diff -r f89ee40fbb08 -r 78d828f43cdf Attic/Parser.thy --- a/Attic/Parser.thy Sat Dec 17 16:57:25 2011 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,670 +0,0 @@ -theory Parser -imports "../Nominal-General/Nominal2_Atoms" - "../Nominal-General/Nominal2_Eqvt" - "../Nominal-General/Nominal2_Supp" - "Perm" "Equivp" "Rsp" "Lift" "Fv" -begin - -section{* Interface for nominal_datatype *} - -text {* - -Nominal-Datatype-part: - - -1nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list - ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - type(s) to be defined constructors list - (ty args, name, syn) (name, typs, syn) - -Binder-Function-part: - -2rd Arg: (binding * typ option * mixfix) list - ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - binding function(s) - to be defined - (name, type, syn) - -3th Arg: term list - ^^^^^^^^^ - the equations of the binding functions - (Trueprop equations) -*} - -ML {* - -*} - -text {*****************************************************} -ML {* -(* nominal datatype parser *) -local - structure P = OuterParse - - fun tuple ((x, y, z), u) = (x, y, z, u) - fun tswap (((x, y), z), u) = (x, y, u, z) -in - -val _ = OuterKeyword.keyword "bind" -val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ - -(* binding specification *) -(* maybe use and_list *) -val bind_parser = - P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name) >> swap) - -val constr_parser = - P.binding -- Scan.repeat anno_typ - -(* datatype parser *) -val dt_parser = - (P.type_args -- P.binding -- P.opt_mixfix >> P.triple1) -- - (P.$$$ "=" |-- P.enum1 "|" (constr_parser -- bind_parser -- P.opt_mixfix >> tswap)) >> tuple - -(* function equation parser *) -val fun_parser = - Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[]) - -(* main parser *) -val main_parser = - (P.and_list1 dt_parser) -- fun_parser >> P.triple2 - -end -*} - -(* adds "_raw" to the end of constants and types *) -ML {* -fun add_raw s = s ^ "_raw" -fun add_raws ss = map add_raw ss -fun raw_bind bn = Binding.suffix_name "_raw" bn - -fun replace_str ss s = - case (AList.lookup (op=) ss s) of - SOME s' => s' - | NONE => s - -fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts) - | replace_typ ty_ss T = T - -fun raw_dts ty_ss dts = -let - - fun raw_dts_aux1 (bind, tys, mx) = - (raw_bind bind, map (replace_typ ty_ss) tys, mx) - - fun raw_dts_aux2 (ty_args, bind, mx, constrs) = - (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs) -in - map raw_dts_aux2 dts -end - -fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T) - | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T) - | replace_aterm trm_ss trm = trm - -fun replace_term trm_ss ty_ss trm = - trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) -*} - -ML {* -fun get_cnstrs dts = - map (fn (_, _, _, constrs) => constrs) dts - -fun get_typed_cnstrs dts = - flat (map (fn (_, bn, _, constrs) => - (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts) - -fun get_cnstr_strs dts = - map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts)) - -fun get_bn_fun_strs bn_funs = - map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs -*} - -ML {* -fun rawify_dts dt_names dts dts_env = -let - val raw_dts = raw_dts dts_env dts - val raw_dt_names = add_raws dt_names -in - (raw_dt_names, raw_dts) -end -*} - -ML {* -fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs = -let - val bn_funs' = map (fn (bn, ty, mx) => - (raw_bind bn, replace_typ dts_env ty, mx)) bn_funs - - val bn_eqs' = map (fn (attr, trm) => - (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs -in - (bn_funs', bn_eqs') -end -*} - -ML {* -fun apfst3 f (a, b, c) = (f a, b, c) -*} - -ML {* -fun rawify_binds dts_env cnstrs_env bn_fun_env binds = - map (map (map (map (fn (opt_trm, i, j, aty) => - (Option.map (apfst (replace_term (cnstrs_env @ bn_fun_env) dts_env)) opt_trm, i, j, aty))))) binds -*} - -ML {* -fun find [] _ = error ("cannot find element") - | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y -*} - -ML {* -fun strip_bn_fun t = - case t of - Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r - | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r - | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y => - (i, NONE) :: strip_bn_fun y - | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y => - (i, NONE) :: strip_bn_fun y - | Const (@{const_name bot}, _) => [] - | Const (@{const_name Nil}, _) => [] - | (f as Free _) $ Bound i => [(i, SOME f)] - | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t)) -*} - -ML {* -fun prep_bn dt_names dts eqs = -let - fun aux eq = - let - val (lhs, rhs) = eq - |> strip_qnt_body "all" - |> HOLogic.dest_Trueprop - |> HOLogic.dest_eq - val (bn_fun, [cnstr]) = strip_comb lhs - val (_, ty) = dest_Free bn_fun - val (ty_name, _) = dest_Type (domain_type ty) - val dt_index = find_index (fn x => x = ty_name) dt_names - val (cnstr_head, cnstr_args) = strip_comb cnstr - val rhs_elements = strip_bn_fun rhs - val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements - in - (dt_index, (bn_fun, (cnstr_head, included))) - end - fun order dts i ts = - let - val dt = nth dts i - val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt) - val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts - in - map (find ts') cts - end - - val unordered = AList.group (op=) (map aux eqs) - val unordered' = map (fn (x, y) => (x, AList.group (op=) y)) unordered - val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered' -in - ordered -end -*} - -ML {* -fun add_primrec_wrapper funs eqs lthy = - if null funs then (([], []), lthy) - else - let - val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs - val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs - in - Primrec.add_primrec funs' eqs' lthy - end -*} - -ML {* -fun add_datatype_wrapper dt_names dts = -let - val conf = Datatype.default_config -in - Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts) -end -*} - -ML {* -fun raw_nominal_decls dts bn_funs bn_eqs binds lthy = -let - val thy = ProofContext.theory_of lthy - val thy_name = Context.theory_name thy - - val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts - val dt_full_names = map (Long_Name.qualify thy_name) dt_names - val dt_full_names' = add_raws dt_full_names - val dts_env = dt_full_names ~~ dt_full_names' - - val cnstrs = get_cnstr_strs dts - val cnstrs_ty = get_typed_cnstrs dts - val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs - val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name - (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty - val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names' - - val bn_fun_strs = get_bn_fun_strs bn_funs - val bn_fun_strs' = add_raws bn_fun_strs - val bn_fun_env = bn_fun_strs ~~ bn_fun_strs' - val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name)) - (bn_fun_strs ~~ bn_fun_strs') - - val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env - - val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs - - val raw_binds = rawify_binds dts_env cnstrs_env bn_fun_full_env binds - - val raw_bns = prep_bn dt_full_names' raw_dts (map snd raw_bn_eqs) - -(*val _ = tracing (cat_lines (map PolyML.makestring raw_bns))*) -in - lthy - |> add_datatype_wrapper raw_dt_names raw_dts - ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs - ||>> pair raw_binds - ||>> pair raw_bns -end -*} - -lemma equivp_hack: "equivp x" -sorry -ML {* -fun equivp_hack ctxt rel = -let - val thy = ProofContext.theory_of ctxt - val ty = domain_type (fastype_of rel) - val cty = ctyp_of thy ty - val ct = cterm_of thy rel -in - Drule.instantiate' [SOME cty] [SOME ct] @{thm equivp_hack} -end -*} - -ML {* val cheat_alpha_eqvt = Unsynchronized.ref false *} -ML {* val cheat_equivp = Unsynchronized.ref false *} -ML {* val cheat_fv_rsp = Unsynchronized.ref false *} -ML {* val cheat_const_rsp = Unsynchronized.ref false *} - -(* nominal_datatype2 does the following things in order: - -Parser.thy/raw_nominal_decls - 1) define the raw datatype - 2) define the raw binding functions - -Perm.thy/define_raw_perms - 3) define permutations of the raw datatype and show that the raw type is - in the pt typeclass - -Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha - 4) define fv and fv_bn - 5) define alpha and alpha_bn - -Perm.thy/distinct_rel - 6) prove alpha_distincts (C1 x \ C2 y ...) (Proof by cases; simp) - -Tacs.thy/build_rel_inj - 6) prove alpha_eq_iff (C1 x = C2 y \ P x y ...) - (left-to-right by intro rule, right-to-left by cases; simp) -Equivp.thy/prove_eqvt - 7) prove bn_eqvt (common induction on the raw datatype) - 8) prove fv_eqvt (common induction on the raw datatype with help of above) -Rsp.thy/build_alpha_eqvts - 9) prove alpha_eqvt and alpha_bn_eqvt - (common alpha-induction, unfolding alpha_gen, permute of #* and =) -Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps - 10) prove that alpha and alpha_bn are equivalence relations - (common induction and application of 'compose' lemmas) -Lift.thy/define_quotient_types - 11) define quotient types -Rsp.thy/build_fvbv_rsps - 12) prove bn respects (common induction and simp with alpha_gen) -Rsp.thy/prove_const_rsp - 13) prove fv respects (common induction and simp with alpha_gen) - 14) prove permute respects (unfolds to alpha_eqvt) -Rsp.thy/prove_alpha_bn_rsp - 15) prove alpha_bn respects - (alpha_induct then cases then sym and trans of the relations) -Rsp.thy/prove_alpha_alphabn - 16) show that alpha implies alpha_bn (by unduction, needed in following step) -Rsp.thy/prove_const_rsp - 17) prove respects for all datatype constructors - (unfold eq_iff and alpha_gen; introduce zero permutations; simp) -Perm.thy/quotient_lift_consts_export - 18) define lifted constructors, fv, bn, alpha_bn, permutations -Perm.thy/define_lifted_perms - 19) lift permutation zero and add properties to show that quotient type is in the pt typeclass -Lift.thy/lift_thm - 20) lift permutation simplifications - 21) lift induction - 22) lift fv - 23) lift bn - 24) lift eq_iff - 25) lift alpha_distincts - 26) lift fv and bn eqvts -Equivp.thy/prove_supports - 27) prove that union of arguments supports constructors -Equivp.thy/prove_fs - 28) show that the lifted type is in fs typeclass (* by q_induct, supports *) -Equivp.thy/supp_eq - 29) prove supp = fv -*) -ML {* -fun nominal_datatype2 dts bn_funs bn_eqs binds lthy = -let - val _ = tracing "Raw declarations"; - val thy = ProofContext.theory_of lthy - val thy_name = Context.theory_name thy - val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), raw_bns), lthy2) = - raw_nominal_decls dts bn_funs bn_eqs binds lthy - val morphism_2_1 = ProofContext.export_morphism lthy2 lthy - fun export_fun f (t, l) = (f t, map (map (apsnd (Option.map f))) l); - val raw_bns_exp = map (apsnd (map (export_fun (Morphism.term morphism_2_1)))) raw_bns; - val bn_funs_decls = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) raw_bns_exp); - val raw_bn_funs = map (Morphism.term morphism_2_1) raw_bn_funs_loc - val raw_bn_eqs = ProofContext.export lthy2 lthy raw_bn_eqs_loc - - val dtinfo = Datatype.the_info (ProofContext.theory_of lthy2) (hd raw_dt_names); - val {descr, sorts, ...} = dtinfo; - fun nth_dtyp i = Datatype_Aux.typ_of_dtyp descr sorts (Datatype_Aux.DtRec i); - val raw_tys = map (fn (i, _) => nth_dtyp i) descr; - val all_typs = map (fn i => Datatype_Aux.typ_of_dtyp descr sorts (Datatype_Aux.DtRec i)) (map fst descr) - val all_full_tnames = map (fn (_, (n, _, _)) => n) descr; - val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy2)) all_full_tnames; - val rel_dtinfos = List.take (dtinfos, (length dts)); - val inject = flat (map #inject dtinfos); - val distincts = flat (map #distinct dtinfos); - val rel_distinct = map #distinct rel_dtinfos; - val induct = #induct dtinfo; - val exhausts = map #exhaust dtinfos; - val _ = tracing "Defining permutations, fv and alpha"; - val ((raw_perm_def, raw_perm_simps, perms), lthy3) = - Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy2; - val raw_binds_flat = map (map flat) raw_binds; - val ((((_, fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), lthy4) = - define_fv_alpha_export dtinfo raw_binds_flat bn_funs_decls lthy3; - val (fv, fvbn) = chop (length perms) fv_ts; - - val (alpha_ts_nobn, alpha_ts_bn) = chop (length fv) alpha_ts - val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo); - val bn_tys = map (domain_type o fastype_of) raw_bn_funs; - val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys; - val bns = raw_bn_funs ~~ bn_nos; - val rel_dists = flat (map (distinct_rel lthy4 alpha_cases) - (rel_distinct ~~ alpha_ts_nobn)); - val rel_dists_bn = flat (map (distinct_rel lthy4 alpha_cases) - ((map (fn i => nth rel_distinct i) bn_nos) ~~ alpha_ts_bn)) - val alpha_eq_iff = build_rel_inj alpha_intros (inject @ distincts) alpha_cases lthy4 - val _ = tracing "Proving equivariance"; - val (bv_eqvt, lthy5) = prove_eqvt raw_tys induct (raw_bn_eqs @ raw_perm_def) (map fst bns) lthy4 - val (fv_eqvt, lthy6) = prove_eqvt raw_tys induct (fv_def @ raw_perm_def) (fv @ fvbn) lthy5 - fun alpha_eqvt_tac' _ = - if !cheat_alpha_eqvt then Skip_Proof.cheat_tac thy - else alpha_eqvt_tac alpha_induct (raw_perm_def @ alpha_eq_iff) lthy6 1 - val alpha_eqvt = build_alpha_eqvts alpha_ts alpha_eqvt_tac' lthy6; - val _ = tracing "Proving equivalence"; - val fv_alpha_all = combine_fv_alpha_bns (fv, fvbn) (alpha_ts_nobn, alpha_ts_bn) bn_nos; - val reflps = build_alpha_refl fv_alpha_all alpha_ts induct alpha_eq_iff lthy6; - val alpha_equivp = - if !cheat_equivp then map (equivp_hack lthy6) alpha_ts_nobn - else build_equivps alpha_ts reflps alpha_induct - inject alpha_eq_iff distincts alpha_cases alpha_eqvt lthy6; - 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_typs alpha_ts_nobn alpha_equivp lthy6; - 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)) => - map (fn (cname, dts) => - Const (cname, map (Datatype_Aux.typ_of_dtyp descr sorts) dts ---> - 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 _ = tracing "Proving respects"; - val bns_rsp_pre' = build_fvbv_rsps alpha_ts 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; - val bns_rsp = flat (map snd bns_rsp_pre); - fun fv_rsp_tac _ = if !cheat_fv_rsp then Skip_Proof.cheat_tac thy - else fvbv_rsp_tac alpha_induct fv_def lthy8 1; - val fv_rsps = prove_fv_rsp fv_alpha_all alpha_ts 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) (fv @ fvbn) lthy9; - val fv_rsp = flat (map snd fv_rsp_pre); - val (perms_rsp, lthy11) = prove_const_rsp qtys Binding.empty perms - (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy10; - val alpha_bn_rsp_pre = prove_alpha_bn_rsp alpha_ts alpha_induct (alpha_eq_iff @ rel_dists @ rel_dists_bn) alpha_equivp exhausts alpha_ts_bn lthy11; - val (alpha_bn_rsps, lthy11a) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst] - (fn _ => asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1)) alpha_ts_bn lthy11 -(* val _ = map tracing (map PolyML.makestring alpha_bn_rsps);*) - fun const_rsp_tac _ = - if !cheat_const_rsp then Skip_Proof.cheat_tac thy - else let val alpha_alphabn = prove_alpha_alphabn alpha_ts alpha_induct alpha_eq_iff alpha_ts_bn 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) (fv @ fvbn) - val (qfv_ts, qfv_defs, lthy12a) = quotient_lift_consts_export qtys (qfv_names ~~ (fv @ fvbn)) lthy12; - val (qfv_ts_nobn, qfv_ts_bn) = chop (length perms) 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_ts_bn - val (qalpha_ts_bn, qalphabn_defs, lthy12c) = quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_ts_bn) lthy12b; - val _ = tracing "Lifting permutations"; - val thy = Local_Theory.exit_global lthy12c; - val perm_names = map (fn x => "permute_" ^ x) qty_names - val thy' = define_lifted_perms qtys qty_full_names (perm_names ~~ perms) raw_perm_simps thy; - val lthy13 = Theory_Target.init NONE thy'; - val q_name = space_implode "_" qty_names; - fun suffix_bind s = Binding.qualify true q_name (Binding.name s); - val _ = tracing "Lifting induction"; - val constr_names = map (Long_Name.base_name o fst o dest_Const) consts; - val q_induct = Rule_Cases.name constr_names (lift_thm qtys lthy13 induct); - fun note_suffix s th ctxt = - snd (Local_Theory.note ((suffix_bind s, []), th) ctxt); - fun note_simp_suffix s th ctxt = - snd (Local_Theory.note ((suffix_bind s, [Attrib.internal (K Simplifier.simp_add)]), th) ctxt); - val (_, lthy14) = Local_Theory.note ((suffix_bind "induct", - [Attrib.internal (K (Rule_Cases.case_names constr_names))]), [Rule_Cases.name constr_names q_induct]) lthy13; - val q_inducts = Project_Rule.projects lthy13 (1 upto (length fv)) q_induct - val (_, lthy14a) = Local_Theory.note ((suffix_bind "inducts", []), q_inducts) lthy14; - val q_perm = map (lift_thm qtys lthy14) raw_perm_def; - val lthy15 = note_simp_suffix "perm" q_perm lthy14a; - val q_fv = map (lift_thm qtys lthy15) fv_def; - val lthy16 = note_simp_suffix "fv" q_fv lthy15; - val q_bn = map (lift_thm qtys lthy16) raw_bn_eqs; - val lthy17 = note_simp_suffix "bn" q_bn lthy16; - val _ = tracing "Lifting eq-iff"; -(* val _ = map tracing (map PolyML.makestring alpha_eq_iff);*) - val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas3}) alpha_eq_iff - val eq_iff_unfolded1 = map (Local_Defs.unfold lthy17 @{thms alphas2}) eq_iff_unfolded0 - val eq_iff_unfolded2 = map (Local_Defs.unfold lthy17 @{thms alphas} ) eq_iff_unfolded1 - val q_eq_iff_pre0 = map (lift_thm qtys lthy17) eq_iff_unfolded2; - val q_eq_iff_pre1 = map (Local_Defs.fold lthy17 @{thms alphas3}) q_eq_iff_pre0 - val q_eq_iff_pre2 = map (Local_Defs.fold lthy17 @{thms alphas2}) q_eq_iff_pre1 - val q_eq_iff = map (Local_Defs.fold lthy17 @{thms alphas}) 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 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, - [Attrib.internal (fn _ => Nominal_ThmDecls.eqvt_add)]), q_eqvt) lthy19; - val _ = tracing "Finite Support"; - val supports = map (prove_supports lthy20 q_perm) consts; - val fin_supp = HOLogic.conj_elims (prove_fs lthy20 q_induct supports qtys); - val thy3 = Local_Theory.exit_global lthy20; - 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_nobn, qalpha_ts_bn) bn_nos; - val (names, supp_eq_t) = supp_eq fv_alpha_all; - val q_supp = HOLogic.conj_elims (Goal.prove lthy22 names [] supp_eq_t (fn _ => supp_eq_tac q_induct q_fv q_perm q_eq_iff lthy22 1)) handle _ => []; - val lthy23 = note_suffix "supp" q_supp lthy22; -in - ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy23) -end -*} - - -ML {* -(* parsing the datatypes and declaring *) -(* constructors in the local theory *) -fun prepare_dts dt_strs lthy = -let - val thy = ProofContext.theory_of lthy - - fun mk_type full_tname tvrs = - Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs) - - fun prep_cnstr lthy full_tname tvs (cname, anno_tys, mx, _) = - let - val tys = map (Syntax.read_typ lthy o snd) anno_tys - val ty = mk_type full_tname tvs - in - ((cname, tys ---> ty, mx), (cname, tys, mx)) - end - - fun prep_dt lthy (tvs, tname, mx, cnstrs) = - let - val full_tname = Sign.full_name thy tname - val (cnstrs', cnstrs'') = - split_list (map (prep_cnstr lthy full_tname tvs) cnstrs) - in - (cnstrs', (tvs, tname, mx, cnstrs'')) - end - - val (cnstrs, dts) = - split_list (map (prep_dt lthy) dt_strs) -in - lthy - |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs)) - |> pair dts -end -*} - -ML {* -(* parsing the binding function specification and *) -(* declaring the functions in the local theory *) -fun prepare_bn_funs bn_fun_strs bn_eq_strs lthy = -let - val ((bn_funs, bn_eqs), _) = - Specification.read_spec bn_fun_strs bn_eq_strs lthy - - fun prep_bn_fun ((bn, T), mx) = (bn, T, mx) - val bn_funs' = map prep_bn_fun bn_funs -in - lthy - |> Local_Theory.theory (Sign.add_consts_i bn_funs') - |> pair (bn_funs', bn_eqs) -end -*} - -ML {* -fun find_all eq xs (k',i) = - maps (fn (k, (v1, v2)) => if eq (k, k') then [(v1, v2, i)] else []) xs -*} - -ML {* -(* associates every SOME with the index in the list; drops NONEs *) -fun mk_env xs = - let - fun mapp (_: int) [] = [] - | mapp i (a :: xs) = - case a of - NONE => mapp (i + 1) xs - | SOME x => (x, i) :: mapp (i + 1) xs - in mapp 0 xs end -*} - -ML {* -fun env_lookup xs x = - case AList.lookup (op =) xs x of - SOME x => x - | NONE => error ("cannot find " ^ x ^ " in the binding specification."); -*} - -ML {* -val recursive = Unsynchronized.ref false -val alpha_type = Unsynchronized.ref AlphaGen -*} - -ML {* -fun prepare_binds dt_strs lthy = -let - fun extract_annos_binds dt_strs = - map (map (fn (_, antys, _, bns) => (map fst antys, bns))) dt_strs - - fun prep_bn env bn_str = - case (Syntax.read_term lthy bn_str) of - Free (x, _) => (NONE, env_lookup env x) - | Const (a, T) $ Free (x, _) => (SOME (Const (a, T), !recursive), env_lookup env x) - | _ => error (bn_str ^ " not allowed as binding specification."); - - fun prep_typ env (i, opt_name) = - case opt_name of - NONE => [] - | SOME x => find_all (op=) env (x,i); - - (* annos - list of annotation for each type (either NONE or SOME fo a type *) - - fun prep_binds (annos, bind_strs) = - let - val env = mk_env annos (* for every label the index *) - val binds = map (fn (x, y) => (x, prep_bn env y)) bind_strs - in - map_index (prep_typ binds) annos - end - - val result = map (map (map (map (fn (a, b, c) => - (a, b, c, if !alpha_type=AlphaLst andalso a = NONE then AlphaGen else !alpha_type))))) - (map (map prep_binds) (extract_annos_binds (get_cnstrs dt_strs))) - - val _ = warning (@{make_string} result) - -in - result -end -*} - -ML {* -fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy = -let - fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx) - - val lthy0 = - Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy - val (dts, lthy1) = - prepare_dts dt_strs lthy0 - val ((bn_funs, bn_eqs), lthy2) = - prepare_bn_funs bn_fun_strs bn_eq_strs lthy1 - val binds = prepare_binds dt_strs lthy2 -in - nominal_datatype2 dts bn_funs bn_eqs binds lthy |> snd -end -*} - - -(* Command Keyword *) - -ML {* -let - val kind = OuterKeyword.thy_decl -in - OuterSyntax.local_theory "nominal_datatype" "test" kind - (main_parser >> nominal_datatype2_cmd) -end -*} - - -end - - -