--- a/src/HOL/Nominal/Examples/Class.thy Fri Apr 28 17:56:20 2006 +0200
+++ b/src/HOL/Nominal/Examples/Class.thy Fri Apr 28 17:58:33 2006 +0200
@@ -1,6 +1,7 @@
+(* $Id$ *)
theory Class
-imports "../nominal"
+imports "../Nominal"
begin
section {* Term-Calculus from Urban's PhD *}
@@ -21,185 +22,6 @@
| ImpR "\<guillemotleft>name\<guillemotright>(\<guillemotleft>coname\<guillemotright>trm)" "coname" ("ImpR [_].<_>._ _" [100,100,100,100] 100)
| ImpL "\<guillemotleft>coname\<guillemotright>trm" "\<guillemotleft>name\<guillemotright>trm" "name" ("ImpL <_>._ [_]._ _" [100,100,100,100,100] 100)
-thm trm_rec_set.intros[no_vars]
-
-lemma rec_total:
- shows "\<exists>r. (t,r) \<in> trm_rec_set f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12"
- by (induct t rule: trm.induct_weak, auto intro: trm_rec_set.intros)
-
-lemma rec_prm_eq:
- assumes a: "(t,y) \<in> trm_rec_set f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12"
- and b: "pi1 \<triangleq> pi2"
- and c: "pi3 \<triangleq> pi4"
- shows "y pi1 pi3 = y pi2 pi4"
-using a b c
-apply(induct fixing: pi1 pi2 pi3 pi4)
-(* axiom *)
-apply(simp add: pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-(* Cut *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* NotR *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* NotL *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-(* AndR *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-(* AndL1 *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* AndL1 *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* OrR1 *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-(* OrR2 *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-(* OrL *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* ImpR *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption)
-apply(rule at_prm_eq_append'[OF at_name_inst], assumption)
-(* ImpL *)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(rule_tac f="fresh_fun" in arg_cong)
-apply(simp add: expand_fun_eq)
-apply(rule allI)
-apply(tactic {* DatatypeAux.cong_tac 1 *})+
-apply(simp_all add: pt2[OF pt_name_inst] pt2[OF pt_coname_inst]
- pt3[OF pt_name_inst] pt3[OF pt_coname_inst])
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(rule at_prm_eq_append'[OF at_coname_inst], assumption, assumption)
-apply(drule meta_spec)+
-apply(drule meta_mp, erule_tac [2] meta_mp)
-apply(assumption, rule at_prm_eq_append'[OF at_name_inst], assumption)
-done
-
-lemma rec_fin_supp:
-assumes f: "finite ((supp (f1,f2,f3,f3,f4,f5,f6,f7,f8,f9,f10,f11,f12))::name set)"
- and c: "\<exists>(a::name). a\<sharp>f3 \<and> (\<forall>t (r::'a::pt_name). a\<sharp>f3 a t r)"
- and a: "(t,r) \<in> trm_rec_set f1 f2 f3"
- shows "finite ((supp r)::name set)"
-using a
-proof (induct)
- case goal1 thus ?case using f by (finite_guess add: supp_prod fs_name1)
-next
- case goal2 thus ?case using f by (finite_guess add: supp_prod fs_name1)
-next
- case (goal3 c t r)
- have ih: "finite ((supp r)::name set)" by fact
- let ?g' = "\<lambda>pi a'. f3 a' ((pi@[(c,a')])\<bullet>t) (r (pi@[(c,a')]))" --"helper function"
- have fact1: "\<forall>pi. finite ((supp (?g' pi))::name set)" using f ih
- by (rule_tac allI, finite_guess add: perm_append supp_prod fs_name1)
- have fact2: "\<forall>pi. \<exists>(a''::name). a''\<sharp>(?g' pi) \<and> a''\<sharp>((?g' pi) a'')"
- proof
- fix pi::"name prm"
- show "\<exists>(a''::name). a''\<sharp>(?g' pi) \<and> a''\<sharp>((?g' pi) a'')" using f c ih
- by (rule_tac f3_freshness_conditions_simple, simp_all add: supp_prod)
- qed
- show ?case using fact1 fact2 ih f by (finite_guess add: fresh_fun_eqvt perm_append supp_prod fs_name1)
-qed
text {* Induction principles *}
@@ -221,4 +43,8 @@
substn :: "trm \<Rightarrow> name \<Rightarrow> ctrm \<Rightarrow> trm" ("_[_::=_]" [100,100,100] 100)
substc :: "trm \<Rightarrow> coname \<Rightarrow> ntrm \<Rightarrow> trm" ("_[_::=_]" [100,100,100] 100)
-text {* does not work yet *}
\ No newline at end of file
+text {* does not work yet *}
+
+
+end
+