diff -r 2f1b00d83925 -r b679900fa5f6 Nominal/Term4.thy --- a/Nominal/Term4.thy Tue Mar 23 08:16:39 2010 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,121 +0,0 @@ -theory Term4 -imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove" "Quotient_List" -begin - -atom_decl name - -section {*** lam with indirect list recursion ***} - -datatype rtrm4 = - rVr4 "name" -| rAp4 "rtrm4" "rtrm4 list" -| rLm4 "name" "rtrm4" --"bind (name) in (trm)" -print_theorems - -thm rtrm4.recs - -(* there cannot be a clause for lists, as *) -(* permutations are already defined in Nominal (also functions, options, and so on) *) -setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term4.rtrm4") 1 *} - -(* "repairing" of the permute function *) -lemma repaired: - fixes ts::"rtrm4 list" - shows "permute_rtrm4_list p ts = p \ ts" - apply(induct ts) - apply(simp_all) - done - -thm permute_rtrm4_permute_rtrm4_list.simps -thm permute_rtrm4_permute_rtrm4_list.simps[simplified repaired] - -local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term4.rtrm4") - [[[], [], [(NONE, 0,1)]], [[], []] ] *} -print_theorems - -lemma fix2: "alpha_rtrm4_list = list_rel alpha_rtrm4" -apply (rule ext)+ -apply (induct_tac x xa rule: list_induct2') -apply (simp_all add: alpha_rtrm4_alpha_rtrm4_list.intros) -apply clarify apply (erule alpha_rtrm4_list.cases) apply(simp_all) -apply clarify apply (erule alpha_rtrm4_list.cases) apply(simp_all) -apply rule -apply (erule alpha_rtrm4_list.cases) -apply simp_all -apply (rule alpha_rtrm4_alpha_rtrm4_list.intros) -apply simp_all -done - -(* We need sth like: -lemma fix3: "fv_rtrm4_list = set o map fv_rtrm4" *) - -notation - alpha_rtrm4 ("_ \4 _" [100, 100] 100) and - alpha_rtrm4_list ("_ \4l _" [100, 100] 100) -thm alpha_rtrm4_alpha_rtrm4_list.intros[simplified fix2] - -local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros[simplified fix2]} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases[simplified fix2] alpha_rtrm4_list.cases[simplified fix2]} ctxt)) ctxt)) *} -thm alpha4_inj - -local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_inj_no}, []), (build_alpha_inj @{thms alpha_rtrm4_alpha_rtrm4_list.intros} @{thms rtrm4.distinct rtrm4.inject list.distinct list.inject} @{thms alpha_rtrm4.cases alpha_rtrm4_list.cases} ctxt)) ctxt)) *} -thm alpha4_inj_no - -local_setup {* -snd o build_eqvts @{binding fv_rtrm4_fv_rtrm4_list_eqvt} [@{term fv_rtrm4}, @{term fv_rtrm4_list}] [@{term "permute :: perm \ rtrm4 \ rtrm4"},@{term "permute :: perm \ rtrm4 list \ rtrm4 list"}] (@{thms fv_rtrm4_fv_rtrm4_list.simps permute_rtrm4_permute_rtrm4_list.simps[simplified repaired]}) @{thm rtrm4.induct} -*} -print_theorems - -local_setup {* -(fn ctxt => snd (Local_Theory.note ((@{binding alpha4_eqvt_no}, []), - build_alpha_eqvts [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] [@{term "permute :: perm \ rtrm4 \ rtrm4"},@{term "permute :: perm \ rtrm4 list \ rtrm4 list"}] @{thms permute_rtrm4_permute_rtrm4_list.simps[simplified repaired] alpha4_inj_no} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} ctxt) ctxt)) -*} -lemmas alpha4_eqvt = alpha4_eqvt_no[simplified fix2] - -local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha4_equivp_no}, []), - (build_equivps [@{term alpha_rtrm4}, @{term alpha_rtrm4_list}] @{thm rtrm4.induct} @{thm alpha_rtrm4_alpha_rtrm4_list.induct} @{thms rtrm4.inject list.inject} @{thms alpha4_inj_no} @{thms rtrm4.distinct list.distinct} @{thms alpha_rtrm4_list.cases alpha_rtrm4.cases} @{thms alpha4_eqvt_no} ctxt)) ctxt)) *} -lemmas alpha4_equivp = alpha4_equivp_no[simplified fix2] - -(*lemma fv_rtrm4_rsp: - "xa \4 ya \ fv_rtrm4 xa = fv_rtrm4 ya" - "x \4l y \ fv_rtrm4_list x = fv_rtrm4_list y" - apply (induct rule: alpha_rtrm4_alpha_rtrm4_list.inducts) - apply (simp_all add: alpha_gen) -done*) - - -quotient_type - trm4 = rtrm4 / alpha_rtrm4 -(*and - trm4list = "rtrm4 list" / alpha_rtrm4_list*) - by (simp_all add: alpha4_equivp) - -local_setup {* -(fn ctxt => ctxt - |> snd o (Quotient_Def.quotient_lift_const ("Vr4", @{term rVr4})) - |> snd o (Quotient_Def.quotient_lift_const ("Ap4", @{term rAp4})) - |> snd o (Quotient_Def.quotient_lift_const ("Lm4", @{term rLm4}))) -*} -print_theorems - -local_setup {* snd o prove_const_rsp @{binding fv_rtrm4_rsp} [@{term fv_rtrm4}] - (fn _ => fvbv_rsp_tac @{thm alpha_rtrm4_alpha_rtrm4_list.inducts(1)} @{thms fv_rtrm4_fv_rtrm4_list.simps} 1) *} -print_theorems - -local_setup {* snd o prove_const_rsp @{binding rVr4_rsp} [@{term rVr4}] - (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *} -lemma "(alpha_rtrm4 ===> list_rel alpha_rtrm4 ===> alpha_rtrm4) rAp4 rAp4" -apply simp -apply clarify -apply (simp add: alpha4_inj) - - -local_setup {* snd o prove_const_rsp @{binding rLm4_rsp} [@{term rLm4}] - (fn _ => constr_rsp_tac @{thms alpha4_inj} @{thms fv_rtrm4_rsp} @{thms alpha4_equivp} 1) *} -local_setup {* snd o prove_const_rsp @{binding permute_rtrm4_rsp} - [@{term "permute :: perm \ rtrm4 \ rtrm4"}, @{term "permute :: perm \ rtrm4 list \ rtrm4 list"}] - (fn _ => asm_simp_tac (HOL_ss addsimps @{thms alpha4_eqvt}) 1) *} - -thm rtrm4.induct -lemmas trm1_bp_induct = rtrm4.induct[quot_lifted] - -end