1 theory Parser

     2 imports "../Nominal-General/Nominal2_Atoms" 

     3         "../Nominal-General/Nominal2_Eqvt" 

     4         "../Nominal-General/Nominal2_Supp" 

     5         "Perm" "Equivp" "Rsp" "Lift"

     6 begin

     7 

     8 section{* Interface for nominal_datatype *}

     9 

    10 text {*

    11 

    12 Nominal-Datatype-part:

    13 

    14 

    15 1nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list

    16          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

    17                type(s) to be defined             constructors list

    18                (ty args, name, syn)              (name, typs, syn)

    19 

    20 Binder-Function-part:

    21 

    22 2rd Arg: (binding * typ option * mixfix) list 

    23          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^    

    24             binding function(s)           

    25               to be defined               

    26             (name, type, syn)             

    27 

    28 3th Arg:  term list 

    29           ^^^^^^^^^

    30           the equations of the binding functions

    31           (Trueprop equations)

    32 *}

    33 

    34 ML {*

    35 

    36 *}

    37 

    38 text {*****************************************************}

    39 ML {* 

    40 (* nominal datatype parser *)

    41 local

    42   structure P = OuterParse

    43 

    44   fun tuple ((x, y, z), u) = (x, y, z, u)

    45   fun tswap (((x, y), z), u) = (x, y, u, z)

    46 in

    47 

    48 val _ = OuterKeyword.keyword "bind"

    49 val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ

    50 

    51 (* binding specification *)

    52 (* maybe use and_list *)

    53 val bind_parser = 

    54   P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name) >> swap)

    55 

    56 val constr_parser =

    57   P.binding -- Scan.repeat anno_typ

    58 

    59 (* datatype parser *)

    60 val dt_parser =

    61   (P.type_args -- P.binding -- P.opt_mixfix >> P.triple1) -- 

    62     (P.$$$ "=" |-- P.enum1 "|" (constr_parser -- bind_parser -- P.opt_mixfix >> tswap)) >> tuple

    63 

    64 (* function equation parser *)

    65 val fun_parser = 

    66   Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[])

    67 

    68 (* main parser *)

    69 val main_parser =

    70   (P.and_list1 dt_parser) -- fun_parser >> P.triple2

    71 

    72 end

    73 *}

    74 

    75 (* adds "_raw" to the end of constants and types *)

    76 ML {*

    77 fun add_raw s = s ^ "_raw"

    78 fun add_raws ss = map add_raw ss

    79 fun raw_bind bn = Binding.suffix_name "_raw" bn

    80 

    81 fun replace_str ss s = 

    82   case (AList.lookup (op=) ss s) of 

    83      SOME s' => s'

    84    | NONE => s

    85 

    86 fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)

    87   | replace_typ ty_ss T = T  

    88 

    89 fun raw_dts ty_ss dts =

    90 let

    91 

    92   fun raw_dts_aux1 (bind, tys, mx) =

    93     (raw_bind bind, map (replace_typ ty_ss) tys, mx)

    94 

    95   fun raw_dts_aux2 (ty_args, bind, mx, constrs) =

    96     (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)

    97 in

    98   map raw_dts_aux2 dts

    99 end

   100 

   101 fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)

   102   | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)

   103   | replace_aterm trm_ss trm = trm

   104 

   105 fun replace_term trm_ss ty_ss trm =

   106   trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) 

   107 *}

   108 

   109 ML {*

   110 fun get_cnstrs dts =

   111   map (fn (_, _, _, constrs) => constrs) dts

   112 

   113 fun get_typed_cnstrs dts =

   114   flat (map (fn (_, bn, _, constrs) => 

   115    (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)

   116 

   117 fun get_cnstr_strs dts =

   118   map (fn (bn, _, _) => Binding.name_of bn) (flat (get_cnstrs dts))

   119 

   120 fun get_bn_fun_strs bn_funs =

   121   map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs

   122 *}

   123 

   124 ML {*

   125 fun rawify_dts dt_names dts dts_env =

   126 let

   127   val raw_dts = raw_dts dts_env dts

   128   val raw_dt_names = add_raws dt_names

   129 in

   130   (raw_dt_names, raw_dts)

   131 end 

   132 *}

   133 

   134 ML {*

   135 fun rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs =

   136 let

   137   val bn_funs' = map (fn (bn, ty, mx) => 

   138     (raw_bind bn, replace_typ dts_env ty, mx)) bn_funs

   139   

   140   val bn_eqs' = map (fn (attr, trm) => 

   141     (attr, replace_term (cnstrs_env @ bn_fun_env) dts_env trm)) bn_eqs

   142 in

   143   (bn_funs', bn_eqs') 

   144 end 

   145 *}

   146 

   147 ML {*

   148 fun apfst3 f (a, b, c) = (f a, b, c)

   149 *}

   150 

   151 ML {* 

   152 fun rawify_binds dts_env cnstrs_env bn_fun_env binds =

   153   map (map (map (map (fn (opt_trm, i, j, aty) => 

   154     (Option.map (apfst (replace_term (cnstrs_env @ bn_fun_env) dts_env)) opt_trm, i, j, aty))))) binds

   155 *}

   156 

   157 ML {*

   158 fun find [] _ = error ("cannot find element")

   159   | find ((x, z)::xs) y = if (Long_Name.base_name x) = y then z else find xs y

   160 *}

   161 

   162 ML {*

   163 fun strip_bn_fun t =

   164   case t of

   165     Const (@{const_name sup}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r

   166   | Const (@{const_name append}, _) $ l $ r => strip_bn_fun l @ strip_bn_fun r

   167   | Const (@{const_name insert}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>

   168       (i, NONE) :: strip_bn_fun y

   169   | Const (@{const_name Cons}, _) $ (Const (@{const_name atom}, _) $ Bound i) $ y =>

   170       (i, NONE) :: strip_bn_fun y

   171   | Const (@{const_name bot}, _) => []

   172   | Const (@{const_name Nil}, _) => []

   173   | (f as Free _) $ Bound i => [(i, SOME f)]

   174   | _ => error ("Unsupported binding function: " ^ (PolyML.makestring t))

   175 *}

   176 

   177 ML {*

   178 fun prep_bn dt_names dts eqs = 

   179 let

   180   fun aux eq = 

   181   let

   182     val (lhs, rhs) = eq

   183       |> strip_qnt_body "all" 

   184       |> HOLogic.dest_Trueprop

   185       |> HOLogic.dest_eq

   186     val (bn_fun, [cnstr]) = strip_comb lhs

   187     val (_, ty) = dest_Free bn_fun

   188     val (ty_name, _) = dest_Type (domain_type ty)

   189     val dt_index = find_index (fn x => x = ty_name) dt_names

   190     val (cnstr_head, cnstr_args) = strip_comb cnstr

   191     val rhs_elements = strip_bn_fun rhs

   192     val included = map (apfst (fn i => length (cnstr_args) - i - 1)) rhs_elements

   193   in

   194     (dt_index, (bn_fun, (cnstr_head, included)))

   195   end 

   196   fun order dts i ts = 

   197   let

   198     val dt = nth dts i

   199     val cts = map (fn (x, _, _) => Binding.name_of x) ((fn (_, _, _, x) => x) dt)

   200     val ts' = map (fn (x, y) => (fst (dest_Const x), y)) ts

   201   in

   202     map (find ts') cts

   203   end

   204 

   205   val unordered = AList.group (op=) (map aux eqs)

   206   val unordered' = map (fn (x, y) =>  (x, AList.group (op=) y)) unordered

   207   val ordered = map (fn (x, y) => (x, map (fn (v, z) => (v, order dts x z)) y)) unordered' 

   208 in

   209   ordered

   210 end

   211 *}

   212 

   213 ML {* 

   214 fun add_primrec_wrapper funs eqs lthy = 

   215   if null funs then (([], []), lthy)

   216   else 

   217    let 

   218      val eqs' = map (fn (_, eq) => (Attrib.empty_binding, eq)) eqs

   219      val funs' = map (fn (bn, ty, mx) => (bn, SOME ty, mx)) funs

   220    in 

   221      Primrec.add_primrec funs' eqs' lthy

   222    end

   223 *}

   224 

   225 ML {*

   226 fun add_datatype_wrapper dt_names dts =

   227 let

   228   val conf = Datatype.default_config

   229 in

   230   Local_Theory.theory_result (Datatype.add_datatype conf dt_names dts)

   231 end

   232 *}

   233 

   234 ML {* 

   235 fun raw_nominal_decls dts bn_funs bn_eqs binds lthy =

   236 let

   237   val thy = ProofContext.theory_of lthy

   238   val thy_name = Context.theory_name thy

   239 

   240   val dt_names = map (fn (_, s, _, _) => Binding.name_of s) dts

   241   val dt_full_names = map (Long_Name.qualify thy_name) dt_names 

   242   val dt_full_names' = add_raws dt_full_names

   243   val dts_env = dt_full_names ~~ dt_full_names'

   244 

   245   val cnstrs = get_cnstr_strs dts

   246   val cnstrs_ty = get_typed_cnstrs dts

   247   val cnstrs_full_names = map (Long_Name.qualify thy_name) cnstrs

   248   val cnstrs_full_names' = map (fn (x, y) => Long_Name.qualify thy_name 

   249     (Long_Name.qualify (add_raw x) (add_raw y))) cnstrs_ty

   250   val cnstrs_env = cnstrs_full_names ~~ cnstrs_full_names'

   251 

   252   val bn_fun_strs = get_bn_fun_strs bn_funs

   253   val bn_fun_strs' = add_raws bn_fun_strs

   254   val bn_fun_env = bn_fun_strs ~~ bn_fun_strs'

   255   val bn_fun_full_env = map (pairself (Long_Name.qualify thy_name)) 

   256     (bn_fun_strs ~~ bn_fun_strs')

   257   

   258   val (raw_dt_names, raw_dts) = rawify_dts dt_names dts dts_env

   259 

   260   val (raw_bn_funs, raw_bn_eqs) = rawify_bn_funs dts_env cnstrs_env bn_fun_env bn_funs bn_eqs 

   261   

   262   val raw_binds = rawify_binds dts_env cnstrs_env bn_fun_full_env binds 

   263 

   264   val raw_bns = prep_bn dt_full_names' raw_dts (map snd raw_bn_eqs)

   265 

   266 (*val _ = tracing (cat_lines (map PolyML.makestring raw_bns))*)

   267 in

   268   lthy 

   269   |> add_datatype_wrapper raw_dt_names raw_dts 

   270   ||>> add_primrec_wrapper raw_bn_funs raw_bn_eqs

   271   ||>> pair raw_binds

   272   ||>> pair raw_bns

   273 end

   274 *}

   275 

   276 lemma equivp_hack: "equivp x"

   277 sorry

   278 ML {*

   279 fun equivp_hack ctxt rel =

   280 let

   281   val thy = ProofContext.theory_of ctxt

   282   val ty = domain_type (fastype_of rel)

   283   val cty = ctyp_of thy ty

   284   val ct = cterm_of thy rel

   285 in

   286   Drule.instantiate' [SOME cty] [SOME ct] @{thm equivp_hack}

   287 end

   288 *}

   289 

   290 ML {* val cheat_alpha_eqvt = Unsynchronized.ref false *}

   291 ML {* val cheat_equivp = Unsynchronized.ref false *}

   292 ML {* val cheat_fv_rsp = Unsynchronized.ref false *}

   293 ML {* val cheat_const_rsp = Unsynchronized.ref false *}

   294 

   295 (* nominal_datatype2 does the following things in order:

   296 

   297 Parser.thy/raw_nominal_decls

   298   1) define the raw datatype

   299   2) define the raw binding functions 

   300 

   301 Perm.thy/define_raw_perms

   302   3) define permutations of the raw datatype and show that the raw type is 

   303      in the pt typeclass

   304       

   305 Lift.thy/define_fv_alpha_export, Fv.thy/define_fv & define_alpha

   306   4) define fv and fv_bn

   307   5) define alpha and alpha_bn

   308 

   309 Perm.thy/distinct_rel

   310   6) prove alpha_distincts (C1 x \<notsimeq> C2 y ...)             (Proof by cases; simp)

   311 

   312 Tacs.thy/build_rel_inj

   313   6) prove alpha_eq_iff    (C1 x = C2 y \<leftrightarrow> P x y ...)

   314      (left-to-right by intro rule, right-to-left by cases; simp)

   315 Equivp.thy/prove_eqvt

   316   7) prove bn_eqvt (common induction on the raw datatype)

   317   8) prove fv_eqvt (common induction on the raw datatype with help of above)

   318 Rsp.thy/build_alpha_eqvts

   319   9) prove alpha_eqvt and alpha_bn_eqvt

   320      (common alpha-induction, unfolding alpha_gen, permute of #* and =)

   321 Equivp.thy/build_alpha_refl & Equivp.thy/build_equivps

   322  10) prove that alpha and alpha_bn are equivalence relations

   323      (common induction and application of 'compose' lemmas)

   324 Lift.thy/define_quotient_types

   325  11) define quotient types

   326 Rsp.thy/build_fvbv_rsps

   327  12) prove bn respects     (common induction and simp with alpha_gen)

   328 Rsp.thy/prove_const_rsp

   329  13) prove fv respects     (common induction and simp with alpha_gen)

   330  14) prove permute respects    (unfolds to alpha_eqvt)

   331 Rsp.thy/prove_alpha_bn_rsp

   332  15) prove alpha_bn respects

   333      (alpha_induct then cases then sym and trans of the relations)

   334 Rsp.thy/prove_alpha_alphabn

   335  16) show that alpha implies alpha_bn (by unduction, needed in following step)

   336 Rsp.thy/prove_const_rsp

   337  17) prove respects for all datatype constructors

   338      (unfold eq_iff and alpha_gen; introduce zero permutations; simp)

   339 Perm.thy/quotient_lift_consts_export

   340  18) define lifted constructors, fv, bn, alpha_bn, permutations

   341 Perm.thy/define_lifted_perms

   342  19) lift permutation zero and add properties to show that quotient type is in the pt typeclass

   343 Lift.thy/lift_thm

   344  20) lift permutation simplifications

   345  21) lift induction

   346  22) lift fv

   347  23) lift bn

   348  24) lift eq_iff

   349  25) lift alpha_distincts

   350  26) lift fv and bn eqvts

   351 Equivp.thy/prove_supports

   352  27) prove that union of arguments supports constructors

   353 Equivp.thy/prove_fs

   354  28) show that the lifted type is in fs typeclass     (* by q_induct, supports *)

   355 Equivp.thy/supp_eq

   356  29) prove supp = fv

   357 *)

   358 ML {*

   359 fun nominal_datatype2 dts bn_funs bn_eqs binds lthy =

   360 let

   361   val _ = tracing "Raw declarations";

   362   val thy = ProofContext.theory_of lthy

   363   val thy_name = Context.theory_name thy

   364   val ((((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), raw_bns), lthy2) =

   365     raw_nominal_decls dts bn_funs bn_eqs binds lthy

   366   val morphism_2_1 = ProofContext.export_morphism lthy2 lthy

   367   fun export_fun f (t, l) = (f t, map (map (apsnd (Option.map f))) l);

   368   val raw_bns_exp = map (apsnd (map (export_fun (Morphism.term morphism_2_1)))) raw_bns;

   369   val bn_funs_decls = flat (map (fn (ith, l) => map (fn (bn, data) => (bn, ith, data)) l) raw_bns_exp);

   370   val raw_bn_funs = map (Morphism.term morphism_2_1) raw_bn_funs_loc

   371   val raw_bn_eqs = ProofContext.export lthy2 lthy raw_bn_eqs_loc

   372 

   373   val dtinfo = Datatype.the_info (ProofContext.theory_of lthy2) (hd raw_dt_names);

   374   val {descr, sorts, ...} = dtinfo;

   375   fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);

   376   val raw_tys = map (fn (i, _) => nth_dtyp i) descr;

   377   val all_typs = map (fn i => typ_of_dtyp descr sorts (DtRec i)) (map fst descr)

   378   val all_full_tnames = map (fn (_, (n, _, _)) => n) descr;

   379   val dtinfos = map (Datatype.the_info (ProofContext.theory_of lthy2)) all_full_tnames;

   380   val rel_dtinfos = List.take (dtinfos, (length dts));

   381   val inject = flat (map #inject dtinfos);

   382   val distincts = flat (map #distinct dtinfos);

   383   val rel_distinct = map #distinct rel_dtinfos;

   384   val induct = #induct dtinfo;

   385   val exhausts = map #exhaust dtinfos;

   386   val _ = tracing "Defining permutations, fv and alpha";

   387   val ((raw_perm_def, raw_perm_simps, perms), lthy3) =

   388     Local_Theory.theory_result (define_raw_perms dtinfo (length dts)) lthy2;

   389   val raw_binds_flat = map (map flat) raw_binds;

   390   val ((((_, fv_ts), fv_def), ((alpha_ts, alpha_intros), (alpha_cases, alpha_induct))), lthy4) =

   391     define_fv_alpha_export dtinfo raw_binds_flat bn_funs_decls lthy3;

   392   val (fv, fvbn) = chop (length perms) fv_ts;

   393 

   394   val (alpha_ts_nobn, alpha_ts_bn) = chop (length fv) alpha_ts

   395   val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo);

   396   val bn_tys = map (domain_type o fastype_of) raw_bn_funs;

   397   val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys;

   398   val bns = raw_bn_funs ~~ bn_nos;

   399   val rel_dists = flat (map (distinct_rel lthy4 alpha_cases)

   400     (rel_distinct ~~ alpha_ts_nobn));

   401   val rel_dists_bn = flat (map (distinct_rel lthy4 alpha_cases)

   402     ((map (fn i => nth rel_distinct i) bn_nos) ~~ alpha_ts_bn))

   403   val alpha_eq_iff = build_rel_inj alpha_intros (inject @ distincts) alpha_cases lthy4

   404   val _ = tracing "Proving equivariance";

   405   val (bv_eqvt, lthy5) = prove_eqvt raw_tys induct (raw_bn_eqs @ raw_perm_def) (map fst bns) lthy4

   406   val (fv_eqvt, lthy6) = prove_eqvt raw_tys induct (fv_def @ raw_perm_def) (fv @ fvbn) lthy5

   407   fun alpha_eqvt_tac' _ =

   408     if !cheat_alpha_eqvt then Skip_Proof.cheat_tac thy

   409     else alpha_eqvt_tac alpha_induct (raw_perm_def @ alpha_eq_iff) lthy6 1

   410   val alpha_eqvt = build_alpha_eqvts alpha_ts alpha_eqvt_tac' lthy6;

   411   val _ = tracing "Proving equivalence";

   412   val fv_alpha_all = combine_fv_alpha_bns (fv, fvbn) (alpha_ts_nobn, alpha_ts_bn) bn_nos;

   413   val reflps = build_alpha_refl fv_alpha_all alpha_ts induct alpha_eq_iff lthy6;

   414   val alpha_equivp =

   415     if !cheat_equivp then map (equivp_hack lthy6) alpha_ts_nobn

   416     else build_equivps alpha_ts reflps alpha_induct

   417       inject alpha_eq_iff distincts alpha_cases alpha_eqvt lthy6;

   418   val qty_binds = map (fn (_, b, _, _) => b) dts;

   419   val qty_names = map Name.of_binding qty_binds;

   420   val qty_full_names = map (Long_Name.qualify thy_name) qty_names

   421   val (qtys, lthy7) = define_quotient_types qty_binds all_typs alpha_ts_nobn alpha_equivp lthy6;

   422   val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts));

   423   val raw_consts =

   424     flat (map (fn (i, (_, _, l)) =>

   425       map (fn (cname, dts) =>

   426         Const (cname, map (typ_of_dtyp descr sorts) dts --->

   427           typ_of_dtyp descr sorts (DtRec i))) l) descr);

   428   val (consts, const_defs, lthy8) = quotient_lift_consts_export qtys (const_names ~~ raw_consts) lthy7;

   429   val _ = tracing "Proving respects";

   430   val bns_rsp_pre' = build_fvbv_rsps alpha_ts alpha_induct raw_bn_eqs (map fst bns) lthy8;

   431   val (bns_rsp_pre, lthy9) = fold_map (

   432     fn (bn_t, _) => prove_const_rsp qtys Binding.empty [bn_t] (fn _ =>

   433        resolve_tac bns_rsp_pre' 1)) bns lthy8;

   434   val bns_rsp = flat (map snd bns_rsp_pre);

   435   fun fv_rsp_tac _ = if !cheat_fv_rsp then Skip_Proof.cheat_tac thy

   436     else fvbv_rsp_tac alpha_induct fv_def lthy8 1;

   437   val fv_rsps = prove_fv_rsp fv_alpha_all alpha_ts fv_rsp_tac lthy9;

   438   val (fv_rsp_pre, lthy10) = fold_map

   439     (fn fv => fn ctxt => prove_const_rsp qtys Binding.empty [fv]

   440     (fn _ => asm_simp_tac (HOL_ss addsimps fv_rsps) 1) ctxt) (fv @ fvbn) lthy9;

   441   val fv_rsp = flat (map snd fv_rsp_pre);

   442   val (perms_rsp, lthy11) = prove_const_rsp qtys Binding.empty perms

   443     (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy10;

   444   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;

   445   val (alpha_bn_rsps, lthy11a) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]

   446         (fn _ => asm_simp_tac (HOL_ss addsimps alpha_bn_rsp_pre) 1)) alpha_ts_bn lthy11

   447 (*  val _ = map tracing (map PolyML.makestring alpha_bn_rsps);*)

   448   fun const_rsp_tac _ =

   449     if !cheat_const_rsp then Skip_Proof.cheat_tac thy

   450     else let val alpha_alphabn = prove_alpha_alphabn alpha_ts alpha_induct alpha_eq_iff alpha_ts_bn lthy11a

   451       in constr_rsp_tac alpha_eq_iff (fv_rsp @ bns_rsp @ reflps @ alpha_alphabn) 1 end

   452   val (const_rsps, lthy12) = fold_map (fn cnst => prove_const_rsp qtys Binding.empty [cnst]

   453     const_rsp_tac) raw_consts lthy11a

   454   val qfv_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) (fv @ fvbn)

   455   val (qfv_ts, qfv_defs, lthy12a) = quotient_lift_consts_export qtys (qfv_names ~~ (fv @ fvbn)) lthy12;

   456   val (qfv_ts_nobn, qfv_ts_bn) = chop (length perms) qfv_ts;

   457   val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs

   458   val (qbn_ts, qbn_defs, lthy12b) = quotient_lift_consts_export qtys (qbn_names ~~ raw_bn_funs) lthy12a;

   459   val qalpha_bn_names = map (unsuffix "_raw" o Long_Name.base_name o fst o dest_Const) alpha_ts_bn

   460   val (qalpha_ts_bn, qalphabn_defs, lthy12c) = quotient_lift_consts_export qtys (qalpha_bn_names ~~ alpha_ts_bn) lthy12b;

   461   val _ = tracing "Lifting permutations";

   462   val thy = Local_Theory.exit_global lthy12c;

   463   val perm_names = map (fn x => "permute_" ^ x) qty_names

   464   val thy' = define_lifted_perms qtys qty_full_names (perm_names ~~ perms) raw_perm_simps thy;

   465   val lthy13 = Theory_Target.init NONE thy';

   466   val q_name = space_implode "_" qty_names;

   467   fun suffix_bind s = Binding.qualify true q_name (Binding.name s);

   468   val _ = tracing "Lifting induction";

   469   val constr_names = map (Long_Name.base_name o fst o dest_Const) consts;

   470   val q_induct = Rule_Cases.name constr_names (lift_thm qtys lthy13 induct);

   471   fun note_suffix s th ctxt =

   472     snd (Local_Theory.note ((suffix_bind s, []), th) ctxt);

   473   fun note_simp_suffix s th ctxt =

   474     snd (Local_Theory.note ((suffix_bind s, [Attrib.internal (K Simplifier.simp_add)]), th) ctxt);

   475   val (_, lthy14) = Local_Theory.note ((suffix_bind "induct",

   476     [Attrib.internal (K (Rule_Cases.case_names constr_names))]), [Rule_Cases.name constr_names q_induct]) lthy13;

   477   val q_inducts = Project_Rule.projects lthy13 (1 upto (length fv)) q_induct

   478   val (_, lthy14a) = Local_Theory.note ((suffix_bind "inducts", []), q_inducts) lthy14;

   479   val q_perm = map (lift_thm qtys lthy14) raw_perm_def;

   480   val lthy15 = note_simp_suffix "perm" q_perm lthy14a;

   481   val q_fv = map (lift_thm qtys lthy15) fv_def;

   482   val lthy16 = note_simp_suffix "fv" q_fv lthy15;

   483   val q_bn = map (lift_thm qtys lthy16) raw_bn_eqs;

   484   val lthy17 = note_simp_suffix "bn" q_bn lthy16;

   485   val _ = tracing "Lifting eq-iff";

   486   val _ = map tracing (map PolyML.makestring alpha_eq_iff);

   487   val eq_iff_unfolded0 = map (Local_Defs.unfold lthy17 @{thms alphas3}) alpha_eq_iff

   488   val eq_iff_unfolded1 = map (Local_Defs.unfold lthy17 @{thms alphas2}) eq_iff_unfolded0

   489   val eq_iff_unfolded2 = map (Local_Defs.unfold lthy17 @{thms alphas} ) eq_iff_unfolded1

   490   val q_eq_iff_pre0 = map (lift_thm qtys lthy17) eq_iff_unfolded2;

   491   val q_eq_iff_pre1 = map (Local_Defs.fold lthy17 @{thms alphas3}) q_eq_iff_pre0

   492   val q_eq_iff_pre2 = map (Local_Defs.fold lthy17 @{thms alphas2}) q_eq_iff_pre1

   493   val q_eq_iff = map (Local_Defs.fold lthy17 @{thms alphas}) q_eq_iff_pre2

   494   val (_, lthy18) = Local_Theory.note ((suffix_bind "eq_iff", []), q_eq_iff) lthy17;

   495   val q_dis = map (lift_thm qtys lthy18) rel_dists;

   496   val lthy19 = note_simp_suffix "distinct" q_dis lthy18;

   497   val q_eqvt = map (lift_thm qtys lthy19) (bv_eqvt @ fv_eqvt);

   498   val (_, lthy20) = Local_Theory.note ((Binding.empty,

   499     [Attrib.internal (fn _ => Nominal_ThmDecls.eqvt_add)]), q_eqvt) lthy19;

   500   val _ = tracing "Finite Support";

   501   val supports = map (prove_supports lthy20 q_perm) consts;

   502   val fin_supp = HOLogic.conj_elims (prove_fs lthy20 q_induct supports qtys);

   503   val thy3 = Local_Theory.exit_global lthy20;

   504   val lthy21 = Theory_Target.instantiation (qty_full_names, [], @{sort fs}) thy3;

   505   fun tac _ = Class.intro_classes_tac [] THEN (ALLGOALS (resolve_tac fin_supp))

   506   val lthy22 = Class.prove_instantiation_instance tac lthy21

   507   val fv_alpha_all = combine_fv_alpha_bns (qfv_ts_nobn, qfv_ts_bn) (alpha_ts_nobn, qalpha_ts_bn) bn_nos;

   508   val (names, supp_eq_t) = supp_eq fv_alpha_all;

   509   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 _ => [];

   510   val lthy23 = note_suffix "supp" q_supp lthy22;

   511 in

   512   ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy23)

   513 end

   514 *}

   515 

   516 

   517 ML {* 

   518 (* parsing the datatypes and declaring *)

   519 (* constructors in the local theory    *)

   520 fun prepare_dts dt_strs lthy = 

   521 let

   522   val thy = ProofContext.theory_of lthy

   523   

   524   fun mk_type full_tname tvrs =

   525     Type (full_tname, map (fn a => TVar ((a, 0), [])) tvrs)

   526 

   527   fun prep_cnstr lthy full_tname tvs (cname, anno_tys, mx, _) =

   528   let

   529     val tys = map (Syntax.read_typ lthy o snd) anno_tys

   530     val ty = mk_type full_tname tvs

   531   in

   532     ((cname, tys ---> ty, mx), (cname, tys, mx))

   533   end

   534   

   535   fun prep_dt lthy (tvs, tname, mx, cnstrs) = 

   536   let

   537     val full_tname = Sign.full_name thy tname

   538     val (cnstrs', cnstrs'') = 

   539       split_list (map (prep_cnstr lthy full_tname tvs) cnstrs)

   540   in

   541     (cnstrs', (tvs, tname, mx, cnstrs''))

   542   end 

   543 

   544   val (cnstrs, dts) = 

   545     split_list (map (prep_dt lthy) dt_strs)

   546 in

   547   lthy

   548   |> Local_Theory.theory (Sign.add_consts_i (flat cnstrs))

   549   |> pair dts

   550 end

   551 *}

   552 

   553 ML {*

   554 (* parsing the binding function specification and *)

   555 (* declaring the functions in the local theory    *)

   556 fun prepare_bn_funs bn_fun_strs bn_eq_strs lthy =

   557 let

   558   val ((bn_funs, bn_eqs), _) = 

   559     Specification.read_spec bn_fun_strs bn_eq_strs lthy

   560 

   561   fun prep_bn_fun ((bn, T), mx) = (bn, T, mx) 

   562   val bn_funs' = map prep_bn_fun bn_funs

   563 in

   564   lthy

   565   |> Local_Theory.theory (Sign.add_consts_i bn_funs')

   566   |> pair (bn_funs', bn_eqs) 

   567 end 

   568 *}

   569 

   570 ML {*

   571 fun find_all eq xs (k',i) = 

   572   maps (fn (k, (v1, v2)) => if eq (k, k') then [(v1, v2, i)] else []) xs

   573 *}

   574 

   575 ML {*

   576 (* associates every SOME with the index in the list; drops NONEs *)

   577 fun mk_env xs =

   578   let

   579     fun mapp (_: int) [] = []

   580       | mapp i (a :: xs) = 

   581          case a of

   582            NONE => mapp (i + 1) xs

   583          | SOME x => (x, i) :: mapp (i + 1) xs

   584   in mapp 0 xs end

   585 *}

   586 

   587 ML {*

   588 fun env_lookup xs x =

   589   case AList.lookup (op =) xs x of

   590     SOME x => x

   591   | NONE => error ("cannot find " ^ x ^ " in the binding specification.");

   592 *}

   593 

   594 ML {*

   595 val recursive = Unsynchronized.ref false

   596 val alpha_type = Unsynchronized.ref AlphaGen

   597 *}

   598 

   599 ML {*

   600 fun prepare_binds dt_strs lthy = 

   601 let

   602   fun extract_annos_binds dt_strs =

   603     map (map (fn (_, antys, _, bns) => (map fst antys, bns))) dt_strs

   604 

   605   fun prep_bn env bn_str =

   606     case (Syntax.read_term lthy bn_str) of

   607        Free (x, _) => (NONE, env_lookup env x)

   608      | Const (a, T) $ Free (x, _) => (SOME (Const (a, T), !recursive), env_lookup env x)

   609      | _ => error (bn_str ^ " not allowed as binding specification.");  

   610  

   611   fun prep_typ env (i, opt_name) = 

   612     case opt_name of

   613       NONE => []

   614     | SOME x => find_all (op=) env (x,i);

   615         

   616   (* annos - list of annotation for each type (either NONE or SOME fo a type *)

   617   

   618   fun prep_binds (annos, bind_strs) = 

   619   let

   620     val env = mk_env annos (* for every label the index *)

   621     val binds = map (fn (x, y) => (x, prep_bn env y)) bind_strs  

   622   in

   623     map_index (prep_typ binds) annos

   624   end

   625 

   626   val result = map (map (map (map (fn (a, b, c) => 

   627     (a, b, c, if !alpha_type=AlphaLst andalso a = NONE then AlphaGen else !alpha_type)))))

   628       (map (map prep_binds) (extract_annos_binds (get_cnstrs dt_strs)))

   629  

   630   val _ = warning (@{make_string} result)

   631 

   632 in

   633   result

   634 end

   635 *}

   636 

   637 ML {*

   638 fun nominal_datatype2_cmd (dt_strs, bn_fun_strs, bn_eq_strs) lthy =

   639 let

   640   fun prep_typ (tvs, tname, mx, _) = (tname, length tvs, mx)

   641 

   642   val lthy0 = 

   643     Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) lthy

   644   val (dts, lthy1) = 

   645     prepare_dts dt_strs lthy0

   646   val ((bn_funs, bn_eqs), lthy2) = 

   647     prepare_bn_funs bn_fun_strs bn_eq_strs lthy1

   648   val binds = prepare_binds dt_strs lthy2

   649 in

   650   nominal_datatype2 dts bn_funs bn_eqs binds lthy |> snd

   651 end

   652 *}

   653 

   654 

   655 (* Command Keyword *)

   656 

   657 ML {*

   658 let

   659    val kind = OuterKeyword.thy_decl

   660 in

   661    OuterSyntax.local_theory "nominal_datatype" "test" kind 

   662      (main_parser >> nominal_datatype2_cmd)

   663 end

   664 *}

   665 

   666 

   667 end

   668 

   669 

   670