| author | Christian Urban <urbanc@in.tum.de> |
| Sun, 29 Aug 2010 00:36:47 +0800 | |
| changeset 2449 | 6b51117b8955 |
| parent 2448 | b9d9c4540265 |
| child 2450 | 217ef3e4282e |
| permissions | -rw-r--r-- |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
1 |
theory SingleLet |
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
2 |
imports "../NewParser" |
|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
3 |
begin |
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
4 |
|
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
5 |
atom_decl name |
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
6 |
|
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
7 |
declare [[STEPS = 100]] |
|
2294
72ad4e766acf
properly exported bn_descr
Christian Urban <urbanc@in.tum.de>
parents:
2293
diff
changeset
|
8 |
|
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
9 |
nominal_datatype single_let: trm = |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
10 |
Var "name" |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
11 |
| App "trm" "trm" |
|
2424
621ebd8b13c4
changed parser so that the binding mode is indicated as "bind (list)", "bind (set)" or "bind (res)"; if only "bind" is given, then bind (list) is assumed as default
Christian Urban <urbanc@in.tum.de>
parents:
2410
diff
changeset
|
12 |
| Lam x::"name" t::"trm" bind x in t |
|
621ebd8b13c4
changed parser so that the binding mode is indicated as "bind (list)", "bind (set)" or "bind (res)"; if only "bind" is given, then bind (list) is assumed as default
Christian Urban <urbanc@in.tum.de>
parents:
2410
diff
changeset
|
13 |
| Let a::"assg" t::"trm" bind (set) "bn a" in t |
|
621ebd8b13c4
changed parser so that the binding mode is indicated as "bind (list)", "bind (set)" or "bind (res)"; if only "bind" is given, then bind (list) is assumed as default
Christian Urban <urbanc@in.tum.de>
parents:
2410
diff
changeset
|
14 |
| Foo x::"name" y::"name" t::"trm" t1::"trm" t2::"trm" bind (set) x in y t t1 t2 |
| 2296 | 15 |
| Bar x::"name" y::"name" t::"trm" bind y x in t x y |
| 2316 | 16 |
| Baz x::"name" t1::"trm" t2::"trm" bind x in t1, bind x in t2 |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
17 |
and assg = |
|
2320
d835a2771608
prove that alpha implies alpha_bn (needed for rsp proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2318
diff
changeset
|
18 |
As "name" x::"name" t::"trm" bind x in t |
|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
19 |
binder |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
20 |
bn::"assg \<Rightarrow> atom set" |
|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
21 |
where |
|
2320
d835a2771608
prove that alpha implies alpha_bn (needed for rsp proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2318
diff
changeset
|
22 |
"bn (As x y t) = {atom x}"
|
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
23 |
|
| 2448 | 24 |
thm Ball_def Bex_def mem_def |
25 |
||
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
26 |
thm single_let.distinct |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
27 |
thm single_let.induct |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
28 |
thm single_let.exhaust |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
29 |
thm single_let.fv_defs |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
30 |
thm single_let.bn_defs |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
31 |
thm single_let.perm_simps |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
32 |
thm single_let.eq_iff |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
33 |
thm single_let.fv_bn_eqvt |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
34 |
thm single_let.size_eqvt |
| 2448 | 35 |
thm single_let.supports |
|
2430
a746d49b0240
updated to new Isabelle
Christian Urban <urbanc@in.tum.de>
parents:
2428
diff
changeset
|
36 |
|
| 2448 | 37 |
lemma test: |
38 |
"finite (supp (t::trm)) \<and> finite (supp (a::assg))" |
|
39 |
apply(rule single_let.induct) |
|
40 |
apply(rule supports_finite) |
|
41 |
apply(rule single_let.supports) |
|
|
2449
6b51117b8955
fiexed problem with constructors that have no arguments
Christian Urban <urbanc@in.tum.de>
parents:
2448
diff
changeset
|
42 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
| 2448 | 43 |
apply(rule supports_finite) |
44 |
apply(rule single_let.supports) |
|
45 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
46 |
apply(rule supports_finite) |
|
47 |
apply(rule single_let.supports) |
|
48 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
49 |
apply(rule supports_finite) |
|
50 |
apply(rule single_let.supports) |
|
51 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
52 |
apply(rule supports_finite) |
|
53 |
apply(rule single_let.supports) |
|
54 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
55 |
apply(rule supports_finite) |
|
56 |
apply(rule single_let.supports) |
|
57 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
58 |
apply(rule supports_finite) |
|
59 |
apply(rule single_let.supports) |
|
60 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
61 |
apply(rule supports_finite) |
|
62 |
apply(rule single_let.supports) |
|
63 |
apply(simp only: finite_supp supp_Pair finite_Un, simp) |
|
64 |
done |
|
65 |
||
66 |
instantiation trm and assg :: fs |
|
67 |
begin |
|
68 |
||
69 |
instance |
|
70 |
apply(default) |
|
71 |
apply(simp_all add: test) |
|
72 |
done |
|
73 |
||
74 |
end |
|
|
2406
428d9cb9a243
can also lift the various eqvt lemmas for bn, fv, fv_bn and size
Christian Urban <urbanc@in.tum.de>
parents:
2405
diff
changeset
|
75 |
|
|
2431
331873ebc5cd
can now deal with type variables in nominal datatype definitions
Christian Urban <urbanc@in.tum.de>
parents:
2430
diff
changeset
|
76 |
|
| 2448 | 77 |
|
78 |
||
79 |
lemma test: |
|
80 |
"(\<exists>p. (bs, x) \<approx>lst (op=) f p (cs, y)) \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>lst (op=) supp p (cs, y))" |
|
81 |
oops |
|
82 |
||
83 |
lemma Abs_eq_iff: |
|
84 |
shows "Abs bs x = Abs cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>gen (op =) supp p (cs, y))" |
|
85 |
and "Abs_res bs x = Abs_res cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>res (op =) supp p (cs, y))" |
|
86 |
and "Abs_lst bsl x = Abs_lst csl y \<longleftrightarrow> (\<exists>p. (bsl, x) \<approx>lst (op =) supp p (csl, y))" |
|
87 |
by (lifting alphas_abs) |
|
88 |
||
89 |
(* |
|
| 2361 | 90 |
lemma supp_fv: |
| 2448 | 91 |
"supp t = fv_trm t \<and> supp b = fv_bn b" |
92 |
apply(rule single_let.induct) |
|
93 |
apply(simp_all only: single_let.fv_defs)[2] |
|
94 |
apply(simp_all only: supp_def)[2] |
|
95 |
apply(simp_all only: single_let.perm_simps)[2] |
|
96 |
apply(simp_all only: single_let.eq_iff)[2] |
|
97 |
apply(simp_all only: de_Morgan_conj)[2] |
|
98 |
apply(simp_all only: Collect_disj_eq)[2] |
|
99 |
apply(simp_all only: finite_Un)[2] |
|
100 |
apply(simp_all only: de_Morgan_conj)[2] |
|
101 |
apply(simp_all only: Collect_disj_eq)[2] |
|
102 |
apply(subgoal_tac "supp (Lam name trm) = supp (Abs_lst [atom name] trm)") |
|
103 |
apply(simp only: single_let.fv_defs) |
|
104 |
apply(simp only: supp_abs) |
|
105 |
apply(simp (no_asm) only: supp_def) |
|
106 |
apply(simp only: single_let.perm_simps) |
|
107 |
apply(simp only: single_let.eq_iff) |
|
108 |
apply(subst test) |
|
109 |
apply(simp only: Abs_eq_iff[symmetric]) |
|
110 |
apply(simp only: alphas_abs[symmetric]) |
|
111 |
apply(simp only: eqvts) |
|
112 |
thm Abs_eq_iff |
|
113 |
apply(simp only: alphas) |
|
| 2365 | 114 |
sorry |
| 2448 | 115 |
*) |
116 |
(* |
|
| 2365 | 117 |
|
118 |
consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm" |
|
119 |
consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg" |
|
120 |
||
121 |
lemma y: |
|
122 |
"perm_bn_trm p (Var x) = (Var x)" |
|
123 |
"perm_bn_trm p (App t1 t2) = (App t1 t2)" |
|
124 |
"perm_bn_trm p ("
|
|
125 |
||
126 |
||
| 2361 | 127 |
|
|
2336
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
128 |
typ trm |
|
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
129 |
typ assg |
|
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
130 |
|
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
131 |
thm trm_assg.fv |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
132 |
thm trm_assg.supp |
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
133 |
thm trm_assg.eq_iff |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
134 |
thm trm_assg.bn |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
135 |
thm trm_assg.perm |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
136 |
thm trm_assg.induct |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
137 |
thm trm_assg.inducts |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
138 |
thm trm_assg.distinct |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
139 |
ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
|
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
140 |
*) |
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
141 |
|
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
142 |
|
|
2064
2725853f43b9
solved the problem with equivariance by first eta-normalising the goal
Christian Urban <urbanc@in.tum.de>
parents:
2028
diff
changeset
|
143 |
|
|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
144 |
end |
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
145 |
|
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
146 |
|
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
147 |