diff -r 09bbed4f21d6 -r 9fb315392493 Nominal/NewParser.thy --- a/Nominal/NewParser.thy Tue May 25 00:24:41 2010 +0100 +++ b/Nominal/NewParser.thy Wed May 26 15:34:54 2010 +0200 @@ -287,12 +287,6 @@ ML {* val cheat_alpha_bn_rsp = Unsynchronized.ref false *} ML {* val cheat_supp_eq = Unsynchronized.ref false *} -ML {* -fun remove_loop t = - let val _ = HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of t)) in t end - handle TERM _ => @{thm eqTrueI} OF [t] -*} - ML {* (* for testing porposes - to exit the procedure early *) @@ -305,7 +299,69 @@ setup STEPS_setup -ML {* dtyp_no_of_typ *} +ML {* +fun mk_conjl props = + fold (fn a => fn b => + if a = @{term True} then b else + if b = @{term True} then a else + HOLogic.mk_conj (a, b)) (rev props) @{term True}; +*} + +ML {* +val split_conj_tac = REPEAT o etac conjE THEN' TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI) +*} + +(* Given function for buildng a goal for an input, prepares a + one common goals for all the inputs and proves it by induction + together *) +ML {* +fun prove_by_induct tys build_goal ind utac inputs ctxt = +let + val names = Datatype_Prop.make_tnames tys; + val (names', ctxt') = Variable.variant_fixes names ctxt; + val frees = map Free (names' ~~ tys); + val (gls_lists, ctxt'') = fold_map (build_goal (tys ~~ frees)) inputs ctxt'; + val gls = flat gls_lists; + fun trm_gls_map t = filter (exists_subterm (fn s => s = t)) gls; + val trm_gl_lists = map trm_gls_map frees; + val trm_gl_insts = map2 (fn n => fn l => [NONE, if l = [] then NONE else SOME n]) names' trm_gl_lists + val trm_gls = map mk_conjl trm_gl_lists; + val gl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj trm_gls); + fun tac {context,...} = ( + InductTacs.induct_rules_tac context [(flat trm_gl_insts)] [ind] + THEN_ALL_NEW split_conj_tac THEN_ALL_NEW utac) 1 + val th_loc = Goal.prove ctxt'' [] [] gl tac + val ths_loc = HOLogic.conj_elims th_loc + val ths = Variable.export ctxt'' ctxt ths_loc +in + filter (fn x => not (prop_of x = prop_of @{thm TrueI})) ths +end +*} + +ML {* +fun build_eqvt_gl pi frees fnctn ctxt = +let + val typ = domain_type (fastype_of fnctn); + val arg = the (AList.lookup (op=) frees typ); +in + ([HOLogic.mk_eq (mk_perm pi (fnctn $ arg), fnctn $ (mk_perm pi arg))], ctxt) +end +*} + +ML {* +fun prove_eqvt tys ind simps funs ctxt = +let + val ([p], ctxt') = Variable.variant_fixes ["p"] ctxt; + val p = Free (p, @{typ perm}) + val simp_set = @{thms atom_eqvt permute_list.simps} @ simps @ all_eqvts ctxt' + val tac = asm_full_simp_tac (HOL_ss addsimps simp_set) + val ths_loc = prove_by_induct tys (build_eqvt_gl p) ind tac funs ctxt' + val ths = Variable.export ctxt' ctxt ths_loc + val add_eqvt = Attrib.internal (fn _ => Nominal_ThmDecls.eqvt_add) +in + (ths, snd (Local_Theory.note ((Binding.empty, [add_eqvt]), ths) ctxt)) +end +*} ML {* fun nominal_datatype2 dts bn_funs bn_eqs bclauses lthy = @@ -325,7 +381,7 @@ val inject_thms = flat (map #inject dtinfos); val distinct_thms = flat (map #distinct dtinfos); val rel_dtinfos = List.take (dtinfos, (length dts)); - val rel_distinct = map #distinct rel_dtinfos; (* thm list list *) + val raw_constrs_distinct = (map #distinct rel_dtinfos); val induct_thm = #induct dtinfo; val exhaust_thms = map #exhaust dtinfos; @@ -354,24 +410,21 @@ else raise TEST lthy3 (* definition of raw alphas *) - val (alpha_ts, alpha_bn_ts, alpha_intros, alpha_cases, alpha_induct, lthy4) = + val (alpha_trms, alpha_bn_trms, alpha_intros, alpha_cases, alpha_induct, lthy4) = if get_STEPS lthy > 4 then define_raw_alpha descr sorts raw_bn_info raw_bclauses raw_fvs lthy3a else raise TEST lthy3a - (* HERE *) + (* definition of alpha-distinct lemmas *) + val (alpha_distincts, alpha_bn_distincts) = + mk_alpha_distincts lthy4 alpha_cases raw_constrs_distinct alpha_trms alpha_bn_trms raw_bn_info + (* definition of raw_alpha_eq_iff lemmas *) - val rel_dists = flat (map (distinct_rel lthy4 alpha_cases) (rel_distinct ~~ alpha_ts)); - val rel_dists_bn = flat (map (distinct_rel lthy4 alpha_cases) - ((map (fn i => nth rel_distinct i) bn_nos) ~~ alpha_bn_ts)) - val alpha_eq_iff = if get_STEPS lthy > 5 - then build_rel_inj alpha_intros (inject_thms @ distinct_thms) alpha_cases lthy4 + then mk_alpha_eq_iff lthy4 alpha_intros distinct_thms inject_thms alpha_cases else raise TEST lthy4 - val alpha_eq_iff_simp = map remove_loop alpha_eq_iff; - (* proving equivariance lemmas for bns, fvs and alpha *) val _ = warning "Proving equivariance"; val (bv_eqvt, lthy5) = @@ -386,22 +439,22 @@ val (alpha_eqvt, lthy6a) = if get_STEPS lthy > 8 - then Nominal_Eqvt.equivariance alpha_ts alpha_induct alpha_intros lthy6 + then Nominal_Eqvt.equivariance alpha_trms alpha_induct alpha_intros lthy6 else raise TEST lthy6 (* proving alpha equivalence *) val _ = warning "Proving equivalence"; - val fv_alpha_all = combine_fv_alpha_bns (raw_fvs, raw_fv_bns) (alpha_ts, alpha_bn_ts) bn_nos; - val reflps = build_alpha_refl fv_alpha_all alpha_ts induct_thm alpha_eq_iff_simp lthy6a; + val fv_alpha_all = combine_fv_alpha_bns (raw_fvs, raw_fv_bns) (alpha_trms, alpha_bn_trms) bn_nos; + val reflps = build_alpha_refl fv_alpha_all alpha_trms induct_thm alpha_eq_iff lthy6a; val alpha_equivp = - if !cheat_equivp then map (equivp_hack lthy6a) alpha_ts - else build_equivps alpha_ts reflps alpha_induct - inject_thms alpha_eq_iff_simp distinct_thms alpha_cases alpha_eqvt lthy6a; + if !cheat_equivp then map (equivp_hack lthy6a) alpha_trms + else build_equivps alpha_trms reflps alpha_induct + inject_thms alpha_eq_iff distinct_thms alpha_cases alpha_eqvt lthy6a; val qty_binds = map (fn (_, b, _, _) => b) dts; val qty_names = map Name.of_binding qty_binds; val qty_full_names = map (Long_Name.qualify thy_name) qty_names - val (qtys, lthy7) = define_quotient_types qty_binds all_tys alpha_ts alpha_equivp lthy6a; + val (qtys, lthy7) = define_quotient_types qty_binds all_tys alpha_trms alpha_equivp lthy6a; val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts)); val raw_consts = flat (map (fn (i, (_, _, l)) => @@ -410,7 +463,7 @@ Datatype_Aux.typ_of_dtyp descr sorts (Datatype_Aux.DtRec i))) l) descr); val (consts, const_defs, lthy8) = quotient_lift_consts_export qtys (const_names ~~ raw_consts) lthy7; val _ = warning "Proving respects"; - val bns_rsp_pre' = build_fvbv_rsps alpha_ts alpha_induct raw_bn_eqs (map fst bns) lthy8; + val bns_rsp_pre' = build_fvbv_rsps alpha_trms alpha_induct raw_bn_eqs (map fst bns) lthy8; val (bns_rsp_pre, lthy9) = fold_map ( fn (bn_t, _) => prove_const_rsp qtys Binding.empty [bn_t] (fn _ => resolve_tac bns_rsp_pre' 1)) bns lthy8; @@ -418,7 +471,7 @@ fun fv_rsp_tac _ = if !cheat_fv_rsp then Skip_Proof.cheat_tac thy else fvbv_rsp_tac alpha_induct raw_fv_defs lthy8 1; - val fv_rsps = prove_fv_rsp fv_alpha_all alpha_ts fv_rsp_tac lthy9; + val fv_rsps = prove_fv_rsp fv_alpha_all alpha_trms fv_rsp_tac lthy9; val (fv_rsp_pre, lthy10) = fold_map (fn fv => fn ctxt => prove_const_rsp qtys Binding.empty [fv] (fn _ => asm_simp_tac (HOL_ss addsimps fv_rsps) 1) ctxt) (raw_fvs @ raw_fv_bns) lthy9; @@ -427,12 +480,12 @@ (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy10; fun alpha_bn_rsp_tac _ = if !cheat_alpha_bn_rsp then Skip_Proof.cheat_tac thy else - let val alpha_bn_rsp_pre = prove_alpha_bn_rsp alpha_ts alpha_induct (alpha_eq_iff_simp @ rel_dists @ rel_dists_bn) alpha_equivp exhaust_thms alpha_bn_ts lthy11 in asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1 end; + let val alpha_bn_rsp_pre = prove_alpha_bn_rsp alpha_trms alpha_induct (alpha_eq_iff @ alpha_distincts @ alpha_bn_distincts) alpha_equivp exhaust_thms alpha_bn_trms lthy11 in asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1 end; val (alpha_bn_rsps, lthy11a) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst] - alpha_bn_rsp_tac) alpha_bn_ts lthy11 + alpha_bn_rsp_tac) alpha_bn_trms lthy11 fun const_rsp_tac _ = - let val alpha_alphabn = prove_alpha_alphabn alpha_ts alpha_induct alpha_eq_iff_simp alpha_bn_ts lthy11a - in constr_rsp_tac alpha_eq_iff_simp (fv_rsp @ bns_rsp @ reflps @ alpha_alphabn) 1 end + let val alpha_alphabn = prove_alpha_alphabn alpha_trms alpha_induct alpha_eq_iff alpha_bn_trms lthy11a + in constr_rsp_tac alpha_eq_iff (fv_rsp @ bns_rsp @ reflps @ alpha_alphabn) 1 end val (const_rsps, lthy12) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst] const_rsp_tac) raw_consts lthy11a val qfv_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) (raw_fvs @ raw_fv_bns) @@ -440,9 +493,9 @@ val (qfv_ts_nobn, qfv_ts_bn) = chop (length raw_perm_funs) qfv_ts; val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs val (qbn_ts, qbn_defs, lthy12b) = quotient_lift_consts_export qtys (qbn_names ~~ raw_bn_funs) lthy12a; - val qalpha_bn_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) alpha_bn_ts - val (qalpha_bn_ts, qalphabn_defs, lthy12c) = - quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_bn_ts) lthy12b; + val qalpha_bn_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) alpha_bn_trms + val (qalpha_bn_trms, qalphabn_defs, lthy12c) = + quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_bn_trms) lthy12b; val _ = warning "Lifting permutations"; val thy = Local_Theory.exit_global lthy12c; val perm_names = map (fn x => "permute_" ^ x) qty_names @@ -470,14 +523,14 @@ val lthy17 = note_simp_suffix "bn" q_bn lthy16; val _ = warning "Lifting eq-iff"; (*val _ = map tracing (map PolyML.makestring alpha_eq_iff);*) - val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas}) alpha_eq_iff_simp + val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas}) alpha_eq_iff val eq_iff_unfolded1 = map (Local_Defs.unfold lthy17 @{thms Pair_eqvt}) eq_iff_unfolded0 val q_eq_iff_pre0 = map (lift_thm qtys lthy17) eq_iff_unfolded1; val q_eq_iff_pre1 = map (Local_Defs.fold lthy17 @{thms Pair_eqvt}) q_eq_iff_pre0 val q_eq_iff_pre2 = map (Local_Defs.fold lthy17 @{thms alphas}) q_eq_iff_pre1 val q_eq_iff = map (Local_Defs.unfold lthy17 (Quotient_Info.id_simps_get lthy17)) q_eq_iff_pre2 val (_, lthy18) = Local_Theory.note ((suffix_bind "eq_iff", []), q_eq_iff) lthy17; - val q_dis = map (lift_thm qtys lthy18) rel_dists; + val q_dis = map (lift_thm qtys lthy18) alpha_distincts; val lthy19 = note_simp_suffix "distinct" q_dis lthy18; val q_eqvt = map (lift_thm qtys lthy19) (bv_eqvt @ fv_eqvt); val (_, lthy20) = Local_Theory.note ((Binding.empty, @@ -490,7 +543,7 @@ val lthy21 = Theory_Target.instantiation (qty_full_names, [], @{sort fs}) thy3; fun tac _ = Class.intro_classes_tac [] THEN (ALLGOALS (resolve_tac fin_supp)) val lthy22 = Class.prove_instantiation_instance tac lthy21 - val fv_alpha_all = combine_fv_alpha_bns (qfv_ts_nobn, qfv_ts_bn) (alpha_ts, qalpha_bn_ts) bn_nos; + val fv_alpha_all = combine_fv_alpha_bns (qfv_ts_nobn, qfv_ts_bn) (alpha_trms, qalpha_bn_trms) bn_nos; val (names, supp_eq_t) = supp_eq fv_alpha_all; val _ = warning "Support Equations"; fun supp_eq_tac' _ = if !cheat_supp_eq then Skip_Proof.cheat_tac thy else