
diff -r d804729d6cf4 -r 6542026b95cd Nominal/Term6.thy
--- a/Nominal/Term6.thy	Tue Mar 23 07:04:27 2010 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,155 +0,0 @@
-theory Term6
-imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
-begin
-
-atom_decl name
-
-(* example with a bn function defined over the type itself, NOT respectful. *)
-
-datatype rtrm6 =
-  rVr6 "name"
-| rLm6 "name" "rtrm6" --"bind name in rtrm6"
-| rLt6 "rtrm6" "rtrm6" --"bind (bv6 left) in (right)"
-
-primrec
-  rbv6
-where
-  "rbv6 (rVr6 n) = {}"
-| "rbv6 (rLm6 n t) = {atom n} \<union> rbv6 t"
-| "rbv6 (rLt6 l r) = rbv6 l \<union> rbv6 r"
-
-setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term6.rtrm6") 1 *}
-print_theorems
-
-local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term6.rtrm6") [
-  [[], [(NONE, 0, 1)], [(SOME @{term rbv6}, 0, 1)]]] *}
-notation alpha_rtrm6 ("_ \<approx>6 _" [100, 100] 100)
-thm alpha_rtrm6.intros
-
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha6_inj}, []), (build_alpha_inj @{thms alpha_rtrm6.intros} @{thms rtrm6.distinct rtrm6.inject} @{thms alpha_rtrm6.cases} ctxt)) ctxt)) *}
-thm alpha6_inj
-
-local_setup {*
-snd o (build_eqvts @{binding rbv6_eqvt} [@{term rbv6}] [@{term "permute :: perm \<Rightarrow> rtrm6 \<Rightarrow> rtrm6"}] (@{thms rbv6.simps permute_rtrm6.simps}) @{thm rtrm6.induct})
-*}
-
-local_setup {*
-snd o build_eqvts @{binding fv_rtrm6_eqvt} [@{term fv_rtrm6}] [@{term "permute :: perm \<Rightarrow> rtrm6 \<Rightarrow> rtrm6"}] (@{thms fv_rtrm6.simps permute_rtrm6.simps}) @{thm rtrm6.induct}
-*}
-
-local_setup {*
-(fn ctxt => snd (Local_Theory.note ((@{binding alpha6_eqvt}, []),
-  build_alpha_eqvts [@{term alpha_rtrm6}] [@{term "permute :: perm \<Rightarrow> rtrm6 \<Rightarrow> rtrm6"}] @{thms permute_rtrm6.simps alpha6_inj} @{thm alpha_rtrm6.induct} ctxt) ctxt))
-*}
-thm alpha6_eqvt
-local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha6_equivp}, []),
-  (build_equivps [@{term alpha_rtrm6}] @{thm rtrm6.induct} @{thm alpha_rtrm6.induct} @{thms rtrm6.inject} @{thms alpha6_inj} @{thms rtrm6.distinct} @{thms alpha_rtrm6.cases} @{thms alpha6_eqvt} ctxt)) ctxt)) *}
-thm alpha6_equivp
-
-quotient_type
-  trm6 = rtrm6 / alpha_rtrm6
-  by (auto intro: alpha6_equivp)
-
-local_setup {*
-(fn ctxt => ctxt
- |> snd o (Quotient_Def.quotient_lift_const ("Vr6", @{term rVr6}))
- |> snd o (Quotient_Def.quotient_lift_const ("Lm6", @{term rLm6}))
- |> snd o (Quotient_Def.quotient_lift_const ("Lt6", @{term rLt6}))
- |> snd o (Quotient_Def.quotient_lift_const ("fv_trm6", @{term fv_rtrm6}))
- |> snd o (Quotient_Def.quotient_lift_const ("bv6", @{term rbv6})))
-*}
-print_theorems
-
-lemma [quot_respect]:
-  "(op = ===> alpha_rtrm6 ===> alpha_rtrm6) permute permute"
-by (auto simp add: alpha6_eqvt)
-
-(* Definitely not true , see lemma below *)
-lemma [quot_respect]:"(alpha_rtrm6 ===> op =) rbv6 rbv6"
-apply simp apply clarify
-apply (erule alpha_rtrm6.induct)
-oops
-
-lemma "(a :: name) \<noteq> b \<Longrightarrow> \<not> (alpha_rtrm6 ===> op =) rbv6 rbv6"
-apply simp
-apply (rule_tac x="rLm6 (a::name) (rVr6 (a :: name))" in  exI)
-apply (rule_tac x="rLm6 (b::name) (rVr6 (b :: name))" in  exI)
-apply simp
-apply (simp add: alpha6_inj)
-apply (rule_tac x="(a \<leftrightarrow> b)" in  exI)
-apply (simp add: alpha_gen fresh_star_def)
-apply (simp add: alpha6_inj)
-done
-
-lemma fv6_rsp: "x \<approx>6 y \<Longrightarrow> fv_rtrm6 x = fv_rtrm6 y"
-apply (induct_tac x y rule: alpha_rtrm6.induct)
-apply simp_all
-apply (erule exE)
-apply (simp_all add: alpha_gen)
-done
-
-lemma [quot_respect]:"(alpha_rtrm6 ===> op =) fv_rtrm6 fv_rtrm6"
-by (simp add: fv6_rsp)
-
-lemma [quot_respect]:
- "(op = ===> alpha_rtrm6) rVr6 rVr6"
- "(op = ===> alpha_rtrm6 ===> alpha_rtrm6) rLm6 rLm6"
-apply auto
-apply (simp_all add: alpha6_inj)
-apply (rule_tac x="0::perm" in exI)
-apply (simp add: alpha_gen fv6_rsp fresh_star_def fresh_zero_perm)
-done
-
-lemma [quot_respect]:
- "(alpha_rtrm6 ===> alpha_rtrm6 ===> alpha_rtrm6) rLt6 rLt6"
-apply auto
-apply (simp_all add: alpha6_inj)
-apply (rule_tac [!] x="0::perm" in exI)
-apply (simp_all add: alpha_gen fresh_star_def fresh_zero_perm)
-(* needs rbv6_rsp *)
-oops
-
-instantiation trm6 :: pt begin
-
-quotient_definition
-  "permute_trm6 :: perm \<Rightarrow> trm6 \<Rightarrow> trm6"
-is
-  "permute :: perm \<Rightarrow> rtrm6 \<Rightarrow> rtrm6"
-
-instance
-apply default
-sorry
-end
-
-lemma lifted_induct:
-"\<lbrakk>x1 = x2; \<And>name namea. name = namea \<Longrightarrow> P (Vr6 name) (Vr6 namea);
- \<And>name rtrm6 namea rtrm6a.
-    \<lbrakk>True;
-     \<exists>pi. fv_trm6 rtrm6 - {atom name} = fv_trm6 rtrm6a - {atom namea} \<and>
-          (fv_trm6 rtrm6 - {atom name}) \<sharp>* pi \<and> pi \<bullet> rtrm6 = rtrm6a \<and> P (pi \<bullet> rtrm6) rtrm6a\<rbrakk>
-    \<Longrightarrow> P (Lm6 name rtrm6) (Lm6 namea rtrm6a);
- \<And>rtrm61 rtrm61a rtrm62 rtrm62a.
-    \<lbrakk>rtrm61 = rtrm61a; P rtrm61 rtrm61a;
-     \<exists>pi. fv_trm6 rtrm62 - bv6 rtrm61 = fv_trm6 rtrm62a - bv6 rtrm61a \<and>
-          (fv_trm6 rtrm62 - bv6 rtrm61) \<sharp>* pi \<and> pi \<bullet> rtrm62 = rtrm62a \<and> P (pi \<bullet> rtrm62) rtrm62a\<rbrakk>
-    \<Longrightarrow> P (Lt6 rtrm61 rtrm62) (Lt6 rtrm61a rtrm62a)\<rbrakk>
-\<Longrightarrow> P x1 x2"
-apply (lifting alpha_rtrm6.induct[unfolded alpha_gen])
-apply injection
-(* notice unsolvable goals: (alpha_rtrm6 ===> op =) rbv6 rbv6 *)
-oops
-
-lemma lifted_inject_a3:
-"(Lt6 rtrm61 rtrm62 = Lt6 rtrm61a rtrm62a) =
-(rtrm61 = rtrm61a \<and>
- (\<exists>pi. fv_trm6 rtrm62 - bv6 rtrm61 = fv_trm6 rtrm62a - bv6 rtrm61a \<and>
-       (fv_trm6 rtrm62 - bv6 rtrm61) \<sharp>* pi \<and> pi \<bullet> rtrm62 = rtrm62a))"
-apply(lifting alpha6_inj(3)[unfolded alpha_gen])
-apply injection
-(* notice unsolvable goals: (alpha_rtrm6 ===> op =) rbv6 rbv6 *)
-oops
-
-
-
-
-end




