| author | Christian Urban <urbanc@in.tum.de> |
| Sun, 29 Aug 2010 01:17:36 +0800 | |
| changeset 2450 | 217ef3e4282e |
| parent 2449 | 6b51117b8955 |
| child 2451 | d2e929f51fa9 |
| permissions | -rw-r--r-- |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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1 |
theory SingleLet |
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2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
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imports "../NewParser" |
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begin |
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c69d9fb16785
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c69d9fb16785
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atom_decl name |
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2436
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cleaned up (almost completely) the examples
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parents:
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declare [[STEPS = 100]] |
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2294
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properly exported bn_descr
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parents:
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2436
3885dc2669f9
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Christian Urban <urbanc@in.tum.de>
parents:
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nominal_datatype single_let: trm = |
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1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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Var "name" |
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60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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| App "trm" "trm" |
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2424
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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:
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| Lam x::"name" t::"trm" bind x in t |
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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
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| Let a::"assg" t::"trm" bind (set) "bn a" in t |
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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
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| 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 |
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1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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17 |
and assg = |
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prove that alpha implies alpha_bn (needed for rsp proofs)
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parents:
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As "name" x::"name" t::"trm" bind x in t |
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parents:
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binder |
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1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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bn::"assg \<Rightarrow> atom set" |
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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
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"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
|
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| 2448 | 24 |
thm Ball_def Bex_def mem_def |
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||
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parents:
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thm single_let.distinct |
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cleaned up (almost completely) the examples
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parents:
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thm single_let.induct |
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parents:
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thm single_let.exhaust |
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parents:
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thm single_let.fv_defs |
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parents:
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thm single_let.bn_defs |
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parents:
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thm single_let.perm_simps |
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parents:
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thm single_let.eq_iff |
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parents:
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thm single_let.fv_bn_eqvt |
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parents:
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thm single_let.size_eqvt |
| 2448 | 35 |
thm single_let.supports |
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added proofs for fsupp properties
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parents:
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thm single_let.fsupp |
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| 2448 | 39 |
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instantiation trm and assg :: fs |
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begin |
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instance |
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apply(default) |
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parents:
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apply(simp_all add: single_let.fsupp) |
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done |
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end |
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2406
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can also lift the various eqvt lemmas for bn, fv, fv_bn and size
Christian Urban <urbanc@in.tum.de>
parents:
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can now deal with type variables in nominal datatype definitions
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| 2448 | 51 |
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lemma test: |
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"(\<exists>p. (bs, x) \<approx>lst (op=) f p (cs, y)) \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>lst (op=) supp p (cs, y))" |
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oops |
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lemma Abs_eq_iff: |
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shows "Abs bs x = Abs cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>gen (op =) supp p (cs, y))" |
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and "Abs_res bs x = Abs_res cs y \<longleftrightarrow> (\<exists>p. (bs, x) \<approx>res (op =) supp p (cs, y))" |
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and "Abs_lst bsl x = Abs_lst csl y \<longleftrightarrow> (\<exists>p. (bsl, x) \<approx>lst (op =) supp p (csl, y))" |
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by (lifting alphas_abs) |
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(* |
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lemma supp_fv: |
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"supp t = fv_trm t \<and> supp b = fv_bn b" |
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apply(rule single_let.induct) |
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apply(simp_all only: single_let.fv_defs)[2] |
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apply(simp_all only: supp_def)[2] |
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apply(simp_all only: single_let.perm_simps)[2] |
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apply(simp_all only: single_let.eq_iff)[2] |
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apply(simp_all only: de_Morgan_conj)[2] |
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apply(simp_all only: Collect_disj_eq)[2] |
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apply(simp_all only: finite_Un)[2] |
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apply(simp_all only: de_Morgan_conj)[2] |
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apply(simp_all only: Collect_disj_eq)[2] |
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apply(subgoal_tac "supp (Lam name trm) = supp (Abs_lst [atom name] trm)") |
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apply(simp only: single_let.fv_defs) |
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apply(simp only: supp_abs) |
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apply(simp (no_asm) only: supp_def) |
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apply(simp only: single_let.perm_simps) |
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apply(simp only: single_let.eq_iff) |
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apply(subst test) |
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apply(simp only: Abs_eq_iff[symmetric]) |
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apply(simp only: alphas_abs[symmetric]) |
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apply(simp only: eqvts) |
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thm Abs_eq_iff |
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apply(simp only: alphas) |
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sorry |
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*) |
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(* |
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consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm" |
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consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg" |
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lemma y: |
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"perm_bn_trm p (Var x) = (Var x)" |
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"perm_bn_trm p (App t1 t2) = (App t1 t2)" |
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"perm_bn_trm p ("
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| 2361 | 101 |
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typ trm |
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typ assg |
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1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
105 |
thm trm_assg.fv |
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60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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106 |
thm trm_assg.supp |
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2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
changeset
|
107 |
thm trm_assg.eq_iff |
|
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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108 |
thm trm_assg.bn |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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109 |
thm trm_assg.perm |
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60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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110 |
thm trm_assg.induct |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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111 |
thm trm_assg.inducts |
|
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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112 |
thm trm_assg.distinct |
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60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
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113 |
ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *}
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2436
3885dc2669f9
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Christian Urban <urbanc@in.tum.de>
parents:
2434
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114 |
*) |
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2024
d974059827ad
Equivariance fails for single let?
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
1911
diff
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115 |
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2436
3885dc2669f9
cleaned up (almost completely) the examples
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parents:
2434
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116 |
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2064
2725853f43b9
solved the problem with equivariance by first eta-normalising the goal
Christian Urban <urbanc@in.tum.de>
parents:
2028
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117 |
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1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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118 |
end |
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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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119 |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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120 |
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c69d9fb16785
Move Ex1 and Ex2 out of Test
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parents:
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