 |
(*Simplify #1*n and n*#1 to n*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
398 |
val add_0s = map (rename_numerals thy) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
399 |
[real_add_zero_left, real_add_zero_right]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
400 |
val mult_1s = map (rename_numerals thy) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
401 |
[real_mult_1, real_mult_1_right, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
402 |
real_mult_minus_1, real_mult_minus_1_right]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
403 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
404 |
(*To perform binary arithmetic*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
405 |
val bin_simps = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
406 |
[add_real_number_of, real_add_number_of_left, minus_real_number_of, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
407 |
diff_real_number_of] @ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
408 |
bin_arith_simps @ bin_rel_simps; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
409 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
410 |
(*To evaluate binary negations of coefficients*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
411 |
val real_minus_simps = NCons_simps @ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
412 |
[minus_real_number_of, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
413 |
bin_minus_1, bin_minus_0, bin_minus_Pls, bin_minus_Min, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
414 |
bin_pred_1, bin_pred_0, bin_pred_Pls, bin_pred_Min]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
415 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
416 |
(*To let us treat subtraction as addition*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
417 |
val diff_simps = [real_diff_def, real_minus_add_distrib, real_minus_minus]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
418 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
419 |
(*Apply the given rewrite (if present) just once*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
420 |
fun trans_tac None = all_tac |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
421 |
| trans_tac (Some th) = ALLGOALS (rtac (th RS trans)); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
422 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
423 |
fun prove_conv name tacs sg (t, u) = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
424 |
if t aconv u then None |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
425 |
else |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
426 |
let val ct = cterm_of sg (HOLogic.mk_Trueprop (HOLogic.mk_eq (t, u))) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
427 |
in Some |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
428 |
(prove_goalw_cterm [] ct (K tacs) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
429 |
handle ERROR => error |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
430 |
("The error(s) above occurred while trying to prove " ^ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
431 |
string_of_cterm ct ^ "\nInternal failure of simproc " ^ name)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
432 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
433 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
434 |
(*Final simplification: cancel + and * *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
435 |
val simplify_meta_eq = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
436 |
Int_Numeral_Simprocs.simplify_meta_eq |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
437 |
[real_add_zero_left, real_add_zero_right, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
438 |
real_mult_0, real_mult_0_right, real_mult_1, real_mult_1_right]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
439 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
440 |
fun prep_simproc (name, pats, proc) = Simplifier.mk_simproc name pats proc; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
441 |
fun prep_pat s = Thm.read_cterm (Theory.sign_of RealInt.thy) (s, HOLogic.termT); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
442 |
val prep_pats = map prep_pat; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
443 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
444 |
structure CancelNumeralsCommon = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
445 |
struct |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
446 |
val mk_sum = mk_sum |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
447 |
val dest_sum = dest_sum |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
448 |
val mk_coeff = mk_coeff |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
449 |
val dest_coeff = dest_coeff 1 |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
450 |
val find_first_coeff = find_first_coeff [] |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
451 |
val trans_tac = trans_tac |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
452 |
val norm_tac = ALLGOALS (simp_tac (HOL_ss addsimps add_0s@mult_1s@diff_simps@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
453 |
real_minus_simps@real_add_ac)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
454 |
THEN ALLGOALS |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
455 |
(simp_tac (HOL_ss addsimps [real_minus_mult_eq2]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
456 |
bin_simps@real_add_ac@real_mult_ac)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
457 |
val numeral_simp_tac = ALLGOALS (simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
458 |
val simplify_meta_eq = simplify_meta_eq |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
459 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
460 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
461 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
462 |
structure EqCancelNumerals = CancelNumeralsFun |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
463 |
(open CancelNumeralsCommon |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
464 |
val prove_conv = prove_conv "realeq_cancel_numerals" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
465 |
val mk_bal = HOLogic.mk_eq |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
466 |
val dest_bal = HOLogic.dest_bin "op =" HOLogic.realT |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
467 |
val bal_add1 = real_eq_add_iff1 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
468 |
val bal_add2 = real_eq_add_iff2 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
469 |
); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
470 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
471 |
structure LessCancelNumerals = CancelNumeralsFun |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
472 |
(open CancelNumeralsCommon |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
473 |
val prove_conv = prove_conv "realless_cancel_numerals" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
474 |
val mk_bal = HOLogic.mk_binrel "op <" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
475 |
val dest_bal = HOLogic.dest_bin "op <" HOLogic.realT |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
476 |
val bal_add1 = real_less_add_iff1 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
477 |
val bal_add2 = real_less_add_iff2 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
478 |
); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
479 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
480 |
structure LeCancelNumerals = CancelNumeralsFun |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
481 |
(open CancelNumeralsCommon |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
482 |
val prove_conv = prove_conv "realle_cancel_numerals" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
483 |
val mk_bal = HOLogic.mk_binrel "op <=" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
484 |
val dest_bal = HOLogic.dest_bin "op <=" HOLogic.realT |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
485 |
val bal_add1 = real_le_add_iff1 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
486 |
val bal_add2 = real_le_add_iff2 RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
487 |
); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
488 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
489 |
val cancel_numerals = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
490 |
map prep_simproc |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
491 |
[("realeq_cancel_numerals", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
492 |
prep_pats ["(l::real) + m = n", "(l::real) = m + n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
493 |
"(l::real) - m = n", "(l::real) = m - n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
494 |
"(l::real) * m = n", "(l::real) = m * n"], |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
495 |
EqCancelNumerals.proc), |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
496 |
("realless_cancel_numerals", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
497 |
prep_pats ["(l::real) + m < n", "(l::real) < m + n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
498 |
"(l::real) - m < n", "(l::real) < m - n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
499 |
"(l::real) * m < n", "(l::real) < m * n"], |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
500 |
LessCancelNumerals.proc), |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
501 |
("realle_cancel_numerals", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
502 |
prep_pats ["(l::real) + m <= n", "(l::real) <= m + n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
503 |
"(l::real) - m <= n", "(l::real) <= m - n", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
504 |
"(l::real) * m <= n", "(l::real) <= m * n"], |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
505 |
LeCancelNumerals.proc)]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
506 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
507 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
508 |
structure CombineNumeralsData = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
509 |
struct |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
510 |
val mk_sum = long_mk_sum (*to work for e.g. #2*x + #3*x *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
511 |
val dest_sum = dest_sum |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
512 |
val mk_coeff = mk_coeff |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
513 |
val dest_coeff = dest_coeff 1 |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
514 |
val left_distrib = left_real_add_mult_distrib RS trans |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
515 |
val prove_conv = prove_conv "real_combine_numerals" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
516 |
val trans_tac = trans_tac |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
517 |
val norm_tac = ALLGOALS |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
518 |
(simp_tac (HOL_ss addsimps add_0s@mult_1s@diff_simps@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
519 |
real_minus_simps@real_add_ac)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
520 |
THEN ALLGOALS |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
521 |
(simp_tac (HOL_ss addsimps [real_minus_mult_eq2]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
522 |
bin_simps@real_add_ac@real_mult_ac)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
523 |
val numeral_simp_tac = ALLGOALS |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
524 |
(simp_tac (HOL_ss addsimps add_0s@bin_simps)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
525 |
val simplify_meta_eq = simplify_meta_eq |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
526 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
527 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
528 |
structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
529 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
530 |
val combine_numerals = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
531 |
prep_simproc ("real_combine_numerals", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
532 |
prep_pats ["(i::real) + j", "(i::real) - j"], |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
533 |
CombineNumerals.proc); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
534 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
535 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
536 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
537 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
538 |
Addsimprocs Real_Numeral_Simprocs.cancel_numerals; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
539 |
Addsimprocs [Real_Numeral_Simprocs.combine_numerals]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
540 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
541 |
(*The Abel_Cancel simprocs are now obsolete*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
542 |
Delsimprocs [Real_Cancel.sum_conv, Real_Cancel.rel_conv]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
543 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
544 |
(*examples: |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
545 |
print_depth 22; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
546 |
set timing; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
547 |
set trace_simp; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
548 |
fun test s = (Goal s; by (Simp_tac 1)); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
549 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
550 |
test "l + #2 + #2 + #2 + (l + #2) + (oo + #2) = (uu::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
551 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
552 |
test "#2*u = (u::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
553 |
test "(i + j + #12 + (k::real)) - #15 = y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
554 |
test "(i + j + #12 + (k::real)) - #5 = y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
555 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
556 |
test "y - b < (b::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
557 |
test "y - (#3*b + c) < (b::real) - #2*c"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
558 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
559 |
test "(#2*x - (u*v) + y) - v*#3*u = (w::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
560 |
test "(#2*x*u*v + (u*v)*#4 + y) - v*u*#4 = (w::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
561 |
test "(#2*x*u*v + (u*v)*#4 + y) - v*u = (w::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
562 |
test "u*v - (x*u*v + (u*v)*#4 + y) = (w::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
563 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
564 |
test "(i + j + #12 + (k::real)) = u + #15 + y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
565 |
test "(i + j*#2 + #12 + (k::real)) = j + #5 + y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
566 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
567 |
test "#2*y + #3*z + #6*w + #2*y + #3*z + #2*u = #2*y' + #3*z' + #6*w' + #2*y' + #3*z' + u + (vv::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
568 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
569 |
test "a + -(b+c) + b = (d::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
570 |
test "a + -(b+c) - b = (d::real)"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
571 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
572 |
(*negative numerals*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
573 |
test "(i + j + #-2 + (k::real)) - (u + #5 + y) = zz"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
574 |
test "(i + j + #-3 + (k::real)) < u + #5 + y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
575 |
test "(i + j + #3 + (k::real)) < u + #-6 + y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
576 |
test "(i + j + #-12 + (k::real)) - #15 = y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
577 |
test "(i + j + #12 + (k::real)) - #-15 = y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
578 |
test "(i + j + #-12 + (k::real)) - #-15 = y"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
579 |
*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
580 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
581 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
582 |
(** Constant folding for real plus and times **) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
583 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
584 |
(*We do not need |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
585 |
structure Real_Plus_Assoc = Assoc_Fold (Real_Plus_Assoc_Data); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
586 |
because combine_numerals does the same thing*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
587 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
588 |
structure Real_Times_Assoc_Data : ASSOC_FOLD_DATA = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
589 |
struct |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
590 |
val ss = HOL_ss |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
591 |
val eq_reflection = eq_reflection |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
592 |
val thy = RealBin.thy |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
593 |
val T = HOLogic.realT |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
594 |
val plus = Const ("op *", [HOLogic.realT,HOLogic.realT] ---> HOLogic.realT) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
595 |
val add_ac = real_mult_ac |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
596 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
597 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
598 |
structure Real_Times_Assoc = Assoc_Fold (Real_Times_Assoc_Data); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
599 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
600 |
Addsimprocs [Real_Times_Assoc.conv]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
601 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
602 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
603 |
(*** decision procedure for linear arithmetic ***) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
604 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
605 |
(*---------------------------------------------------------------------------*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
606 |
(* Linear arithmetic *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
607 |
(*---------------------------------------------------------------------------*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
608 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
609 |
(* |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
610 |
Instantiation of the generic linear arithmetic package for real. |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
611 |
*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
612 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
613 |
(* Update parameters of arithmetic prover *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
614 |
let |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
615 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
616 |
(* reduce contradictory <= to False *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
617 |
val add_rules = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
618 |
real_diff_def :: |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
619 |
map (rename_numerals thy) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
620 |
[real_add_zero_left, real_add_zero_right, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
621 |
real_add_minus, real_add_minus_left, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
622 |
real_mult_0, real_mult_0_right, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
623 |
real_mult_1, real_mult_1_right, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
624 |
real_mult_minus_1, real_mult_minus_1_right]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
625 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
626 |
val simprocs = [Real_Times_Assoc.conv, Real_Numeral_Simprocs.combine_numerals]@ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
627 |
Real_Numeral_Simprocs.cancel_numerals; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
628 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
629 |
val add_mono_thms = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
630 |
map (fn s => prove_goal RealBin.thy s |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
631 |
(fn prems => [cut_facts_tac prems 1, |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
632 |
asm_simp_tac (simpset() addsimps [real_add_le_mono]) 1])) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
633 |
["(i <= j) & (k <= l) ==> i + k <= j + (l::real)", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
634 |
"(i = j) & (k <= l) ==> i + k <= j + (l::real)", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
635 |
"(i <= j) & (k = l) ==> i + k <= j + (l::real)", |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
636 |
"(i = j) & (k = l) ==> i + k = j + (l::real)" |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
637 |
]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
638 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
639 |
in |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
640 |
LA_Data_Ref.add_mono_thms := !LA_Data_Ref.add_mono_thms @ add_mono_thms; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
641 |
(*We don't change LA_Data_Ref.lessD and LA_Data_Ref.discrete |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
642 |
because the real ordering is dense!*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
643 |
LA_Data_Ref.ss_ref := !LA_Data_Ref.ss_ref addsimps add_rules |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
644 |
addsimprocs simprocs |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
645 |
addcongs [if_weak_cong] |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
646 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
647 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
648 |
let |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
649 |
val real_arith_simproc_pats = |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
650 |
map (fn s => Thm.read_cterm (Theory.sign_of RealDef.thy) (s, HOLogic.boolT)) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
651 |
["(m::real) < n","(m::real) <= n", "(m::real) = n"]; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
652 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
653 |
val fast_real_arith_simproc = mk_simproc |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
654 |
"fast_real_arith" real_arith_simproc_pats Fast_Arith.lin_arith_prover; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
655 |
in |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
656 |
Addsimprocs [fast_real_arith_simproc] |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
657 |
end; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
658 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
659 |
(* Some test data [omitting examples thet assume the ordering to be discrete!] |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
660 |
Goal "!!a::real. [| a <= b; c <= d; x+y<z |] ==> a+c <= b+d"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
661 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
662 |
Goal "!!a::real. [| a <= b; b+b <= c |] ==> a+a <= c"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
663 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
664 |
Goal "!!a::real. [| a+b <= i+j; a<=b; i<=j |] ==> a+a <= j+j"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
665 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
666 |
Goal "!!a::real. a+b+c <= i+j+k & a<=b & b<=c & i<=j & j<=k --> a+a+a <= k+k+k"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
667 |
by (arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
668 |
Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
669 |
\ ==> a <= l"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
670 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
671 |
Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
672 |
\ ==> a+a+a+a <= l+l+l+l"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
673 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
674 |
Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
675 |
\ ==> a+a+a+a+a <= l+l+l+l+i"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
676 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
677 |
Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
678 |
\ ==> a+a+a+a+a+a <= l+l+l+l+i+l"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
679 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
680 |
Goal "!!a::real. [| a+b+c+d <= i+j+k+l; a<=b; b<=c; c<=d; i<=j; j<=k; k<=l |] \ |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
681 |
\ ==> #6*a <= #5*l+i"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
682 |
by (fast_arith_tac 1); |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
683 |
*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
684 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
685 |
(*---------------------------------------------------------------------------*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
686 |
(* End of linear arithmetic *) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
687 |
(*---------------------------------------------------------------------------*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
688 |
|
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
689 |
(*useful??*) |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
690 |
Goal "(z = z + w) = (w = (#0::real))"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
691 |
by Auto_tac; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
692 |
qed "real_add_left_cancel0"; |
202fdf72cf23
installing the cancel_numerals and combine_numerals simprocs
paulson
parents:
9043
diff
changeset
|
693 |
Addsimps [real_add_left_cancel0]; |