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theory CoreHaskell
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imports "../NewParser"
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begin
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(* core haskell *)
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2100
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(* at the moment it is hard coded that shallow binders
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need to use bind_set *)
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atom_decl var
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atom_decl cvar
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atom_decl tvar
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nominal_datatype tkind =
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KStar
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| KFun "tkind" "tkind"
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and ckind =
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CKEq "ty" "ty"
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and ty =
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TVar "tvar"
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| TC "string"
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| TApp "ty" "ty"
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| TFun "string" "ty_lst"
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| TAll tv::"tvar" "tkind" T::"ty" bind_set tv in T
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| TEq "ckind" "ty"
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and ty_lst =
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TsNil
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| TsCons "ty" "ty_lst"
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and co =
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CVar "cvar"
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| CConst "string"
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| CApp "co" "co"
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| CFun "string" "co_lst"
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| CAll cv::"cvar" "ckind" C::"co" bind_set cv in C
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| CEq "ckind" "co"
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| CRefl "ty"
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| CSym "co"
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| CCir "co" "co"
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| CAt "co" "ty"
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| CLeft "co"
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| CRight "co"
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| CSim "co" "co"
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| CRightc "co"
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| CLeftc "co"
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| CCoe "co" "co"
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and co_lst =
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CsNil
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| CsCons "co" "co_lst"
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c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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and trm =
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Var "var"
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| K "string"
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| LAMT tv::"tvar" "tkind" t::"trm" bind_set tv in t
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| LAMC cv::"cvar" "ckind" t::"trm" bind_set cv in t
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| AppT "trm" "ty"
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| AppC "trm" "co"
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| Lam v::"var" "ty" t::"trm" bind_set v in t
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| App "trm" "trm"
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| Let x::"var" "ty" "trm" t::"trm" bind_set x in t
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c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 59
| Case "trm" "assoc_lst"
c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 60
| Cast "trm" "ty" --"ty is supposed to be a coercion type only"
c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 61
and assoc_lst =
c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 62
ANil
c9bc3b61046c
Modification to Core Haskell to make it accepted with an empty binding function.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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| ACons p::"pat" t::"trm" "assoc_lst" bind "bv p" in t
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and pat =
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Kpat "string" "tvars" "cvars" "vars"
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and vars =
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VsNil
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| VsCons "var" "ty" "vars"
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and tvars =
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TvsNil
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| TvsCons "tvar" "tkind" "tvars"
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and cvars =
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CvsNil
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| CvsCons "cvar" "ckind" "cvars"
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binder
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bv :: "pat \<Rightarrow> atom list"
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and bv_vs :: "vars \<Rightarrow> atom list"
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and bv_tvs :: "tvars \<Rightarrow> atom list"
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and bv_cvs :: "cvars \<Rightarrow> atom list"
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where
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"bv (Kpat s tvts tvcs vs) = append (bv_tvs tvts) (append (bv_cvs tvcs) (bv_vs vs))"
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| "bv_vs VsNil = []"
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| "bv_vs (VsCons v k t) = (atom v) # bv_vs t"
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| "bv_tvs TvsNil = []"
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| "bv_tvs (TvsCons v k t) = (atom v) # bv_tvs t"
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| "bv_cvs CvsNil = []"
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
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| "bv_cvs (CvsCons v k t) = (atom v) # bv_cvs t"
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lemmas fv_supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.supp(1-9,11,13,15)
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lemmas supp=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.fv[simplified fv_supp]
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lemmas perm=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.perm
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lemmas eq_iff=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.eq_iff
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lemmas inducts=tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.inducts
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lemmas alpha_inducts=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.inducts
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lemmas alpha_intros=alpha_tkind_raw_alpha_ckind_raw_alpha_ty_raw_alpha_ty_lst_raw_alpha_co_raw_alpha_co_lst_raw_alpha_trm_raw_alpha_assoc_lst_raw_alpha_pat_raw_alpha_vars_raw_alpha_tvars_raw_alpha_cvars_raw_alpha_bv_raw_alpha_bv_vs_raw_alpha_bv_tvs_raw_alpha_bv_cvs_raw.intros
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lemma fresh_star_minus_perm: "as \<sharp>* - p = as \<sharp>* (p :: perm)"
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unfolding fresh_star_def Ball_def
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by auto (simp_all add: fresh_minus_perm)
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0ea578c6dae3
Parsing bn functions that call other bn functions and transmitting this information to fv/alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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primrec permute_bv_vs_raw
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where "permute_bv_vs_raw p VsNil_raw = VsNil_raw"
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| "permute_bv_vs_raw p (VsCons_raw v t l) = VsCons_raw (p \<bullet> v) t (permute_bv_vs_raw p l)"
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primrec permute_bv_cvs_raw
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where "permute_bv_cvs_raw p CvsNil_raw = CvsNil_raw"
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| "permute_bv_cvs_raw p (CvsCons_raw v t l) = CvsCons_raw (p \<bullet> v) t (permute_bv_cvs_raw p l)"
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primrec permute_bv_tvs_raw
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where "permute_bv_tvs_raw p TvsNil_raw = TvsNil_raw"
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| "permute_bv_tvs_raw p (TvsCons_raw v t l) = TvsCons_raw (p \<bullet> v) t (permute_bv_tvs_raw p l)"
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primrec permute_bv_raw
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where "permute_bv_raw p (Kpat_raw c l1 l2 l3) =
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Kpat_raw c (permute_bv_tvs_raw p l1) (permute_bv_cvs_raw p l2) (permute_bv_vs_raw p l3)"
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quotient_definition "permute_bv_vs :: perm \<Rightarrow> vars \<Rightarrow> vars"
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is "permute_bv_vs_raw"
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quotient_definition "permute_bv_cvs :: perm \<Rightarrow> cvars \<Rightarrow> cvars"
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is "permute_bv_cvs_raw"
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quotient_definition "permute_bv_tvs :: perm \<Rightarrow> tvars \<Rightarrow> tvars"
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is "permute_bv_tvs_raw"
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quotient_definition "permute_bv :: perm \<Rightarrow> pat \<Rightarrow> pat"
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is "permute_bv_raw"
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lemma rsp_pre:
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"alpha_tvars_raw d a \<Longrightarrow> alpha_tvars_raw (permute_bv_tvs_raw x d) (permute_bv_tvs_raw x a)"
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"alpha_cvars_raw e b \<Longrightarrow> alpha_cvars_raw (permute_bv_cvs_raw x e) (permute_bv_cvs_raw x b)"
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"alpha_vars_raw f c \<Longrightarrow> alpha_vars_raw (permute_bv_vs_raw x f) (permute_bv_vs_raw x c)"
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apply (erule_tac [!] alpha_inducts)
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apply (simp_all only: alpha_intros perm permute_bv_tvs_raw.simps permute_bv_cvs_raw.simps permute_bv_vs_raw.simps)
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done
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Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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lemma [quot_respect]:
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"(op = ===> alpha_pat_raw ===> alpha_pat_raw) permute_bv_raw permute_bv_raw"
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"(op = ===> alpha_tvars_raw ===> alpha_tvars_raw) permute_bv_tvs_raw permute_bv_tvs_raw"
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"(op = ===> alpha_cvars_raw ===> alpha_cvars_raw) permute_bv_cvs_raw permute_bv_cvs_raw"
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"(op = ===> alpha_vars_raw ===> alpha_vars_raw) permute_bv_vs_raw permute_bv_vs_raw"
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apply (simp_all add: rsp_pre)
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apply clarify
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apply (erule_tac alpha_inducts)
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apply (simp_all)
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apply (rule alpha_intros)
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apply (simp_all add: rsp_pre)
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done
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thm permute_bv_raw.simps[no_vars]
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permute_bv_vs_raw.simps[quot_lifted]
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permute_bv_cvs_raw.simps[quot_lifted]
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permute_bv_tvs_raw.simps[quot_lifted]
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lemma permute_bv_pre:
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"permute_bv p (Kpat c l1 l2 l3) =
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Kpat c (permute_bv_tvs p l1) (permute_bv_cvs p l2) (permute_bv_vs p l3)"
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by (lifting permute_bv_raw.simps)
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lemmas permute_bv[simp] =
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permute_bv_pre
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permute_bv_vs_raw.simps[quot_lifted]
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permute_bv_cvs_raw.simps[quot_lifted]
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permute_bv_tvs_raw.simps[quot_lifted]
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733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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lemma perm_bv1:
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"p \<bullet> bv_cvs b = bv_cvs (permute_bv_cvs p b)"
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"p \<bullet> bv_tvs c = bv_tvs (permute_bv_tvs p c)"
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"p \<bullet> bv_vs d = bv_vs (permute_bv_vs p d)"
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apply(induct b rule: inducts(12))
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apply(simp_all add:permute_bv eqvts)
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apply(induct c rule: inducts(11))
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apply(simp_all add:permute_bv eqvts)
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apply(induct d rule: inducts(10))
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apply(simp_all add:permute_bv eqvts)
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done
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lemma perm_bv2:
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"p \<bullet> bv l = bv (permute_bv p l)"
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apply(induct l rule: inducts(9))
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apply(simp_all add:permute_bv)
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apply(simp add: perm_bv1[symmetric])
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apply(simp add: eqvts)
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done
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
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1648
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lemma alpha_perm_bn1:
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"alpha_bv_tvs tvars (permute_bv_tvs q tvars)"
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"alpha_bv_cvs cvars (permute_bv_cvs q cvars)"
+ − 184
"alpha_bv_vs vars (permute_bv_vs q vars)"
+ − 185
apply(induct tvars rule: inducts(11))
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+ − 186
apply(simp_all add:permute_bv eqvts eq_iff)
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apply(induct cvars rule: inducts(12))
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apply(simp_all add:permute_bv eqvts eq_iff)
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+ − 189
apply(induct vars rule: inducts(10))
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apply(simp_all add:permute_bv eqvts eq_iff)
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done
+ − 192
+ − 193
lemma alpha_perm_bn:
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 194
"alpha_bv pt (permute_bv q pt)"
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 195
apply(induct pt rule: inducts(9))
1648
+ − 196
apply(simp_all add:permute_bv eqvts eq_iff alpha_perm_bn1)
+ − 197
done
+ − 198
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 199
lemma ACons_subst:
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 200
"supp (Abs_lst (bv pt) trm) \<sharp>* q \<Longrightarrow> (ACons pt trm al) = ACons (permute_bv q pt) (q \<bullet> trm) al"
1648
+ − 201
apply (simp only: eq_iff)
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apply (simp add: alpha_perm_bn)
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+ − 203
apply (rule_tac x="q" in exI)
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apply (simp add: alphas)
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apply (simp add: perm_bv2[symmetric])
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apply (simp add: supp_abs)
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apply (simp add: fv_supp)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 208
apply (simp add: supp_eqvt[symmetric] set_eqvt[symmetric] Diff_eqvt[symmetric])
1648
+ − 209
apply (rule supp_perm_eq[symmetric])
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apply (subst supp_finite_atom_set)
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apply (rule finite_Diff)
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apply (simp add: finite_supp)
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apply (assumption)
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done
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 215
1647
+ − 216
lemma permute_bv_zero1:
1700
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"permute_bv_cvs 0 b = b"
+ − 218
"permute_bv_tvs 0 c = c"
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"permute_bv_vs 0 d = d"
1647
+ − 220
apply(induct b rule: inducts(12))
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apply(simp_all add:permute_bv eqvts)
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apply(induct c rule: inducts(11))
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apply(simp_all add:permute_bv eqvts)
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apply(induct d rule: inducts(10))
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apply(simp_all add:permute_bv eqvts)
+ − 226
done
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 227
1647
+ − 228
lemma permute_bv_zero2:
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"permute_bv 0 a = a"
+ − 230
apply(induct a rule: inducts(9))
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apply(simp_all add:permute_bv eqvts permute_bv_zero1)
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done
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 233
1700
+ − 234
lemma fv_alpha1: "fv_bv_tvs x \<sharp>* pa \<Longrightarrow> alpha_bv_tvs (pa \<bullet> x) x"
2044
+ − 235
apply (induct x rule: inducts(11))
+ − 236
apply (simp_all add: eq_iff fresh_star_union)
+ − 237
done
1635
+ − 238
1700
+ − 239
lemma fv_alpha2: "fv_bv_cvs x \<sharp>* pa \<Longrightarrow> alpha_bv_cvs (pa \<bullet> x) x"
1635
+ − 240
apply (induct x rule: inducts(12))
2044
+ − 241
apply (rule TrueI)+
1635
+ − 242
apply (simp_all add: eq_iff fresh_star_union)
+ − 243
apply (subst supp_perm_eq)
+ − 244
apply (simp_all add: fv_supp)
+ − 245
done
+ − 246
1700
+ − 247
lemma fv_alpha3: "fv_bv_vs x \<sharp>* pa \<Longrightarrow> alpha_bv_vs (pa \<bullet> x) x"
1635
+ − 248
apply (induct x rule: inducts(10))
2044
+ − 249
apply (rule TrueI)+
+ − 250
apply (simp_all add: fresh_star_union eq_iff)
1635
+ − 251
apply (subst supp_perm_eq)
+ − 252
apply (simp_all add: fv_supp)
+ − 253
done
+ − 254
+ − 255
lemma fv_alpha: "fv_bv x \<sharp>* pa \<Longrightarrow> alpha_bv (pa \<bullet> x) x"
+ − 256
apply (induct x rule: inducts(9))
2044
+ − 257
apply (rule TrueI)+
1635
+ − 258
apply (simp_all add: eq_iff fresh_star_union)
+ − 259
apply (simp add: fv_alpha1 fv_alpha2 fv_alpha3)
2044
+ − 260
apply (subst supp_perm_eq)
+ − 261
apply (simp_all add: fv_supp)
1635
+ − 262
done
+ − 263
1700
+ − 264
lemma fin1: "finite (fv_bv_tvs x)"
1635
+ − 265
apply (induct x rule: inducts(11))
+ − 266
apply (simp_all add: fv_supp finite_supp)
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done
+ − 268
1700
+ − 269
lemma fin2: "finite (fv_bv_cvs x)"
1635
+ − 270
apply (induct x rule: inducts(12))
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apply (simp_all add: fv_supp finite_supp)
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done
+ − 273
1700
+ − 274
lemma fin3: "finite (fv_bv_vs x)"
1635
+ − 275
apply (induct x rule: inducts(10))
+ − 276
apply (simp_all add: fv_supp finite_supp)
+ − 277
done
+ − 278
+ − 279
lemma fin_fv_bv: "finite (fv_bv x)"
+ − 280
apply (induct x rule: inducts(9))
2044
+ − 281
apply (rule TrueI)+
+ − 282
defer
+ − 283
apply (rule TrueI)+
1635
+ − 284
apply (simp add: fin1 fin2 fin3)
2044
+ − 285
apply (rule finite_supp)
1635
+ − 286
done
+ − 287
1700
+ − 288
lemma finb1: "finite (set (bv_tvs x))"
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+ − 289
apply (induct x rule: inducts(11))
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apply (simp_all add: fv_supp finite_supp)
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done
+ − 292
1700
+ − 293
lemma finb2: "finite (set (bv_cvs x))"
1635
+ − 294
apply (induct x rule: inducts(12))
+ − 295
apply (simp_all add: fv_supp finite_supp)
+ − 296
done
+ − 297
1700
+ − 298
lemma finb3: "finite (set (bv_vs x))"
1635
+ − 299
apply (induct x rule: inducts(10))
+ − 300
apply (simp_all add: fv_supp finite_supp)
+ − 301
done
+ − 302
1695
+ − 303
lemma fin_bv: "finite (set (bv x))"
1635
+ − 304
apply (induct x rule: inducts(9))
2044
+ − 305
apply (simp_all add: finb1 finb2 finb3)
1635
+ − 306
done
+ − 307
1701
+ − 308
lemma strong_induction_principle:
1631
+ − 309
assumes a01: "\<And>b. P1 b KStar"
+ − 310
and a02: "\<And>tkind1 tkind2 b. \<lbrakk>\<And>c. P1 c tkind1; \<And>c. P1 c tkind2\<rbrakk> \<Longrightarrow> P1 b (KFun tkind1 tkind2)"
+ − 311
and a03: "\<And>ty1 ty2 b. \<lbrakk>\<And>c. P3 c ty1; \<And>c. P3 c ty2\<rbrakk> \<Longrightarrow> P2 b (CKEq ty1 ty2)"
+ − 312
and a04: "\<And>tvar b. P3 b (TVar tvar)"
1684
+ − 313
and a05: "\<And>string b. P3 b (TC string)"
1631
+ − 314
and a06: "\<And>ty1 ty2 b. \<lbrakk>\<And>c. P3 c ty1; \<And>c. P3 c ty2\<rbrakk> \<Longrightarrow> P3 b (TApp ty1 ty2)"
1684
+ − 315
and a07: "\<And>string ty_lst b. \<lbrakk>\<And>c. P4 c ty_lst\<rbrakk> \<Longrightarrow> P3 b (TFun string ty_lst)"
1632
+ − 316
and a08: "\<And>tvar tkind ty b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P3 c ty; atom tvar \<sharp> b\<rbrakk>
+ − 317
\<Longrightarrow> P3 b (TAll tvar tkind ty)"
1701
+ − 318
and a09: "\<And>ck ty b. \<lbrakk>\<And>c. P2 c ck; \<And>c. P3 c ty\<rbrakk> \<Longrightarrow> P3 b (TEq ck ty)"
+ − 319
and a10: "\<And>b. P4 b TsNil"
+ − 320
and a11: "\<And>ty ty_lst b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P4 c ty_lst\<rbrakk> \<Longrightarrow> P4 b (TsCons ty ty_lst)"
+ − 321
and a12: "\<And>string b. P5 b (CVar string)"
+ − 322
and a12a:"\<And>str b. P5 b (CConst str)"
1631
+ − 323
and a13: "\<And>co1 co2 b. \<lbrakk>\<And>c. P5 c co1; \<And>c. P5 c co2\<rbrakk> \<Longrightarrow> P5 b (CApp co1 co2)"
1684
+ − 324
and a14: "\<And>string co_lst b. \<lbrakk>\<And>c. P6 c co_lst\<rbrakk> \<Longrightarrow> P5 b (CFun string co_lst)"
1632
+ − 325
and a15: "\<And>tvar ckind co b. \<lbrakk>\<And>c. P2 c ckind; \<And>c. P5 c co; atom tvar \<sharp> b\<rbrakk>
+ − 326
\<Longrightarrow> P5 b (CAll tvar ckind co)"
1701
+ − 327
and a16: "\<And>ck co b. \<lbrakk>\<And>c. P2 c ck; \<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CEq ck co)"
+ − 328
and a17: "\<And>ty b. \<lbrakk>\<And>c. P3 c ty\<rbrakk> \<Longrightarrow> P5 b (CRefl ty)"
+ − 329
and a17a: "\<And>co b. \<lbrakk>\<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CSym co)"
1631
+ − 330
and a18: "\<And>co1 co2 b. \<lbrakk>\<And>c. P5 c co1; \<And>c. P5 c co2\<rbrakk> \<Longrightarrow> P5 b (CCir co1 co2)"
1701
+ − 331
and a18a:"\<And>co ty b. \<lbrakk>\<And>c. P5 c co; \<And>c. P3 c ty\<rbrakk> \<Longrightarrow> P5 b (CAt co ty)"
1631
+ − 332
and a19: "\<And>co b. \<lbrakk>\<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CLeft co)"
+ − 333
and a20: "\<And>co b. \<lbrakk>\<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CRight co)"
1701
+ − 334
and a21: "\<And>co1 co2 b. \<lbrakk>\<And>c. P5 c co1; \<And>c. P5 c co2\<rbrakk> \<Longrightarrow> P5 b (CSim co1 co2)"
1631
+ − 335
and a22: "\<And>co b. \<lbrakk>\<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CRightc co)"
+ − 336
and a23: "\<And>co b. \<lbrakk>\<And>c. P5 c co\<rbrakk> \<Longrightarrow> P5 b (CLeftc co)"
+ − 337
and a24: "\<And>co1 co2 b. \<lbrakk>\<And>c. P5 c co1; \<And>c. P5 c co2\<rbrakk> \<Longrightarrow> P5 b (CCoe co1 co2)"
+ − 338
and a25: "\<And>b. P6 b CsNil"
+ − 339
and a26: "\<And>co co_lst b. \<lbrakk>\<And>c. P5 c co; \<And>c. P6 c co_lst\<rbrakk> \<Longrightarrow> P6 b (CsCons co co_lst)"
+ − 340
and a27: "\<And>var b. P7 b (Var var)"
1701
+ − 341
and a28: "\<And>string b. P7 b (K string)"
1632
+ − 342
and a29: "\<And>tvar tkind trm b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P7 c trm; atom tvar \<sharp> b\<rbrakk>
+ − 343
\<Longrightarrow> P7 b (LAMT tvar tkind trm)"
+ − 344
and a30: "\<And>tvar ckind trm b. \<lbrakk>\<And>c. P2 c ckind; \<And>c. P7 c trm; atom tvar \<sharp> b\<rbrakk>
+ − 345
\<Longrightarrow> P7 b (LAMC tvar ckind trm)"
1701
+ − 346
and a31: "\<And>trm ty b. \<lbrakk>\<And>c. P7 c trm; \<And>c. P3 c ty\<rbrakk> \<Longrightarrow> P7 b (AppT trm ty)"
+ − 347
and a31a:"\<And>trm co b. \<lbrakk>\<And>c. P7 c trm; \<And>c. P5 c co\<rbrakk> \<Longrightarrow> P7 b (AppC trm co)"
1632
+ − 348
and a32: "\<And>var ty trm b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P7 c trm; atom var \<sharp> b\<rbrakk> \<Longrightarrow> P7 b (Lam var ty trm)"
1631
+ − 349
and a33: "\<And>trm1 trm2 b. \<lbrakk>\<And>c. P7 c trm1; \<And>c. P7 c trm2\<rbrakk> \<Longrightarrow> P7 b (App trm1 trm2)"
1632
+ − 350
and a34: "\<And>var ty trm1 trm2 b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P7 c trm1; \<And>c. P7 c trm2; atom var \<sharp> b\<rbrakk>
1631
+ − 351
\<Longrightarrow> P7 b (Let var ty trm1 trm2)"
+ − 352
and a35: "\<And>trm assoc_lst b. \<lbrakk>\<And>c. P7 c trm; \<And>c. P8 c assoc_lst\<rbrakk> \<Longrightarrow> P7 b (Case trm assoc_lst)"
+ − 353
and a36: "\<And>trm ty b. \<lbrakk>\<And>c. P7 c trm; \<And>c. P3 c ty\<rbrakk> \<Longrightarrow> P7 b (Cast trm ty)"
+ − 354
and a37: "\<And>b. P8 b ANil"
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 355
and a38: "\<And>pt trm assoc_lst b. \<lbrakk>\<And>c. P9 c pt; \<And>c. P7 c trm; \<And>c. P8 c assoc_lst; set (bv (pt)) \<sharp>* b\<rbrakk>
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 356
\<Longrightarrow> P8 b (ACons pt trm assoc_lst)"
1700
+ − 357
and a39: "\<And>string tvars cvars vars b. \<lbrakk>\<And>c. P11 c tvars; \<And>c. P12 c cvars; \<And>c. P10 c vars\<rbrakk>
1701
+ − 358
\<Longrightarrow> P9 b (Kpat string tvars cvars vars)"
1700
+ − 359
and a40: "\<And>b. P10 b VsNil"
+ − 360
and a41: "\<And>var ty vars b. \<lbrakk>\<And>c. P3 c ty; \<And>c. P10 c vars\<rbrakk> \<Longrightarrow> P10 b (VsCons var ty vars)"
+ − 361
and a42: "\<And>b. P11 b TvsNil"
+ − 362
and a43: "\<And>tvar tkind tvars b. \<lbrakk>\<And>c. P1 c tkind; \<And>c. P11 c tvars\<rbrakk>
+ − 363
\<Longrightarrow> P11 b (TvsCons tvar tkind tvars)"
+ − 364
and a44: "\<And>b. P12 b CvsNil"
+ − 365
and a45: "\<And>tvar ckind cvars b. \<lbrakk>\<And>c. P2 c ckind; \<And>c. P12 c cvars\<rbrakk>
+ − 366
\<Longrightarrow> P12 b (CvsCons tvar ckind cvars)"
1632
+ − 367
shows "P1 (a :: 'a :: pt) tkind \<and>
1631
+ − 368
P2 (b :: 'b :: pt) ckind \<and>
1634
+ − 369
P3 (c :: 'c :: {pt,fs}) ty \<and>
1631
+ − 370
P4 (d :: 'd :: pt) ty_lst \<and>
1635
+ − 371
P5 (e :: 'e :: {pt,fs}) co \<and>
1631
+ − 372
P6 (f :: 'f :: pt) co_lst \<and>
1645
+ − 373
P7 (g :: 'g :: {pt,fs}) trm \<and>
1635
+ − 374
P8 (h :: 'h :: {pt,fs}) assoc_lst \<and>
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 375
P9 (i :: 'i :: pt) pt \<and>
1700
+ − 376
P10 (j :: 'j :: pt) vars \<and>
+ − 377
P11 (k :: 'k :: pt) tvars \<and>
+ − 378
P12 (l :: 'l :: pt) cvars"
1631
+ − 379
proof -
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 380
have a1: "(\<forall>p a. P1 a (p \<bullet> tkind))" and "(\<forall>p b. P2 b (p \<bullet> ckind))" and "(\<forall>p c. P3 c (p \<bullet> ty))" and "(\<forall>p d. P4 d (p \<bullet> ty_lst))" and "(\<forall>p e. P5 e (p \<bullet> co))" and " (\<forall>p f. P6 f (p \<bullet> co_lst))" and "(\<forall>p g. P7 g (p \<bullet> trm))" and "(\<forall>p h. P8 h (p \<bullet> assoc_lst))" and a1:"(\<forall>p q i. P9 i (permute_bv p (q \<bullet> pt)))" and a2:"(\<forall>p q j. P10 j (permute_bv_vs q (p \<bullet> vars)))" and a3:"(\<forall>p q k. P11 k ( permute_bv_tvs q (p \<bullet> tvars)))" and a4:"(\<forall>p q l. P12 l (permute_bv_cvs q (p \<bullet> cvars)))"
1700
+ − 381
apply (induct rule: tkind_ckind_ty_ty_lst_co_co_lst_trm_assoc_lst_pat_vars_tvars_cvars.inducts)
1632
+ − 382
apply (tactic {* ALLGOALS (REPEAT o rtac allI) *})
+ − 383
apply (tactic {* ALLGOALS (TRY o SOLVED' (simp_tac @{simpset} THEN_ALL_NEW resolve_tac @{thms assms} THEN_ALL_NEW asm_full_simp_tac @{simpset})) *})
1635
+ − 384
+ − 385
(* GOAL1 *)
+ − 386
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> tvar))) \<sharp> c \<and>
+ − 387
supp (Abs (p \<bullet> {atom tvar}) (p \<bullet> ty)) \<sharp>* pa)")
+ − 388
apply clarify
+ − 389
apply (simp only: perm)
+ − 390
apply(rule_tac t="TAll (p \<bullet> tvar) (p \<bullet> tkind) (p \<bullet> ty)"
+ − 391
and s="TAll (pa \<bullet> p \<bullet> tvar) (p \<bullet> tkind) (pa \<bullet> p \<bullet> ty)" in subst)
2044
+ − 392
apply (simp add: eq_iff)
1635
+ − 393
apply (rule_tac x="-pa" in exI)
1658
+ − 394
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1635
+ − 395
apply (rule_tac t="supp (pa \<bullet> p \<bullet> ty) - {atom (pa \<bullet> p \<bullet> tvar)}"
+ − 396
and s="pa \<bullet> (p \<bullet> supp ty - {p \<bullet> atom tvar})" in subst)
+ − 397
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 398
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1635
+ − 399
apply (rule conjI)
+ − 400
apply (rule supp_perm_eq)
+ − 401
apply (simp add: eqvts)
+ − 402
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 403
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1635
+ − 404
apply (simp add: eqvts)
+ − 405
apply (subst supp_perm_eq)
+ − 406
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 407
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1635
+ − 408
apply assumption
+ − 409
apply (simp add: fresh_star_minus_perm)
+ − 410
apply (rule a08)
+ − 411
apply simp
+ − 412
apply(rotate_tac 1)
+ − 413
apply(erule_tac x="(pa + p)" in allE)
+ − 414
apply simp
+ − 415
apply (simp add: eqvts eqvts_raw)
1634
+ − 416
apply (rule at_set_avoiding2_atom)
+ − 417
apply (simp add: finite_supp)
+ − 418
apply (simp add: finite_supp)
+ − 419
apply (simp add: fresh_def)
1658
+ − 420
apply (simp only: supp_abs eqvts)
1634
+ − 421
apply blast
1635
+ − 422
+ − 423
(* GOAL2 *)
1701
+ − 424
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> cvar))) \<sharp> e \<and>
+ − 425
supp (Abs (p \<bullet> {atom cvar}) (p \<bullet> co)) \<sharp>* pa)")
1634
+ − 426
apply clarify
+ − 427
apply (simp only: perm)
1701
+ − 428
apply(rule_tac t="CAll (p \<bullet> cvar) (p \<bullet> ckind) (p \<bullet> co)"
+ − 429
and s="CAll (pa \<bullet> p \<bullet> cvar) (p \<bullet> ckind) (pa \<bullet> p \<bullet> co)" in subst)
2044
+ − 430
apply (simp add: eq_iff)
1634
+ − 431
apply (rule_tac x="-pa" in exI)
1658
+ − 432
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1701
+ − 433
apply (rule_tac t="supp (pa \<bullet> p \<bullet> co) - {atom (pa \<bullet> p \<bullet> cvar)}"
+ − 434
and s="pa \<bullet> (p \<bullet> supp co - {p \<bullet> atom cvar})" in subst)
1635
+ − 435
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 436
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1634
+ − 437
apply (rule conjI)
+ − 438
apply (rule supp_perm_eq)
+ − 439
apply (simp add: eqvts)
+ − 440
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 441
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1634
+ − 442
apply (simp add: eqvts)
+ − 443
apply (subst supp_perm_eq)
+ − 444
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 445
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1634
+ − 446
apply assumption
+ − 447
apply (simp add: fresh_star_minus_perm)
1635
+ − 448
apply (rule a15)
+ − 449
apply simp
+ − 450
apply(rotate_tac 1)
+ − 451
apply(erule_tac x="(pa + p)" in allE)
+ − 452
apply simp
+ − 453
apply (simp add: eqvts eqvts_raw)
+ − 454
apply (rule at_set_avoiding2_atom)
+ − 455
apply (simp add: finite_supp)
+ − 456
apply (simp add: finite_supp)
+ − 457
apply (simp add: fresh_def)
1658
+ − 458
apply (simp only: supp_abs eqvts)
1635
+ − 459
apply blast
+ − 460
1645
+ − 461
+ − 462
(* GOAL3 a copy-and-paste of Goal2 with consts and variable names changed *)
+ − 463
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> tvar))) \<sharp> g \<and>
+ − 464
supp (Abs (p \<bullet> {atom tvar}) (p \<bullet> trm)) \<sharp>* pa)")
+ − 465
apply clarify
+ − 466
apply (simp only: perm)
+ − 467
apply(rule_tac t="LAMT (p \<bullet> tvar) (p \<bullet> tkind) (p \<bullet> trm)"
+ − 468
and s="LAMT (pa \<bullet> p \<bullet> tvar) (p \<bullet> tkind) (pa \<bullet> p \<bullet> trm)" in subst)
2044
+ − 469
apply (simp add: eq_iff)
1645
+ − 470
apply (rule_tac x="-pa" in exI)
1658
+ − 471
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1645
+ − 472
apply (rule_tac t="supp (pa \<bullet> p \<bullet> trm) - {atom (pa \<bullet> p \<bullet> tvar)}"
+ − 473
and s="pa \<bullet> (p \<bullet> supp trm - {p \<bullet> atom tvar})" in subst)
+ − 474
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 475
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1645
+ − 476
apply (rule conjI)
+ − 477
apply (rule supp_perm_eq)
+ − 478
apply (simp add: eqvts)
+ − 479
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 480
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1645
+ − 481
apply (simp add: eqvts)
+ − 482
apply (subst supp_perm_eq)
+ − 483
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 484
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1645
+ − 485
apply assumption
+ − 486
apply (simp add: fresh_star_minus_perm)
+ − 487
apply (rule a29)
+ − 488
apply simp
+ − 489
apply(rotate_tac 1)
+ − 490
apply(erule_tac x="(pa + p)" in allE)
+ − 491
apply simp
+ − 492
apply (simp add: eqvts eqvts_raw)
+ − 493
apply (rule at_set_avoiding2_atom)
+ − 494
apply (simp add: finite_supp)
+ − 495
apply (simp add: finite_supp)
+ − 496
apply (simp add: fresh_def)
1658
+ − 497
apply (simp only: supp_abs eqvts)
1645
+ − 498
apply blast
+ − 499
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 500
(* GOAL4 a copy-and-paste *)
1701
+ − 501
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> cvar))) \<sharp> g \<and>
+ − 502
supp (Abs (p \<bullet> {atom cvar}) (p \<bullet> trm)) \<sharp>* pa)")
1635
+ − 503
apply clarify
+ − 504
apply (simp only: perm)
1701
+ − 505
apply(rule_tac t="LAMC (p \<bullet> cvar) (p \<bullet> ckind) (p \<bullet> trm)"
+ − 506
and s="LAMC (pa \<bullet> p \<bullet> cvar) (p \<bullet> ckind) (pa \<bullet> p \<bullet> trm)" in subst)
2044
+ − 507
apply (simp add: eq_iff)
1635
+ − 508
apply (rule_tac x="-pa" in exI)
1658
+ − 509
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1701
+ − 510
apply (rule_tac t="supp (pa \<bullet> p \<bullet> trm) - {atom (pa \<bullet> p \<bullet> cvar)}"
+ − 511
and s="pa \<bullet> (p \<bullet> supp trm - {p \<bullet> atom cvar})" in subst)
1635
+ − 512
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 513
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1635
+ − 514
apply (rule conjI)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 515
apply (rule supp_perm_eq)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 516
apply (simp add: eqvts)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 517
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 518
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 519
apply (simp add: eqvts)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 520
apply (subst supp_perm_eq)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 521
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 522
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 523
apply assumption
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 524
apply (simp add: fresh_star_minus_perm)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 525
apply (rule a30)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 526
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 527
apply(rotate_tac 1)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 528
apply(erule_tac x="(pa + p)" in allE)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 529
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 530
apply (simp add: eqvts eqvts_raw)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 531
apply (rule at_set_avoiding2_atom)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 532
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 533
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 534
apply (simp add: fresh_def)
1658
+ − 535
apply (simp only: supp_abs eqvts)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 536
apply blast
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 537
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 538
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 539
(* GOAL5 a copy-and-paste *)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 540
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> var))) \<sharp> g \<and>
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 541
supp (Abs (p \<bullet> {atom var}) (p \<bullet> trm)) \<sharp>* pa)")
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 542
apply clarify
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 543
apply (simp only: perm)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 544
apply(rule_tac t="Lam (p \<bullet> var) (p \<bullet> ty) (p \<bullet> trm)"
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 545
and s="Lam (pa \<bullet> p \<bullet> var) (p \<bullet> ty) (pa \<bullet> p \<bullet> trm)" in subst)
2044
+ − 546
apply (simp add: eq_iff)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 547
apply (rule_tac x="-pa" in exI)
1658
+ − 548
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 549
apply (rule_tac t="supp (pa \<bullet> p \<bullet> trm) - {atom (pa \<bullet> p \<bullet> var)}"
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 550
and s="pa \<bullet> (p \<bullet> supp trm - {p \<bullet> atom var})" in subst)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 551
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 552
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1635
+ − 553
apply (rule conjI)
+ − 554
apply (rule supp_perm_eq)
+ − 555
apply (simp add: eqvts)
+ − 556
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 557
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1635
+ − 558
apply (simp add: eqvts)
+ − 559
apply (subst supp_perm_eq)
+ − 560
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 561
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1635
+ − 562
apply assumption
+ − 563
apply (simp add: fresh_star_minus_perm)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 564
apply (rule a32)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 565
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 566
apply(rotate_tac 1)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 567
apply(erule_tac x="(pa + p)" in allE)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 568
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 569
apply (simp add: eqvts eqvts_raw)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 570
apply (rule at_set_avoiding2_atom)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 571
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 572
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 573
apply (simp add: fresh_def)
1658
+ − 574
apply (simp only: supp_abs eqvts)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 575
apply blast
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 576
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 577
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 578
(* GOAL6 a copy-and-paste *)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 579
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (atom (p \<bullet> var))) \<sharp> g \<and>
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 580
supp (Abs (p \<bullet> {atom var}) (p \<bullet> trm2)) \<sharp>* pa)")
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 581
apply clarify
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 582
apply (simp only: perm)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 583
apply(rule_tac t="Let (p \<bullet> var) (p \<bullet> ty) (p \<bullet> trm1) (p \<bullet> trm2)"
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 584
and s="Let (pa \<bullet> p \<bullet> var) (p \<bullet> ty) (p \<bullet> trm1) (pa \<bullet> p \<bullet> trm2)" in subst)
2044
+ − 585
apply (simp add: eq_iff)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 586
apply (rule_tac x="-pa" in exI)
1658
+ − 587
apply (simp add: alphas eqvts eqvts_raw supp_abs fv_supp)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 588
apply (rule_tac t="supp (pa \<bullet> p \<bullet> trm2) - {atom (pa \<bullet> p \<bullet> var)}"
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 589
and s="pa \<bullet> (p \<bullet> supp trm2 - {p \<bullet> atom var})" in subst)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 590
apply (simp add: eqvts)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 591
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric])
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 592
apply (rule conjI)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 593
apply (rule supp_perm_eq)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 594
apply (simp add: eqvts)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 595
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 596
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 597
apply (simp add: eqvts)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 598
apply (subst supp_perm_eq)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 599
apply (subst supp_finite_atom_set)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 600
apply (simp add: supp_eqvt[symmetric] atom_eqvt[symmetric] Diff_eqvt[symmetric] finite_eqvt[symmetric] finite_supp True_eqvt)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 601
apply assumption
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 602
apply (simp add: fresh_star_minus_perm)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 603
apply (rule a34)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 604
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 605
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 606
apply(rotate_tac 2)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 607
apply(erule_tac x="(pa + p)" in allE)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 608
apply simp
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 609
apply (simp add: eqvts eqvts_raw)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 610
apply (rule at_set_avoiding2_atom)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 611
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 612
apply (simp add: finite_supp)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 613
apply (simp add: fresh_def)
1658
+ − 614
apply (simp only: supp_abs eqvts)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 615
apply blast
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 616
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 617
(* MAIN ACons Goal *)
1695
+ − 618
apply(subgoal_tac "\<exists>pa. ((pa \<bullet> (set (bv (p \<bullet> pat)))) \<sharp>* h \<and>
+ − 619
supp (Abs_lst (p \<bullet> (bv pat)) (p \<bullet> trm)) \<sharp>* pa)")
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 620
apply clarify
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 621
apply (simp only: perm eqvts)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 622
apply (subst ACons_subst)
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 623
apply assumption
1635
+ − 624
apply (rule a38)
+ − 625
apply simp
+ − 626
apply(rotate_tac 1)
+ − 627
apply(erule_tac x="(pa + p)" in allE)
+ − 628
apply simp
+ − 629
apply simp
1647
+ − 630
apply (simp add: perm_bv2[symmetric])
1635
+ − 631
apply (simp add: eqvts eqvts_raw)
+ − 632
apply (rule at_set_avoiding2)
+ − 633
apply (simp add: fin_bv)
+ − 634
apply (simp add: finite_supp)
1658
+ − 635
apply (simp add: supp_abs)
1646
733bac87d5bf
Solved all boring subgoals, and looking at properly defning permute_bv
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 636
apply (simp add: finite_supp)
1658
+ − 637
apply (simp add: fresh_star_def fresh_def supp_abs eqvts)
1647
+ − 638
done
+ − 639
then have b: "P1 a (0 \<bullet> tkind)" and "P2 b (0 \<bullet> ckind)" "P3 c (0 \<bullet> ty)" and "P4 d (0 \<bullet> ty_lst)" and "P5 e (0 \<bullet> co)" and "P6 f (0 \<bullet> co_lst)" and "P7 g (0 \<bullet> trm)" and "P8 h (0 \<bullet> assoc_lst)" by (blast+)
2142
c39d4fe31100
moved the exporting part into the parser (this is still a hack); re-added CoreHaskell again to the examples - there seems to be a problem with the variable name pat
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 640
moreover have "P9 i (permute_bv 0 (0 \<bullet> pt))" and "P10 j (permute_bv_vs 0 (0 \<bullet> vars))" and "P11 k (permute_bv_tvs 0 (0 \<bullet> tvars))" and "P12 l (permute_bv_cvs 0 (0 \<bullet> cvars))" using a1 a2 a3 a4 by (blast+)
1647
+ − 641
ultimately show ?thesis by (simp_all add: permute_bv_zero1 permute_bv_zero2)
1631
+ − 642
qed
1615
0ea578c6dae3
Parsing bn functions that call other bn functions and transmitting this information to fv/alpha.
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 643
1868
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 644
section {* test about equivariance for alpha *}
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 645
2044
+ − 646
(* this should not be an equivariance rule *)
+ − 647
(* for the moment, we force it to be *)
+ − 648
+ − 649
(*declare permute_pure[eqvt]*)
2104
2205b572bc9b
Declare alpha_gen_eqvt as eqvt and change the proofs that used 'eqvts[symmetric]'
Cezary Kaliszyk <kaliszyk@in.tum.de>
diff
changeset
+ − 650
(*setup {* Context.theory_map (Nominal_ThmDecls.add_thm @{thm "permute_pure"}) *} *)
2044
+ − 651
1868
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 652
thm eqvts
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 653
thm eqvts_raw
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 654
26c0c35641cb
equivariance for alpha_raw in CoreHaskell is automatically derived
Christian Urban <urbanc@in.tum.de>
diff
changeset
+ − 655
1601
+ − 656
end
+ − 657