| author | Christian Urban <urbanc@in.tum.de> |
| Wed, 04 Jan 2012 17:42:16 +0000 | |
| changeset 3105 | 1b0d230445ce |
| parent 2969 | 0f1b44c9c5a0 |
| child 3235 | 5ebd327ffb96 |
| permissions | -rw-r--r-- |
| 2952 | 1 |
theory Lambda |
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imports |
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"../Nominal2" |
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begin |
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atom_decl name |
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nominal_datatype lam = |
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Var "name" |
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| App "lam" "lam" |
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| Lam x::"name" l::"lam" binds x in l ("Lam [_]. _" [100, 100] 100)
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nominal_datatype sem = |
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L e::"env" x::"name" l::"lam" binds x "bn e" in l |
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| N "neu" |
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and neu = |
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V "name" |
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| A "neu" "sem" |
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and env = |
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ENil |
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| ECons "env" "name" "sem" |
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parents:
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binder |
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bn |
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Christian Urban <urbanc@in.tum.de>
parents:
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where |
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parents:
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"bn ENil = []" |
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parents:
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| "bn (ECons env x v) = (atom x) # (bn env)" |
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defined a function directly over a nominal datatype with bn
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parents:
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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thm sem_neu_env.supp |
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parents:
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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lemma [simp]: |
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shows "finite (fv_bn env)" |
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apply(induct env rule: sem_neu_env.inducts(3)) |
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parents:
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apply(rule TrueI)+ |
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parents:
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apply(auto simp add: sem_neu_env.supp finite_supp) |
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done |
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defined a function directly over a nominal datatype with bn
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parents:
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defined a function directly over a nominal datatype with bn
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parents:
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lemma test1: |
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shows "supp p \<sharp>* (fv_bn env) \<Longrightarrow> (p \<bullet> env) = permute_bn p env" |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(induct env rule: sem_neu_env.inducts(3)) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(rule TrueI)+ |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(auto simp add: sem_neu_env.perm_bn_simps sem_neu_env.supp) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(drule meta_mp) |
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apply(drule fresh_star_supp_conv) |
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defined a function directly over a nominal datatype with bn
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apply(subst (asm) supp_finite_atom_set) |
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defined a function directly over a nominal datatype with bn
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apply(simp add: finite_supp) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(simp add: fresh_star_Un) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(rule fresh_star_supp_conv) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(subst supp_finite_atom_set) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(simp) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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apply(simp) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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apply(simp) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(rule perm_supp_eq) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(drule fresh_star_supp_conv) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(subst (asm) supp_finite_atom_set) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(simp add: finite_supp) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(simp add: fresh_star_Un) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(rule fresh_star_supp_conv) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(simp) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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done |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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thm alpha_sem_raw_alpha_neu_raw_alpha_env_raw_alpha_bn_raw.inducts(4)[no_vars] |
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defined a function directly over a nominal datatype with bn
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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lemma alpha_bn_inducts_raw[consumes 1]: |
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"\<lbrakk>alpha_bn_raw x7 x8; |
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defined a function directly over a nominal datatype with bn
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P4 ENil_raw ENil_raw; |
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\<And>env_raw env_rawa sem_raw sem_rawa name namea. |
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\<lbrakk>alpha_bn_raw env_raw env_rawa; P4 env_raw env_rawa; alpha_sem_raw sem_raw sem_rawa\<rbrakk> |
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\<Longrightarrow> P4 (ECons_raw env_raw name sem_raw) (ECons_raw env_rawa namea sem_rawa)\<rbrakk> |
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\<Longrightarrow> P4 x7 x8" |
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defined a function directly over a nominal datatype with bn
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apply(induct rule: alpha_sem_raw_alpha_neu_raw_alpha_env_raw_alpha_bn_raw.inducts(4)) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(rule TrueI)+ |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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apply(auto) |
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defined a function directly over a nominal datatype with bn
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done |
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defined a function directly over a nominal datatype with bn
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parents:
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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lemmas alpha_bn_inducts[consumes 1] = alpha_bn_inducts_raw[quot_lifted] |
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defined a function directly over a nominal datatype with bn
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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lemma test2: |
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defined a function directly over a nominal datatype with bn
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parents:
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shows "alpha_bn env1 env2 \<Longrightarrow> p \<bullet> (bn env1) = q \<bullet> (bn env2) \<Longrightarrow> permute_bn p env1 = permute_bn q env2" |
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defined a function directly over a nominal datatype with bn
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apply(induct rule: alpha_bn_inducts) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(auto simp add: sem_neu_env.perm_bn_simps sem_neu_env.bn_defs) |
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defined a function directly over a nominal datatype with bn
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parents:
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apply(simp add: atom_eqvt) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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done |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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lemma fresh_star_Union: |
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defined a function directly over a nominal datatype with bn
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parents:
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assumes "as \<subseteq> bs" "bs \<sharp>* x" |
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defined a function directly over a nominal datatype with bn
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shows "as \<sharp>* x" |
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using assms by (auto simp add: fresh_star_def) |
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0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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parents:
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| 2956 | 90 |
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nominal_primrec (invariant "\<lambda>x y. case x of Inl (x1, y1) \<Rightarrow> |
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supp y \<subseteq> (supp y1 - set (bn x1)) \<union> (fv_bn x1) | Inr (x2, y2) \<Rightarrow> supp y \<subseteq> supp x2 \<union> supp y2") |
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evals :: "env \<Rightarrow> lam \<Rightarrow> sem" and |
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evals_aux :: "sem \<Rightarrow> sem \<Rightarrow> sem" |
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where |
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"evals ENil (Var x) = N (V x)" |
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| "evals (ECons tail y v) (Var x) = (if x = y then v else evals tail (Var x))" |
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some improvements to the NBE example
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| "atom x \<sharp> env \<Longrightarrow> evals env (Lam [x]. t) = L env x t" |
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| "evals env (App t1 t2) = evals_aux (evals env t1) (evals env t2)" |
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| "set (atom x # bn env) \<sharp>* (fv_bn env, t') \<Longrightarrow> evals_aux (L env x t) t' = evals (ECons env x t') t" |
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| "evals_aux (N n) t' = N (A n t')" |
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apply(simp add: eqvt_def evals_evals_aux_graph_def) |
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parents:
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apply(perm_simp) |
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parents:
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apply(simp) |
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apply(erule evals_evals_aux_graph.induct) |
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106 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
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parents:
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107 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
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parents:
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108 |
apply(rule conjI) |
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109 |
apply(rule impI) |
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110 |
apply(blast) |
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parents:
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111 |
apply(rule impI) |
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112 |
apply(simp add: supp_at_base) |
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113 |
apply(blast) |
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parents:
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114 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
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ddb69d9f45d0
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parents:
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115 |
apply(blast) |
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parents:
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116 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
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ddb69d9f45d0
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parents:
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117 |
apply(blast) |
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ddb69d9f45d0
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parents:
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118 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
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ddb69d9f45d0
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parents:
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119 |
apply(blast) |
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ddb69d9f45d0
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parents:
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120 |
apply(simp add: sem_neu_env.supp lam.supp sem_neu_env.bn_defs) |
| 2952 | 121 |
--"completeness" |
122 |
apply(case_tac x) |
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123 |
apply(simp) |
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124 |
apply(case_tac a) |
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125 |
apply(simp) |
|
126 |
apply(case_tac aa rule: sem_neu_env.exhaust(3)) |
|
|
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|
127 |
apply(simp add: sem_neu_env.fresh) |
| 2952 | 128 |
apply(case_tac b rule: lam.exhaust) |
129 |
apply(metis)+ |
|
|
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|
130 |
apply(case_tac aa rule: sem_neu_env.exhaust(3)) |
|
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|
131 |
apply(rule_tac y="b" and c="env" in lam.strong_exhaust) |
| 2952 | 132 |
apply(metis)+ |
|
2967
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|
133 |
apply(simp add: fresh_star_def) |
|
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|
134 |
apply(simp) |
|
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changeset
|
135 |
apply(rule_tac y="b" and c="ECons env name sem" in lam.strong_exhaust) |
|
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|
136 |
apply(metis)+ |
|
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|
137 |
apply(simp add: fresh_star_def) |
| 2952 | 138 |
apply(simp) |
139 |
apply(case_tac b) |
|
140 |
apply(simp) |
|
|
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|
141 |
apply(rule_tac y="a" and c="(a, ba)" in sem_neu_env.strong_exhaust(1)) |
|
0f1b44c9c5a0
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|
142 |
apply(simp) |
|
0f1b44c9c5a0
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|
143 |
apply(rotate_tac 4) |
|
0f1b44c9c5a0
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|
144 |
apply(drule_tac x="name" in meta_spec) |
|
0f1b44c9c5a0
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|
145 |
apply(drule_tac x="env" in meta_spec) |
|
0f1b44c9c5a0
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changeset
|
146 |
apply(drule_tac x="ba" in meta_spec) |
|
0f1b44c9c5a0
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|
147 |
apply(drule_tac x="lam" in meta_spec) |
|
0f1b44c9c5a0
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|
148 |
apply(simp add: sem_neu_env.alpha_refl) |
|
0f1b44c9c5a0
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|
149 |
apply(rotate_tac 9) |
|
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|
150 |
apply(drule_tac meta_mp) |
|
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|
151 |
apply(simp (no_asm_use) add: fresh_star_def sem_neu_env.fresh fresh_Pair) |
|
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|
152 |
apply(simp) |
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|
153 |
apply(subst fresh_finite_atom_set) |
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|
154 |
defer |
|
0f1b44c9c5a0
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|
155 |
apply(simp) |
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|
156 |
apply(subst fresh_finite_atom_set) |
|
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changeset
|
157 |
defer |
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|
158 |
apply(simp) |
| 2952 | 159 |
apply(metis)+ |
160 |
--"compatibility" |
|
161 |
apply(all_trivials) |
|
162 |
apply(simp) |
|
163 |
apply(simp) |
|
|
2955
4049a2651dd9
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|
164 |
defer |
| 2952 | 165 |
apply(simp) |
166 |
apply(simp) |
|
|
2953
80f01215d1a6
Setup eqvt_at for first goal
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|
167 |
apply (simp add: meta_eq_to_obj_eq[OF evals_def, symmetric, unfolded fun_eq_iff]) |
|
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|
168 |
apply (subgoal_tac "eqvt_at (\<lambda>(a, b). evals a b) (ECons env x t'a, t)") |
|
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|
169 |
apply (subgoal_tac "eqvt_at (\<lambda>(a, b). evals a b) (ECons enva xa t'a, ta)") |
|
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|
170 |
apply (thin_tac "eqvt_at evals_evals_aux_sumC (Inl (ECons env x t'a, t))") |
|
0f1b44c9c5a0
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|
171 |
apply (thin_tac "eqvt_at evals_evals_aux_sumC (Inl (ECons enva xa t'a, ta))") |
|
2954
dc6007dd9c30
a little further with NBE
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changeset
|
172 |
apply(erule conjE)+ |
| 2952 | 173 |
defer |
|
2953
80f01215d1a6
Setup eqvt_at for first goal
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changeset
|
174 |
apply (simp_all add: eqvt_at_def evals_def)[3] |
|
2969
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changeset
|
175 |
defer |
|
0f1b44c9c5a0
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changeset
|
176 |
defer |
|
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some improvements to the NBE example
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changeset
|
177 |
apply(simp add: sem_neu_env.alpha_refl) |
|
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some improvements to the NBE example
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changeset
|
178 |
apply(erule conjE)+ |
|
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some improvements to the NBE example
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changeset
|
179 |
apply(erule_tac c="(env, enva)" in Abs_lst1_fcb2) |
|
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|
180 |
apply(simp add: Abs_fresh_iff) |
|
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some improvements to the NBE example
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changeset
|
181 |
apply(simp add: fresh_star_def) |
|
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some improvements to the NBE example
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changeset
|
182 |
apply(perm_simp) |
|
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some improvements to the NBE example
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changeset
|
183 |
apply(simp add: fresh_star_Pair perm_supp_eq) |
|
d7e8b9b78e28
some improvements to the NBE example
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parents:
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changeset
|
184 |
apply(perm_simp) |
|
d7e8b9b78e28
some improvements to the NBE example
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changeset
|
185 |
apply(simp add: fresh_star_Pair perm_supp_eq) |
|
2968
ddb69d9f45d0
more one the NBE example
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changeset
|
186 |
apply(simp add: sem_neu_env.bn_defs sem_neu_env.supp) |
|
ddb69d9f45d0
more one the NBE example
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changeset
|
187 |
using at_set_avoiding3 |
|
ddb69d9f45d0
more one the NBE example
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changeset
|
188 |
apply - |
|
2969
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
189 |
apply(drule_tac x="set (atom x # bn env)" in meta_spec) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
190 |
apply(drule_tac x="(fv_bn env, fv_bn enva, env, enva, x, xa, t, ta, t'a)" in meta_spec) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
191 |
apply(drule_tac x="[atom x # bn env]lst. t" in meta_spec) |
|
2968
ddb69d9f45d0
more one the NBE example
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changeset
|
192 |
apply(simp (no_asm_use) add: finite_supp Abs_fresh_star_iff) |
|
ddb69d9f45d0
more one the NBE example
Christian Urban <urbanc@in.tum.de>
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changeset
|
193 |
apply(drule meta_mp) |
|
2969
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changeset
|
194 |
apply(simp add: supp_Pair finite_supp supp_finite_atom_set) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
195 |
apply(drule meta_mp) |
|
2968
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more one the NBE example
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changeset
|
196 |
apply(simp add: fresh_star_def) |
|
ddb69d9f45d0
more one the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
197 |
apply(erule exE) |
|
ddb69d9f45d0
more one the NBE example
Christian Urban <urbanc@in.tum.de>
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changeset
|
198 |
apply(erule conjE)+ |
|
2969
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changeset
|
199 |
apply(rule trans) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
200 |
apply(rule sym) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
201 |
apply(rule_tac p="p" in perm_supp_eq) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
202 |
apply(simp) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
203 |
apply(perm_simp) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
204 |
apply(simp add: fresh_star_Un fresh_star_insert) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
205 |
apply(rule conjI) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
206 |
apply(simp (no_asm_use) add: fresh_star_def fresh_Pair) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
207 |
apply(simp add: fresh_def) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
208 |
apply(simp add: supp_finite_atom_set) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
209 |
apply(blast) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
210 |
apply(rule conjI) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
211 |
apply(simp (no_asm_use) add: fresh_star_def fresh_Pair) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
212 |
apply(simp add: fresh_def) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
213 |
apply(simp add: supp_finite_atom_set) |
|
2968
ddb69d9f45d0
more one the NBE example
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parents:
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changeset
|
214 |
apply(blast) |
|
2969
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
215 |
apply(rule conjI) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
216 |
apply(simp (no_asm_use) add: fresh_star_def fresh_Pair) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
217 |
apply(simp add: fresh_def) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
218 |
apply(simp add: supp_finite_atom_set) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
219 |
apply(blast) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
220 |
apply(simp (no_asm_use) add: fresh_star_def fresh_Pair) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
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changeset
|
221 |
apply(simp add: fresh_def) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
222 |
apply(simp add: supp_finite_atom_set) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
223 |
apply(blast) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
224 |
apply(simp add: eqvt_at_def perm_supp_eq) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
225 |
apply(subst (3) perm_supp_eq) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
226 |
apply(simp) |
|
0f1b44c9c5a0
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changeset
|
227 |
apply(simp add: fresh_star_def fresh_Pair) |
|
0f1b44c9c5a0
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changeset
|
228 |
apply(auto)[1] |
|
0f1b44c9c5a0
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changeset
|
229 |
apply(rotate_tac 6) |
|
0f1b44c9c5a0
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changeset
|
230 |
apply(drule sym) |
|
0f1b44c9c5a0
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changeset
|
231 |
apply(simp) |
|
0f1b44c9c5a0
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changeset
|
232 |
apply(rotate_tac 11) |
|
2968
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|
233 |
apply(drule trans) |
|
ddb69d9f45d0
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changeset
|
234 |
apply(rule sym) |
|
2969
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changeset
|
235 |
apply(rule_tac p="p" in supp_perm_eq) |
|
0f1b44c9c5a0
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changeset
|
236 |
apply(assumption) |
|
0f1b44c9c5a0
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changeset
|
237 |
apply(rotate_tac 11) |
|
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
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changeset
|
238 |
apply(rule sym) |
|
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|
239 |
apply(simp add: atom_eqvt) |
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|
240 |
apply(simp (no_asm_use) add: Abs_eq_iff2 alphas) |
|
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|
241 |
apply(erule conjE | erule exE)+ |
|
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|
242 |
apply(rule trans) |
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243 |
apply(rule sym) |
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|
244 |
apply(rule_tac p="pa" in perm_supp_eq) |
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245 |
apply(erule fresh_star_Union) |
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|
246 |
apply(simp (no_asm_use) add: fresh_star_insert fresh_star_Un) |
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|
247 |
apply(rule conjI) |
|
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|
248 |
apply(perm_simp) |
|
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249 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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250 |
apply(simp add: fresh_Pair) |
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251 |
apply(simp add: fresh_def) |
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252 |
apply(simp add: supp_finite_atom_set) |
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|
253 |
apply(blast) |
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|
254 |
apply(rule conjI) |
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|
255 |
apply(perm_simp) |
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|
256 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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|
257 |
apply(simp add: fresh_Pair) |
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|
258 |
apply(simp add: fresh_def) |
|
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|
259 |
apply(simp add: supp_finite_atom_set) |
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|
260 |
apply(blast) |
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|
261 |
apply(rule conjI) |
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|
262 |
apply(perm_simp) |
|
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|
263 |
defer |
|
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|
264 |
apply(perm_simp) |
|
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|
265 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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|
266 |
apply(simp add: fresh_star_Pair) |
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|
267 |
apply(simp add: fresh_star_def fresh_def) |
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|
268 |
apply(simp add: supp_finite_atom_set) |
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|
269 |
apply(blast) |
|
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|
270 |
apply(simp) |
|
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|
271 |
apply(perm_simp) |
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|
272 |
apply(subst (3) perm_supp_eq) |
|
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|
273 |
apply(erule fresh_star_Union) |
|
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|
274 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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|
275 |
apply(simp add: fresh_star_def fresh_Pair) |
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|
276 |
apply(subgoal_tac "pa \<bullet> enva = p \<bullet> env") |
|
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|
277 |
apply(simp) |
|
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|
278 |
defer |
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|
279 |
apply(simp (no_asm_use) add: fresh_star_insert fresh_star_Un) |
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|
280 |
apply(simp (no_asm_use) add: fresh_star_def) |
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|
281 |
apply(rule ballI) |
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|
282 |
apply(subgoal_tac "a \<notin> supp ta - insert (atom xa) (set (bn enva)) \<union> (fv_bn enva \<union> supp t'a)") |
|
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|
283 |
apply(simp only: fresh_def) |
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|
284 |
apply(blast) |
|
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|
285 |
apply(simp (no_asm_use)) |
|
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|
286 |
apply(rule conjI) |
|
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|
287 |
apply(blast) |
|
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|
288 |
apply(simp add: fresh_Pair) |
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|
289 |
apply(simp add: fresh_star_def fresh_def) |
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|
290 |
apply(simp add: supp_finite_atom_set) |
|
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|
291 |
apply(subst test1) |
|
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|
292 |
apply(erule fresh_star_Union) |
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|
293 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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|
294 |
apply(simp add: fresh_star_def fresh_Pair) |
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|
295 |
apply(subst test1) |
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|
296 |
apply(simp) |
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|
297 |
apply(simp add: fresh_star_insert fresh_star_Un) |
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|
298 |
apply(simp add: fresh_star_def fresh_Pair) |
|
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|
299 |
apply(rule sym) |
|
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|
300 |
apply(erule test2) |
|
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|
301 |
apply(perm_simp) |
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|
302 |
apply(simp) |
|
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|
303 |
done |
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|
304 |
|
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|
305 |
|
|
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|
306 |
|
| 2952 | 307 |
|
|
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|
308 |
text {* can probably not proved by a trivial size argument *}
|
|
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|
309 |
termination (* apply(lexicographic_order) *) |
|
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|
310 |
sorry |
| 2952 | 311 |
|
|
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|
312 |
lemma [eqvt]: |
|
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|
313 |
shows "(p \<bullet> evals env t) = evals (p \<bullet> env) (p \<bullet> t)" |
|
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|
314 |
and "(p \<bullet> evals_aux v s) = evals_aux (p \<bullet> v) (p \<bullet> s)" |
|
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|
315 |
sorry |
|
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|
316 |
|
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|
317 |
(* fixme: should be a provided lemma *) |
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|
318 |
lemma fv_bn_finite: |
|
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|
319 |
shows "finite (fv_bn env)" |
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|
320 |
apply(induct env rule: sem_neu_env.inducts(3)) |
|
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|
321 |
apply(auto simp add: sem_neu_env.supp finite_supp) |
|
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|
322 |
done |
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|
323 |
|
|
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|
324 |
lemma test: |
| 2956 | 325 |
fixes env::"env" |
|
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|
326 |
shows "supp (evals env t) \<subseteq> (supp t - set (bn env)) \<union> (fv_bn env)" |
|
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|
327 |
and "supp (evals_aux s v) \<subseteq> (supp s) \<union> (supp v)" |
|
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|
328 |
apply(induct env t and s v rule: evals_evals_aux.induct) |
|
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|
329 |
apply(simp add: sem_neu_env.supp lam.supp supp_Nil sem_neu_env.bn_defs) |
|
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|
330 |
apply(simp add: sem_neu_env.supp lam.supp supp_Nil supp_Cons sem_neu_env.bn_defs) |
|
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|
331 |
apply(rule conjI) |
|
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|
332 |
apply(auto)[1] |
|
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|
333 |
apply(rule impI) |
|
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|
334 |
apply(simp) |
| 2956 | 335 |
apply(simp add: supp_at_base) |
336 |
apply(blast) |
|
|
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|
337 |
apply(simp) |
|
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|
338 |
apply(subst sem_neu_env.supp) |
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|
339 |
apply(simp add: sem_neu_env.supp lam.supp) |
|
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|
340 |
apply(auto)[1] |
| 2956 | 341 |
apply(simp add: lam.supp sem_neu_env.supp) |
342 |
apply(blast) |
|
343 |
apply(simp add: sem_neu_env.supp sem_neu_env.bn_defs) |
|
|
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|
344 |
apply(blast) |
| 2956 | 345 |
apply(simp add: sem_neu_env.supp) |
346 |
done |
|
347 |
||
|
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|
348 |
|
|
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|
349 |
nominal_primrec |
|
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|
350 |
reify :: "sem \<Rightarrow> lam" and |
|
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|
351 |
reifyn :: "neu \<Rightarrow> lam" |
|
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|
352 |
where |
|
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4049a2651dd9
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Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
353 |
"atom x \<sharp> (env, y, t) \<Longrightarrow> reify (L env y t) = Lam [x]. (reify (evals (ECons env y (N (V x))) t))" |
|
2954
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
354 |
| "reify (N n) = reifyn n" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
355 |
| "reifyn (V x) = Var x" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
356 |
| "reifyn (A n d) = App (reifyn n) (reify d)" |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
357 |
apply(subgoal_tac "\<And>p x y. reify_reifyn_graph x y \<Longrightarrow> reify_reifyn_graph (p \<bullet> x) (p \<bullet> y)") |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
358 |
apply(simp add: eqvt_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
359 |
apply(simp add: permute_fun_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
360 |
apply(rule allI) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
361 |
apply(rule ext) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
362 |
apply(rule ext) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
363 |
apply(rule iffI) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
364 |
apply(drule_tac x="p" in meta_spec) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
365 |
apply(drule_tac x="- p \<bullet> x" in meta_spec) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
366 |
apply(drule_tac x="- p \<bullet> xa" in meta_spec) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
367 |
apply(simp add: permute_bool_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
368 |
apply(simp add: permute_bool_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
369 |
apply(erule reify_reifyn_graph.induct) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
370 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
371 |
apply(rule reify_reifyn_graph.intros) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
372 |
apply(rule_tac p="-p" in permute_boolE) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
373 |
apply(perm_simp add: permute_minus_cancel) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
374 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
375 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
376 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
377 |
apply(rule reify_reifyn_graph.intros) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
378 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
379 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
380 |
apply(rule reify_reifyn_graph.intros) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
381 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
382 |
apply(rule reify_reifyn_graph.intros) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
383 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
384 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
385 |
apply(rule TrueI) |
|
2954
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
386 |
--"completeness" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
387 |
apply(case_tac x) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
388 |
apply(simp) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
389 |
apply(case_tac a rule: sem_neu_env.exhaust(1)) |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
390 |
apply(subgoal_tac "\<exists>x::name. atom x \<sharp> (env, name, lam)") |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
391 |
apply(metis) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
392 |
apply(rule obtain_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
393 |
apply(blast) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
394 |
apply(blast) |
|
2954
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
395 |
apply(case_tac b rule: sem_neu_env.exhaust(2)) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
396 |
apply(simp) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
397 |
apply(simp) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
398 |
apply(metis) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
399 |
--"compatibility" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
400 |
apply(all_trivials) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
401 |
defer |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
402 |
apply(simp) |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
403 |
apply(simp) |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
404 |
apply(simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
405 |
apply(erule conjE) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
406 |
apply (simp add: meta_eq_to_obj_eq[OF reify_def, symmetric, unfolded fun_eq_iff]) |
| 2956 | 407 |
apply (subgoal_tac "eqvt_at (\<lambda>t. reify t) (evals (ECons env y (N (V x))) t)") |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
408 |
apply (subgoal_tac "eqvt_at (\<lambda>t. reify t) (evals (ECons enva ya (N (V xa))) ta)") |
| 2956 | 409 |
apply (thin_tac "eqvt_at reify_reifyn_sumC (Inl (evals (ECons env y (N (V x))) t))") |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
410 |
apply (thin_tac "eqvt_at reify_reifyn_sumC (Inl (evals (ECons enva ya (N (V xa))) ta))") |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
411 |
defer |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
412 |
apply (simp_all add: eqvt_at_def reify_def)[2] |
| 2956 | 413 |
apply(subgoal_tac "\<exists>c::name. atom c \<sharp> (x, xa, env, enva, y, ya, t, ta)") |
|
2955
4049a2651dd9
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Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
414 |
prefer 2 |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
415 |
apply(rule obtain_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
416 |
apply(blast) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
417 |
apply(erule exE) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
418 |
apply(rule trans) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
419 |
apply(rule sym) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
420 |
apply(rule_tac a="x" and b="c" in flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
421 |
apply(simp add: Abs_fresh_iff) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
422 |
apply(simp add: Abs_fresh_iff fresh_Pair) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
423 |
apply(auto)[1] |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
424 |
apply(rule fresh_eqvt_at) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
425 |
back |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
426 |
apply(assumption) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
427 |
apply(simp add: finite_supp) |
| 2956 | 428 |
apply(rule_tac S="supp (env, y, x, t)" in supports_fresh) |
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
429 |
apply(simp add: supports_def fresh_def[symmetric]) |
|
4049a2651dd9
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Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
430 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
431 |
apply(simp add: swap_fresh_fresh fresh_Pair) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
432 |
apply(simp add: finite_supp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
433 |
apply(simp add: fresh_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
434 |
apply(simp add: eqvt_at_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
435 |
apply(simp add: eqvt_at_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
436 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
437 |
apply(simp add: flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
438 |
apply(rule sym) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
439 |
apply(rule trans) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
440 |
apply(rule sym) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
441 |
apply(rule_tac a="xa" and b="c" in flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
442 |
apply(simp add: Abs_fresh_iff) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
443 |
apply(simp add: Abs_fresh_iff fresh_Pair) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
444 |
apply(auto)[1] |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
445 |
apply(rule fresh_eqvt_at) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
446 |
back |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
447 |
apply(assumption) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
448 |
apply(simp add: finite_supp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
449 |
apply(rule_tac S="supp (enva, ya, xa, ta)" in supports_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
450 |
apply(simp add: supports_def fresh_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
451 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
452 |
apply(simp add: swap_fresh_fresh fresh_Pair) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
453 |
apply(simp add: finite_supp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
454 |
apply(simp add: fresh_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
455 |
apply(simp add: eqvt_at_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
456 |
apply(simp add: eqvt_at_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
457 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
458 |
apply(simp add: flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
459 |
apply(simp (no_asm) add: Abs1_eq_iff) |
|
2969
0f1b44c9c5a0
defined a function directly over a nominal datatype with bn
Christian Urban <urbanc@in.tum.de>
parents:
2968
diff
changeset
|
460 |
(* HERE *) |
| 2956 | 461 |
thm at_set_avoiding3 |
462 |
using at_set_avoiding3 |
|
463 |
apply - |
|
464 |
apply(drule_tac x="set (atom y # bn env)" in meta_spec) |
|
465 |
apply(drule_tac x="(env, enva)" in meta_spec) |
|
466 |
apply(drule_tac x="[atom y # bn env]lst. t" in meta_spec) |
|
467 |
apply(simp (no_asm_use) add: finite_supp) |
|
468 |
apply(drule meta_mp) |
|
469 |
apply(rule Abs_fresh_star) |
|
470 |
apply(auto)[1] |
|
471 |
apply(erule exE) |
|
472 |
apply(erule conjE)+ |
|
473 |
apply(drule_tac q="(x \<leftrightarrow> c)" in eqvt_at_perm) |
|
474 |
apply(perm_simp) |
|
475 |
apply(simp add: flip_fresh_fresh fresh_Pair) |
|
476 |
apply(drule_tac q="(xa \<leftrightarrow> c)" in eqvt_at_perm) |
|
477 |
apply(perm_simp) |
|
478 |
apply(simp add: flip_fresh_fresh fresh_Pair) |
|
479 |
apply(drule sym) |
|
|
2967
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
480 |
(* HERE *) |
|
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
481 |
apply(rotate_tac 9) |
|
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
482 |
apply(drule sym) |
| 2956 | 483 |
apply(rotate_tac 9) |
484 |
apply(drule trans) |
|
485 |
apply(rule sym) |
|
486 |
apply(rule_tac p="p" in supp_perm_eq) |
|
|
2967
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
487 |
apply(assumption) |
| 2956 | 488 |
apply(simp) |
489 |
apply(perm_simp) |
|
|
2967
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
490 |
apply(simp (no_asm_use) add: Abs_eq_iff2 alphas) |
|
d7e8b9b78e28
some improvements to the NBE example
Christian Urban <urbanc@in.tum.de>
parents:
2956
diff
changeset
|
491 |
apply(erule conjE | erule exE)+ |
| 2956 | 492 |
apply(clarify) |
493 |
apply(rule trans) |
|
494 |
apply(rule sym) |
|
495 |
apply(rule_tac p="pa" in perm_supp_eq) |
|
496 |
defer |
|
497 |
apply(rule sym) |
|
498 |
apply(rule trans) |
|
499 |
apply(rule sym) |
|
500 |
apply(rule_tac p="p" in perm_supp_eq) |
|
501 |
defer |
|
502 |
apply(simp add: atom_eqvt) |
|
503 |
apply(drule_tac q="(x \<leftrightarrow> c)" in eqvt_at_perm) |
|
504 |
apply(perm_simp) |
|
505 |
apply(simp add: flip_fresh_fresh fresh_Pair) |
|
506 |
||
|
2955
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
507 |
apply(rule sym) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
508 |
apply(erule_tac Abs_lst1_fcb2') |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
509 |
apply(rule fresh_eqvt_at) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
510 |
back |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
511 |
apply(drule_tac q="(c \<leftrightarrow> x)" in eqvt_at_perm) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
512 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
513 |
apply(simp add: flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
514 |
apply(simp add: finite_supp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
515 |
apply(rule supports_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
516 |
apply(rule_tac S="supp (enva, ya, xa, ta)" in supports_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
517 |
apply(simp add: supports_def fresh_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
518 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
519 |
apply(simp add: swap_fresh_fresh fresh_Pair) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
520 |
apply(simp add: finite_supp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
521 |
apply(simp add: fresh_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
522 |
apply(simp add: eqvt_at_def) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
523 |
apply(simp add: eqvt_at_def[symmetric]) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
524 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
525 |
apply(rule fresh_eqvt_at) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
526 |
back |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
527 |
apply(drule_tac q="(c \<leftrightarrow> x)" in eqvt_at_perm) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
528 |
apply(perm_simp) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
529 |
apply(simp add: flip_fresh_fresh) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
530 |
apply(assumption) |
|
4049a2651dd9
more on the NBE function
Christian Urban <urbanc@in.tum.de>
parents:
2954
diff
changeset
|
531 |
apply(simp add: finite_supp) |
|
2954
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
532 |
sorry |
| 2952 | 533 |
|
|
2954
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
534 |
termination sorry |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
535 |
|
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
536 |
definition |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
537 |
eval :: "lam \<Rightarrow> sem" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
538 |
where |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
539 |
"eval t = evals ENil t" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
540 |
|
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
541 |
definition |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
542 |
normalize :: "lam \<Rightarrow> lam" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
543 |
where |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
544 |
"normalize t = reify (eval t)" |
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
545 |
|
|
dc6007dd9c30
a little further with NBE
Christian Urban <urbanc@in.tum.de>
parents:
2953
diff
changeset
|
546 |
end |