author | paulson |
Wed, 05 Jul 2000 16:37:52 +0200 | |
changeset 9248 | e1dee89de037 |
parent 9169 | 85a47aa21f74 |
child 10835 | f4745d77e620 |
permissions | -rw-r--r-- |
1461 | 1 |
(* Title: HOLCF/ex/Loop.ML |
244 | 2 |
ID: $Id$ |
1461 | 3 |
Author: Franz Regensburger |
4 |
Copyright 1993 Technische Universitaet Muenchen |
|
244 | 5 |
|
9169 | 6 |
Theory for a loop primitive like while |
244 | 7 |
*) |
8 |
||
9169 | 9 |
(* ------------------------------------------------------------------------- *) |
10 |
(* access to definitions *) |
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11 |
(* ------------------------------------------------------------------------- *) |
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244 | 12 |
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||
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
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14 |
Goalw [step_def] "step`b`g`x = If b`x then g`x else x fi"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
15 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
16 |
qed "step_def2"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
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changeset
|
17 |
|
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
18 |
Goalw [while_def] "while`b`g = fix`(LAM f x. If b`x then f`(g`x) else x fi)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
19 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
20 |
qed "while_def2"; |
244 | 21 |
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22 |
||
23 |
(* ------------------------------------------------------------------------- *) |
|
24 |
(* rekursive properties of while *) |
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25 |
(* ------------------------------------------------------------------------- *) |
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26 |
||
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
27 |
Goal "while`b`g`x = If b`x then while`b`g`(g`x) else x fi"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
28 |
by (fix_tac5 while_def2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
29 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
30 |
qed "while_unfold"; |
244 | 31 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
32 |
Goal "ALL x. while`b`g`x = while`b`g`(iterate k (step`b`g) x)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
33 |
by (nat_ind_tac "k" 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
34 |
by (simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
35 |
by (rtac allI 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
36 |
by (rtac trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
37 |
by (stac while_unfold 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
38 |
by (rtac refl 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
39 |
by (stac iterate_Suc2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
40 |
by (rtac trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
41 |
by (etac spec 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
42 |
by (stac step_def2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
43 |
by (res_inst_tac [("p","b`x")] trE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
44 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
45 |
by (stac while_unfold 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
46 |
by (res_inst_tac [("s","UU"),("t","b`UU")]ssubst 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
47 |
by (etac (flat_codom RS disjE) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
48 |
by (atac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
49 |
by (etac spec 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
50 |
by (simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
51 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
52 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
53 |
by (stac while_unfold 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
54 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
55 |
qed "while_unfold2"; |
244 | 56 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
57 |
Goal "while`b`g`x = while`b`g`(step`b`g`x)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
58 |
by (res_inst_tac [("s", "while`b`g`(iterate (Suc 0) (step`b`g) x)")] trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
59 |
by (rtac (while_unfold2 RS spec) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
60 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
61 |
qed "while_unfold3"; |
244 | 62 |
|
63 |
||
9169 | 64 |
(* ------------------------------------------------------------------------- *) |
65 |
(* properties of while and iterations *) |
|
66 |
(* ------------------------------------------------------------------------- *) |
|
244 | 67 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
68 |
Goal "[| EX y. b`y=FF; iterate k (step`b`g) x = UU |] \ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
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changeset
|
69 |
\ ==>iterate(Suc k) (step`b`g) x=UU"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
70 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
71 |
by (rtac trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
72 |
by (rtac step_def2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
73 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
74 |
by (etac exE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
75 |
by (etac (flat_codom RS disjE) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
76 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
77 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
78 |
qed "loop_lemma1"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
79 |
|
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
80 |
Goal "[|EX y. b`y=FF;iterate (Suc k) (step`b`g) x ~=UU |]==>\ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
81 |
\ iterate k (step`b`g) x ~=UU"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
82 |
|
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
83 |
by (blast_tac (claset() addIs [loop_lemma1]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
84 |
qed "loop_lemma2"; |
244 | 85 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
86 |
Goal "[| ALL x. INV x & b`x=TT & g`x~=UU --> INV (g`x);\ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
87 |
\ EX y. b`y=FF; INV x |] \ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
88 |
\ ==> iterate k (step`b`g) x ~=UU --> INV (iterate k (step`b`g) x)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
89 |
by (nat_ind_tac "k" 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
90 |
by (Asm_simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
91 |
by (strip_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
92 |
by (simp_tac (simpset() addsimps [step_def2]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
93 |
by (res_inst_tac [("p","b`(iterate k (step`b`g) x)")] trE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
94 |
by (etac notE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
95 |
by (asm_simp_tac (HOLCF_ss addsimps [step_def2] ) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
96 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
97 |
by (rtac mp 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
98 |
by (etac spec 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
99 |
by (asm_simp_tac (HOLCF_ss delsimps [iterate_Suc] addsimps [loop_lemma2] ) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
100 |
by (res_inst_tac [("s","iterate (Suc k) (step`b`g) x"), |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
101 |
("t","g`(iterate k (step`b`g) x)")] ssubst 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
102 |
by (atac 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
103 |
by (asm_simp_tac (HOLCF_ss addsimps [step_def2] ) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
104 |
by (asm_simp_tac (HOLCF_ss delsimps [iterate_Suc] addsimps [loop_lemma2] ) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
105 |
qed_spec_mp "loop_lemma3"; |
244 | 106 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
107 |
Goal "ALL x. b`(iterate k (step`b`g) x)=FF --> while`b`g`x= iterate k (step`b`g) x"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
108 |
by (nat_ind_tac "k" 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
109 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
110 |
by (strip_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
111 |
by (stac while_unfold 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
112 |
by (asm_simp_tac HOLCF_ss 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
113 |
by (rtac allI 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
114 |
by (stac iterate_Suc2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
115 |
by (strip_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
116 |
by (rtac trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
117 |
by (rtac while_unfold3 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
118 |
by (Asm_simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
119 |
qed_spec_mp "loop_lemma4"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
120 |
|
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
121 |
Goal "ALL k. b`(iterate k (step`b`g) x) ~= FF ==>\ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
122 |
\ ALL m. while`b`g`(iterate m (step`b`g) x)=UU"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
123 |
by (stac while_def2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
124 |
by (rtac fix_ind 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
125 |
by (rtac (allI RS adm_all) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
126 |
by (rtac adm_eq 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
127 |
by (cont_tacR 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
128 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
129 |
by (rtac allI 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
130 |
by (Simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
131 |
by (res_inst_tac [("p","b`(iterate m (step`b`g) x)")] trE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
132 |
by (Asm_simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
133 |
by (Asm_simp_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
134 |
by (res_inst_tac [("s","xa`(iterate (Suc m) (step`b`g) x)")] trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
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changeset
|
135 |
by (etac spec 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
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diff
changeset
|
136 |
by (rtac cfun_arg_cong 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
137 |
by (rtac trans 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
138 |
by (rtac (iterate_Suc RS sym) 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
139 |
by (asm_simp_tac (HOLCF_ss addsimps [step_def2]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
140 |
by (Blast_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
141 |
qed_spec_mp "loop_lemma5"; |
244 | 142 |
|
143 |
||
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
144 |
Goal "ALL k. b`(iterate k (step`b`g) x) ~= FF ==> while`b`g`x=UU"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
145 |
by (res_inst_tac [("t","x")] (iterate_0 RS subst) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
146 |
by (etac (loop_lemma5) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
147 |
qed "loop_lemma6"; |
244 | 148 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
149 |
Goal "while`b`g`x ~= UU ==> EX k. b`(iterate k (step`b`g) x) = FF"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
150 |
by (blast_tac (claset() addIs [loop_lemma6]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
151 |
qed "loop_lemma7"; |
244 | 152 |
|
153 |
||
1168
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
154 |
(* ------------------------------------------------------------------------- *) |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
155 |
(* an invariant rule for loops *) |
74be52691d62
The curried version of HOLCF is now just called HOLCF. The old
regensbu
parents:
1043
diff
changeset
|
156 |
(* ------------------------------------------------------------------------- *) |
244 | 157 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
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diff
changeset
|
158 |
Goal |
9169 | 159 |
"[| (ALL y. INV y & b`y=TT & g`y ~= UU --> INV (g`y));\ |
160 |
\ (ALL y. INV y & b`y=FF --> Q y);\ |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
161 |
\ INV x; while`b`g`x~=UU |] ==> Q (while`b`g`x)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
162 |
by (res_inst_tac [("P","%k. b`(iterate k (step`b`g) x)=FF")] exE 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
163 |
by (etac loop_lemma7 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
164 |
by (stac (loop_lemma4) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
165 |
by (atac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
166 |
by (dtac spec 1 THEN etac mp 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
167 |
by (rtac conjI 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
168 |
by (atac 2); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
169 |
by (rtac (loop_lemma3) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
170 |
by (assume_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
171 |
by (blast_tac (claset() addIs [loop_lemma6]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
172 |
by (assume_tac 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
173 |
by (rotate_tac ~1 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
174 |
by (asm_full_simp_tac (simpset() addsimps [loop_lemma4]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
175 |
qed "loop_inv2"; |
244 | 176 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
177 |
val [premP,premI,premTT,premFF,premW] = Goal |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
178 |
"[| P(x); \ |
3842 | 179 |
\ !!y. P y ==> INV y;\ |
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
180 |
\ !!y. [| INV y; b`y=TT; g`y~=UU|] ==> INV (g`y);\ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
181 |
\ !!y. [| INV y; b`y=FF|] ==> Q y;\ |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
182 |
\ while`b`g`x ~= UU |] ==> Q (while`b`g`x)"; |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
183 |
by (rtac loop_inv2 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
184 |
by (rtac (premP RS premI) 3); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
185 |
by (rtac premW 3); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
186 |
by (blast_tac (claset() addIs [premTT]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
187 |
by (blast_tac (claset() addIs [premFF]) 1); |
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9169
diff
changeset
|
188 |
qed "loop_inv"; |