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} \ rbv6 t" -| "rbv6 (rLt6 l r) = rbv6 l \ 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 ("_ \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 \ rtrm6 \ 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 \ rtrm6 \ 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 \ rtrm6 \ 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) \ b \ \ (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 \ b)" in exI) -apply (simp add: alpha_gen fresh_star_def) -apply (simp add: alpha6_inj) -done - -lemma fv6_rsp: "x \6 y \ 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 \ trm6 \ trm6" -is - "permute :: perm \ rtrm6 \ rtrm6" - -instance -apply default -sorry -end - -lemma lifted_induct: -"\x1 = x2; \name namea. name = namea \ P (Vr6 name) (Vr6 namea); - \name rtrm6 namea rtrm6a. - \True; - \pi. fv_trm6 rtrm6 - {atom name} = fv_trm6 rtrm6a - {atom namea} \ - (fv_trm6 rtrm6 - {atom name}) \* pi \ pi \ rtrm6 = rtrm6a \ P (pi \ rtrm6) rtrm6a\ - \ P (Lm6 name rtrm6) (Lm6 namea rtrm6a); - \rtrm61 rtrm61a rtrm62 rtrm62a. - \rtrm61 = rtrm61a; P rtrm61 rtrm61a; - \pi. fv_trm6 rtrm62 - bv6 rtrm61 = fv_trm6 rtrm62a - bv6 rtrm61a \ - (fv_trm6 rtrm62 - bv6 rtrm61) \* pi \ pi \ rtrm62 = rtrm62a \ P (pi \ rtrm62) rtrm62a\ - \ P (Lt6 rtrm61 rtrm62) (Lt6 rtrm61a rtrm62a)\ -\ 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 \ - (\pi. fv_trm6 rtrm62 - bv6 rtrm61 = fv_trm6 rtrm62a - bv6 rtrm61a \ - (fv_trm6 rtrm62 - bv6 rtrm61) \* pi \ pi \ rtrm62 = rtrm62a))" -apply(lifting alpha6_inj(3)[unfolded alpha_gen]) -apply injection -(* notice unsolvable goals: (alpha_rtrm6 ===> op =) rbv6 rbv6 *) -oops - - - - -end