| author | Christian Urban <urbanc@in.tum.de> |
| Fri, 30 Jul 2010 00:40:32 +0100 | |
| changeset 2388 | ebf253d80670 |
| parent 2387 | 082d9fd28f89 |
| child 2389 | 0f24c961b5f6 |
| 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 |
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2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
2 |
imports "../NewParser" |
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1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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3 |
begin |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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4 |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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5 |
atom_decl name |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
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parents:
diff
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6 |
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| 2388 | 7 |
declare [[STEPS = 17]] |
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2294
72ad4e766acf
properly exported bn_descr
Christian Urban <urbanc@in.tum.de>
parents:
2293
diff
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8 |
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2336
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
9 |
nominal_datatype 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" |
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2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
12 |
| Lam x::"name" t::"trm" bind_set x in t |
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d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
13 |
| Let a::"assg" t::"trm" bind_set "bn a" in t |
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2311
4da5c5c29009
work on transitivity proof
Christian Urban <urbanc@in.tum.de>
parents:
2308
diff
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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 = |
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2320
d835a2771608
prove that alpha implies alpha_bn (needed for rsp proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2318
diff
changeset
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18 |
As "name" x::"name" t::"trm" bind x in t |
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1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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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 |
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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}"
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|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
23 |
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| 2388 | 24 |
thm size_eqvt |
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2384
841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
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25 |
thm alpha_bn_imps |
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841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
|
26 |
thm distinct |
|
841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
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27 |
thm eq_iff |
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2387
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helper lemmas for rsp-lemmas
Christian Urban <urbanc@in.tum.de>
parents:
2386
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28 |
thm eq_iff_simps |
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2384
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fixed order of fold_union to make alpha and fv agree
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parents:
2382
diff
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29 |
thm fv_defs |
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841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
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30 |
thm perm_simps |
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841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
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|
31 |
thm perm_laws |
| 2388 | 32 |
thm funs_rsp |
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2384
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parents:
2382
diff
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33 |
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841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
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34 |
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| 2359 | 35 |
typ trm |
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typ assg |
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| 2338 | 37 |
term Var |
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term App |
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term Baz |
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more quotient-definitions
Christian Urban <urbanc@in.tum.de>
parents:
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40 |
term bn |
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1e0b3992189c
more quotient-definitions
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parents:
2338
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41 |
term fv_trm |
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2384
841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
|
42 |
term alpha_bn |
| 2338 | 43 |
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2384
841b7e34e70a
fixed order of fold_union to make alpha and fv agree
Christian Urban <urbanc@in.tum.de>
parents:
2382
diff
changeset
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44 |
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| 2388 | 45 |
lemma exi_zero: "P 0 \<Longrightarrow> \<exists>(x::perm). P x" by auto |
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ML {*
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val pre_ss = @{thms fun_rel_def}
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val post_ss = @{thms alphas prod_alpha_def prod_rel.simps
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prod_fv.simps fresh_star_zero permute_zero funs_rsp prod.cases alpha_bn_imps} |
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val tac = |
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asm_full_simp_tac (HOL_ss addsimps pre_ss) |
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THEN' REPEAT o (resolve_tac @{thms allI impI})
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THEN' resolve_tac @{thms alpha_trm_raw_alpha_assg_raw_alpha_bn_raw.intros}
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THEN_ALL_NEW (TRY o (rtac @{thm exi_zero}) THEN' asm_full_simp_tac (HOL_ss addsimps post_ss))
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*} |
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| 2361 | 58 |
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| 2359 | 59 |
lemma [quot_respect]: |
| 2361 | 60 |
"(op= ===> alpha_trm_raw) Var_raw Var_raw" |
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"(alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) App_raw App_raw" |
| 2361 | 62 |
"(op= ===> alpha_trm_raw ===> alpha_trm_raw) Lam_raw Lam_raw" |
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"(alpha_assg_raw ===> alpha_trm_raw ===> alpha_trm_raw) Let_raw Let_raw" |
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| 2388 | 64 |
"(op= ===> op= ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) |
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Foo_raw Foo_raw" |
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"(op= ===> op= ===> alpha_trm_raw ===> alpha_trm_raw) Bar_raw Bar_raw" |
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"(op= ===> alpha_trm_raw ===> alpha_trm_raw ===> alpha_trm_raw) Baz_raw Baz_raw" |
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"(op = ===> op = ===> alpha_trm_raw ===> alpha_assg_raw) As_raw As_raw" |
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| 2388 | 69 |
apply(tactic {* ALLGOALS tac *})
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| 2359 | 70 |
done |
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| 2361 | 72 |
lemma [quot_respect]: |
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"(alpha_trm_raw ===> op =) fv_trm_raw fv_trm_raw" |
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"(alpha_assg_raw ===> op =) fv_bn_raw fv_bn_raw" |
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"(alpha_assg_raw ===> op =) bn_raw bn_raw" |
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"(alpha_assg_raw ===> op =) fv_assg_raw fv_assg_raw" |
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"(op = ===> alpha_trm_raw ===> alpha_trm_raw) permute permute" |
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| 2388 | 78 |
apply(simp_all add: alpha_bn_imps funs_rsp) |
| 2361 | 79 |
sorry |
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ML {*
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val thms_d = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms distinct}
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*} |
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ML {*
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val thms_i = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw_assg_raw.inducts}
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*} |
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ML {*
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val thms_f = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms fv_defs}
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*} |
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thm perm_defs[no_vars] |
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instance trm :: pt sorry |
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instance assg :: pt sorry |
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| 2365 | 98 |
lemma b1: |
| 2361 | 99 |
"p \<bullet> Var name = Var (p \<bullet> name)" |
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"p \<bullet> App trm1 trm2 = App (p \<bullet> trm1) (p \<bullet> trm2)" |
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"p \<bullet> Lam name trm = Lam (p \<bullet> name) (p \<bullet> trm)" |
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"p \<bullet> Let assg trm = Let (p \<bullet> assg) (p \<bullet> trm)" |
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"p \<bullet> Foo name1 name2 trm1 trm2 trm3 = |
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Foo (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm1) (p \<bullet> trm2) (p \<bullet> trm3)" |
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"p \<bullet> Bar name1 name2 trm = Bar (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm)" |
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"p \<bullet> Baz name trm1 trm2 = Baz (p \<bullet> name) (p \<bullet> trm1) (p \<bullet> trm2)" |
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"p \<bullet> As name1 name2 trm = As (p \<bullet> name1) (p \<bullet> name2) (p \<bullet> trm)" |
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sorry |
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(* |
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112 |
ML {*
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val thms_p = map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms perm_defs}
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114 |
*} |
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*) |
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| 2365 | 117 |
thm eq_iff[no_vars] |
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ML {*
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val q1 = lift_thm [@{typ trm}, @{typ assg}] @{context} @{thm "eq_iff"(1)}
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121 |
*} |
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| 2361 | 123 |
local_setup {* Local_Theory.note ((@{binding d1}, []), thms_d) #> snd *}
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local_setup {* Local_Theory.note ((@{binding i1}, []), thms_i) #> snd *}
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local_setup {* Local_Theory.note ((@{binding f1}, []), thms_f) #> snd *}
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| 2365 | 126 |
local_setup {* Local_Theory.note ((@{binding q1}, []), [q1]) #> snd *}
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127 |
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| 2361 | 128 |
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129 |
thm perm_defs |
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130 |
thm perm_simps |
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131 |
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132 |
lemma supp_fv: |
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133 |
"supp t = fv_trm t" |
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134 |
"supp b = fv_bn b" |
|
135 |
apply(induct t and b rule: i1) |
|
136 |
apply(simp_all add: f1) |
|
137 |
apply(simp_all add: supp_def) |
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| 2365 | 138 |
apply(simp_all add: b1) |
139 |
sorry |
|
140 |
||
141 |
consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm" |
|
142 |
consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg" |
|
143 |
||
144 |
lemma y: |
|
145 |
"perm_bn_trm p (Var x) = (Var x)" |
|
146 |
"perm_bn_trm p (App t1 t2) = (App t1 t2)" |
|
147 |
"perm_bn_trm p ("
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148 |
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149 |
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| 2361 | 150 |
|
151 |
ML {*
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152 |
map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms eq_iff}
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153 |
*} |
|
154 |
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155 |
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156 |
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| 2359 | 157 |
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158 |
||
159 |
lemma "Var x \<noteq> App y1 y2" |
|
160 |
apply(descending) |
|
161 |
apply(simp add: trm_raw.distinct) |
|
162 |
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163 |
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164 |
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165 |
ML {*
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166 |
map (lift_thm [@{typ trm}, @{typ assg}] @{context}) @{thms trm_raw.distinct(1)}
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167 |
*} |
|
168 |
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169 |
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170 |
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| 2338 | 171 |
|
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2336
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
172 |
typ trm |
|
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
173 |
typ assg |
|
f2d545b77b31
added definition of the quotient types
Christian Urban <urbanc@in.tum.de>
parents:
2330
diff
changeset
|
174 |
|
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
175 |
thm trm_assg.fv |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
176 |
thm trm_assg.supp |
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
177 |
thm trm_assg.eq_iff |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
178 |
thm trm_assg.bn |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
179 |
thm trm_assg.perm |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
180 |
thm trm_assg.induct |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
181 |
thm trm_assg.inducts |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
182 |
thm trm_assg.distinct |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
183 |
ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
|
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
184 |
|
|
2288
3b83960f9544
new fv/fv_bn function (supp breaks now); exported raw perms and raw funs into separate ML-files
Christian Urban <urbanc@in.tum.de>
parents:
2146
diff
changeset
|
185 |
(* TEMPORARY |
|
2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
186 |
thm trm_assg.fv[simplified trm_assg.supp(1-2)] |
|
2288
3b83960f9544
new fv/fv_bn function (supp breaks now); exported raw perms and raw funs into separate ML-files
Christian Urban <urbanc@in.tum.de>
parents:
2146
diff
changeset
|
187 |
*) |
|
2064
2725853f43b9
solved the problem with equivariance by first eta-normalising the goal
Christian Urban <urbanc@in.tum.de>
parents:
2028
diff
changeset
|
188 |
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|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
189 |
end |
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
190 |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
191 |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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192 |