src/Pure/Isar/class.ML
author haftmann
Wed Jul 30 07:33:58 2008 +0200 (2008-07-30)
changeset 27708 7471449b9695
parent 27690 24738db98d34
child 27761 b95e9ba0ca1d
permissions -rw-r--r--
improved morphism
     1 (*  Title:      Pure/Isar/class.ML
     2     ID:         $Id$
     3     Author:     Florian Haftmann, TU Muenchen
     4 
     5 Type classes derived from primitive axclasses and locales.
     6 *)
     7 
     8 signature CLASS =
     9 sig
    10   (*classes*)
    11   val class: bstring -> class list -> Element.context_i list
    12     -> theory -> string * Proof.context
    13   val class_cmd: bstring -> xstring list -> Element.context list
    14     -> theory -> string * Proof.context
    15 
    16   val init: class -> theory -> Proof.context
    17   val declare: class -> Markup.property list
    18     -> (string * mixfix) * term -> theory -> theory
    19   val abbrev: class -> Syntax.mode -> Markup.property list
    20     -> (string * mixfix) * term -> theory -> theory
    21   val note: class -> string
    22     -> ((string * Attrib.src list) * (thm list * Attrib.src list) list) list
    23     -> theory -> (bstring * thm list) list * theory
    24   val declaration: class -> declaration -> theory -> theory
    25   val refresh_syntax: class -> Proof.context -> Proof.context
    26 
    27   val intro_classes_tac: thm list -> tactic
    28   val default_intro_tac: Proof.context -> thm list -> tactic
    29   val prove_subclass: class * class -> thm option -> theory -> theory
    30 
    31   val class_prefix: string -> string
    32   val is_class: theory -> class -> bool
    33   val these_params: theory -> sort -> (string * (class * (string * typ))) list
    34   val print_classes: theory -> unit
    35 
    36   (*instances*)
    37   val init_instantiation: string list * (string * sort) list * sort
    38     -> theory -> local_theory
    39   val instantiation_instance: (local_theory -> local_theory)
    40     -> local_theory -> Proof.state
    41   val prove_instantiation_instance: (Proof.context -> tactic)
    42     -> local_theory -> local_theory
    43   val conclude_instantiation: local_theory -> local_theory
    44   val instantiation_param: local_theory -> string -> string option
    45   val confirm_declaration: string -> local_theory -> local_theory
    46   val pretty_instantiation: local_theory -> Pretty.T
    47   val type_name: string -> string
    48 
    49   (*old axclass layer*)
    50   val axclass_cmd: bstring * xstring list
    51     -> ((bstring * Attrib.src list) * string list) list
    52     -> theory -> class * theory
    53   val classrel_cmd: xstring * xstring -> theory -> Proof.state
    54 
    55   (*old instance layer*)
    56   val instance_arity: (theory -> theory) -> arity -> theory -> Proof.state
    57   val instance_arity_cmd: bstring * xstring list * xstring -> theory -> Proof.state
    58 end;
    59 
    60 structure Class : CLASS =
    61 struct
    62 
    63 (** auxiliary **)
    64 
    65 fun prove_interpretation tac prfx_atts expr inst =
    66   Locale.interpretation_i I prfx_atts expr inst
    67   #> Proof.global_terminal_proof
    68       (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
    69   #> ProofContext.theory_of;
    70 
    71 fun prove_interpretation_in tac after_qed (name, expr) =
    72   Locale.interpretation_in_locale
    73       (ProofContext.theory after_qed) (name, expr)
    74   #> Proof.global_terminal_proof
    75       (Method.Basic (K (Method.SIMPLE_METHOD tac), Position.none), NONE)
    76   #> ProofContext.theory_of;
    77 
    78 
    79 (** primitive axclass and instance commands **)
    80 
    81 fun axclass_cmd (class, raw_superclasses) raw_specs thy =
    82   let
    83     val ctxt = ProofContext.init thy;
    84     val superclasses = map (Sign.read_class thy) raw_superclasses;
    85     val name_atts = map ((apsnd o map) (Attrib.attribute thy) o fst)
    86       raw_specs;
    87     val axiomss = ProofContext.read_propp (ctxt, map (map (rpair []) o snd)
    88           raw_specs)
    89       |> snd
    90       |> (map o map) fst;
    91   in
    92     AxClass.define_class (class, superclasses) []
    93       (name_atts ~~ axiomss) thy
    94   end;
    95 
    96 local
    97 
    98 fun gen_instance mk_prop add_thm after_qed insts thy =
    99   let
   100     fun after_qed' results =
   101       ProofContext.theory ((fold o fold) add_thm results #> after_qed);
   102   in
   103     thy
   104     |> ProofContext.init
   105     |> Proof.theorem_i NONE after_qed' ((map (fn t => [(t, [])])
   106         o mk_prop thy) insts)
   107   end;
   108 
   109 in
   110 
   111 val instance_arity =
   112   gen_instance (Logic.mk_arities oo Sign.cert_arity) AxClass.add_arity;
   113 val instance_arity_cmd =
   114   gen_instance (Logic.mk_arities oo Sign.read_arity) AxClass.add_arity I;
   115 val classrel =
   116   gen_instance (single oo (Logic.mk_classrel oo AxClass.cert_classrel)) AxClass.add_classrel I;
   117 val classrel_cmd =
   118   gen_instance (single oo (Logic.mk_classrel oo AxClass.read_classrel)) AxClass.add_classrel I;
   119 
   120 end; (*local*)
   121 
   122 
   123 (** class data **)
   124 
   125 datatype class_data = ClassData of {
   126   consts: (string * string) list
   127     (*locale parameter ~> constant name*),
   128   base_sort: sort,
   129   inst: term option list
   130     (*canonical interpretation*),
   131   morphism: theory -> thm list -> morphism,
   132     (*partial morphism of canonical interpretation*)
   133   assm_intro: thm option,
   134   of_class: thm,
   135   axiom: thm option,
   136   defs: thm list,
   137   operations: (string * (class * (typ * term))) list
   138 };
   139 
   140 fun rep_class_data (ClassData d) = d;
   141 fun mk_class_data ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
   142     (defs, operations)) =
   143   ClassData { consts = consts, base_sort = base_sort, inst = inst,
   144     morphism = morphism, assm_intro = assm_intro, of_class = of_class, axiom = axiom,
   145     defs = defs, operations = operations };
   146 fun map_class_data f (ClassData { consts, base_sort, inst, morphism,
   147     assm_intro, of_class, axiom, defs, operations }) =
   148   mk_class_data (f ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
   149     (defs, operations)));
   150 fun merge_class_data _ (ClassData { consts = consts,
   151     base_sort = base_sort, inst = inst, morphism = morphism, assm_intro = assm_intro,
   152     of_class = of_class, axiom = axiom, defs = defs1, operations = operations1 },
   153   ClassData { consts = _, base_sort = _, inst = _, morphism = _, assm_intro = _,
   154     of_class = _, axiom = _, defs = defs2, operations = operations2 }) =
   155   mk_class_data ((consts, base_sort, inst, morphism, assm_intro, of_class, axiom),
   156     (Thm.merge_thms (defs1, defs2),
   157       AList.merge (op =) (K true) (operations1, operations2)));
   158 
   159 structure ClassData = TheoryDataFun
   160 (
   161   type T = class_data Graph.T
   162   val empty = Graph.empty;
   163   val copy = I;
   164   val extend = I;
   165   fun merge _ = Graph.join merge_class_data;
   166 );
   167 
   168 
   169 (* queries *)
   170 
   171 val lookup_class_data = Option.map rep_class_data oo try o Graph.get_node o ClassData.get;
   172 
   173 fun the_class_data thy class = case lookup_class_data thy class
   174  of NONE => error ("Undeclared class " ^ quote class)
   175   | SOME data => data;
   176 
   177 val is_class = is_some oo lookup_class_data;
   178 
   179 val ancestry = Graph.all_succs o ClassData.get;
   180 
   181 fun these_params thy =
   182   let
   183     fun params class =
   184       let
   185         val const_typs = (#params o AxClass.get_info thy) class;
   186         val const_names = (#consts o the_class_data thy) class;
   187       in
   188         (map o apsnd)
   189           (fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names
   190       end;
   191   in maps params o ancestry thy end;
   192 
   193 fun these_defs thy = maps (these o Option.map #defs o lookup_class_data thy) o ancestry thy;
   194 
   195 fun morphism thy class = #morphism (the_class_data thy class) thy (these_defs thy [class]);
   196 
   197 fun these_assm_intros thy =
   198   Graph.fold (fn (_, (data, _)) => fold (insert Thm.eq_thm)
   199     ((the_list o #assm_intro o rep_class_data) data)) (ClassData.get thy) [];
   200 
   201 fun these_operations thy =
   202   maps (#operations o the_class_data thy) o ancestry thy;
   203 
   204 fun print_classes thy =
   205   let
   206     val ctxt = ProofContext.init thy;
   207     val algebra = Sign.classes_of thy;
   208     val arities =
   209       Symtab.empty
   210       |> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) =>
   211            Symtab.map_default (class, []) (insert (op =) tyco)) arities)
   212              ((#arities o Sorts.rep_algebra) algebra);
   213     val the_arities = these o Symtab.lookup arities;
   214     fun mk_arity class tyco =
   215       let
   216         val Ss = Sorts.mg_domain algebra tyco [class];
   217       in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end;
   218     fun mk_param (c, ty) = Pretty.str (Sign.extern_const thy c ^ " :: "
   219       ^ setmp show_sorts false (Syntax.string_of_typ ctxt o Type.strip_sorts) ty);
   220     fun mk_entry class = (Pretty.block o Pretty.fbreaks o map_filter I) [
   221       (SOME o Pretty.str) ("class " ^ Sign.extern_class thy class ^ ":"),
   222       (SOME o Pretty.block) [Pretty.str "supersort: ",
   223         (Syntax.pretty_sort ctxt o Sign.minimize_sort thy o Sign.super_classes thy) class],
   224       if is_class thy class then (SOME o Pretty.str)
   225         ("locale: " ^ Locale.extern thy class) else NONE,
   226       ((fn [] => NONE | ps => (SOME o Pretty.block o Pretty.fbreaks)
   227           (Pretty.str "parameters:" :: ps)) o map mk_param
   228         o these o Option.map #params o try (AxClass.get_info thy)) class,
   229       (SOME o Pretty.block o Pretty.breaks) [
   230         Pretty.str "instances:",
   231         Pretty.list "" "" (map (mk_arity class) (the_arities class))
   232       ]
   233     ]
   234   in
   235     (Pretty.writeln o Pretty.chunks o separate (Pretty.str "")
   236       o map mk_entry o Sorts.all_classes) algebra
   237   end;
   238 
   239 
   240 (* updaters *)
   241 
   242 fun add_class_data ((class, superclasses),
   243     (params, base_sort, inst, phi, axiom, assm_intro, of_class)) thy =
   244   let
   245     val operations = map (fn (v_ty as (_, ty), (c, _)) =>
   246       (c, (class, (ty, Free v_ty)))) params;
   247     val add_class = Graph.new_node (class,
   248         mk_class_data (((map o pairself) fst params, base_sort,
   249           map (SOME o Const) inst, phi, assm_intro, of_class, axiom), ([], operations)))
   250       #> fold (curry Graph.add_edge class) superclasses;
   251   in ClassData.map add_class thy end;
   252 
   253 fun register_operation class (c, (t, some_def)) thy =
   254   let
   255     val base_sort = (#base_sort o the_class_data thy) class;
   256     val prep_typ = map_type_tvar
   257       (fn (vi as (v, _), sort) => if Name.aT = v
   258         then TFree (v, base_sort) else TVar (vi, sort));
   259     val t' = map_types prep_typ t;
   260     val ty' = Term.fastype_of t';
   261   in
   262     thy
   263     |> (ClassData.map o Graph.map_node class o map_class_data o apsnd)
   264       (fn (defs, operations) =>
   265         (fold cons (the_list some_def) defs,
   266           (c, (class, (ty', t'))) :: operations))
   267   end;
   268 
   269 
   270 (** rule calculation, tactics and methods **)
   271 
   272 val class_prefix = Logic.const_of_class o Sign.base_name;
   273 
   274 fun calculate sups base_sort assm_axiom param_map class thy =
   275   let
   276     (*static parts of morphism*)
   277     val subst_typ = map_type_tfree (fn (v, sort) =>
   278           if v = Name.aT then TVar ((v, 0), [class]) else TVar ((v, 0), sort));
   279     fun subst_aterm (t as Free (v, ty)) = (case AList.lookup (op =) param_map v
   280          of SOME (c, _) => Const (c, ty)
   281           | NONE => t)
   282       | subst_aterm t = t;
   283     fun instantiate thy sort = Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o pair (Name.aT, 0))
   284       (base_sort, sort)], map (fn (v, (c, ty)) => pairself (Thm.cterm_of thy)
   285         (Var ((v, 0), map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty),
   286           Const (c, map_atyps (fn _ => TVar ((Name.aT, 0), sort)) ty))) param_map);
   287     (*fun inst thy sort thm = (tracing (makestring thm); instantiate thy sort thm);
   288     val instantiate = inst;*)
   289     val (proto_assm_intro, locale_intro) = Locale.intros thy class
   290       |> pairself (try the_single);
   291     val axiom_premises = map_filter (#axiom o the_class_data thy) sups
   292       @ the_list assm_axiom;
   293     val axiom = locale_intro
   294       |> Option.map (Thm.close_derivation o Drule.standard' o (fn thm => thm OF axiom_premises) o instantiate thy [class])
   295       |> (fn x as SOME _ => x | NONE => assm_axiom);
   296     val lift_axiom = case axiom
   297      of SOME axiom => (fn thm => ((*tracing "-(morphism)-";
   298           tracing (makestring thm);
   299           tracing (makestring axiom);*)
   300           Thm.implies_elim thm axiom))
   301       | NONE => I;
   302 
   303     (*dynamic parts of morphism*)
   304     fun avoid_a thy thm =
   305       let
   306         val tvars = Term.add_tvars (Thm.prop_of thm) [];
   307         val thm' = case AList.lookup (op =) tvars (Name.aT, 0)
   308          of SOME sort => Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o rpair sort o rpair 0)
   309               (Name.aT, Name.variant (map (fst o fst) tvars) Name.aT)], []) thm
   310           | NONE => thm;
   311       in thm' end;
   312     fun rew_term thy defs = Pattern.rewrite_term thy
   313       (map (Logic.dest_equals o Thm.prop_of) defs) [];
   314     fun subst_term thy defs = map_aterms subst_aterm #> rew_term thy defs
   315       #> map_types subst_typ;
   316     fun subst_thm thy defs = Drule.zero_var_indexes #> avoid_a thy
   317       #> Drule.standard' #> instantiate thy [class] #> lift_axiom
   318       #> MetaSimplifier.rewrite_rule defs;
   319     fun morphism thy defs =
   320       Morphism.typ_morphism subst_typ
   321       $> Morphism.term_morphism (subst_term thy defs)
   322       $> Morphism.thm_morphism (subst_thm thy defs);
   323 
   324     (*class rules*)
   325     val defs = these_defs thy sups;
   326     val assm_intro = proto_assm_intro
   327       |> Option.map (instantiate thy base_sort)
   328       |> Option.map (MetaSimplifier.rewrite_rule defs)
   329       |> Option.map Thm.close_derivation;
   330     val class_intro = (#intro o AxClass.get_info thy) class;
   331     val fixate = Thm.instantiate
   332       (map (pairself (Thm.ctyp_of thy)) [(TVar ((Name.aT, 0), []), TFree (Name.aT, base_sort)),
   333         (TVar ((Name.aT, 0), base_sort), TFree (Name.aT, base_sort))], [])
   334     val of_class_sups = if null sups
   335       then map (fixate o Thm.class_triv thy) base_sort
   336       else map (fixate o #of_class o the_class_data thy) sups;
   337     val locale_dests = map Drule.standard' (Locale.dests thy class);
   338     val num_trivs = case length locale_dests
   339      of 0 => if is_none axiom then 0 else 1
   340       | n => n;
   341     val pred_trivs = if num_trivs = 0 then []
   342       else the axiom
   343         |> Thm.prop_of
   344         |> (map_types o map_atyps o K) (TFree (Name.aT, base_sort))
   345         |> (Thm.assume o Thm.cterm_of thy)
   346         |> replicate num_trivs;
   347     val of_class = (fixate class_intro OF of_class_sups OF locale_dests OF pred_trivs)
   348       |> Drule.standard'
   349       |> Thm.close_derivation;
   350     val this_intro = assm_intro |> the_default class_intro;
   351   in
   352     thy
   353     |> Sign.sticky_prefix (class_prefix class ^ "_" ^ AxClass.axiomsN)
   354     |> PureThy.store_thm (AxClass.introN, this_intro)
   355     |> snd
   356     |> Sign.restore_naming thy
   357     |> pair (morphism, axiom, assm_intro, of_class)
   358   end;
   359 
   360 fun class_interpretation class facts defs thy = thy;
   361 
   362 fun class_interpretation class facts defs thy =
   363   let
   364     val consts = map (apsnd fst o snd) (these_params thy [class]);
   365     val constraints = map (fn (class, c) => map_atyps (K (TFree (Name.aT,
   366       [class]))) (Sign.the_const_type thy c)) consts;
   367     val no_constraints = map (map_atyps (K (TFree (Name.aT, [])))) constraints;
   368     fun add_constraint c T = Sign.add_const_constraint (c, SOME T);
   369     val inst = (#inst o the_class_data thy) class;
   370     val tac = ALLGOALS (ProofContext.fact_tac facts);
   371     val prfx = class_prefix class;
   372   in
   373     thy
   374     |> fold2 add_constraint (map snd consts) no_constraints
   375     |> prove_interpretation tac ((false, prfx), []) (Locale.Locale class)
   376           (inst, map (fn def => (("", []), def)) defs)
   377     |> fold2 add_constraint (map snd consts) constraints
   378   end;
   379 
   380 fun prove_subclass (sub, sup) some_thm thy =
   381   let
   382     val of_class = (#of_class o the_class_data thy) sup;
   383     val intro = case some_thm
   384      of SOME thm => Drule.standard' (of_class OF [Drule.standard' thm])
   385       | NONE => Thm.instantiate ([pairself (Thm.ctyp_of thy o TVar o pair (Name.aT, 0))
   386           ([], [sub])], []) of_class;
   387     val classrel = (intro OF (the_list o #axiom o the_class_data thy) sub)
   388       |> Thm.close_derivation;
   389   in
   390     thy
   391     |> AxClass.add_classrel classrel
   392     |> prove_interpretation_in (ALLGOALS (ProofContext.fact_tac (the_list some_thm)))
   393          I (sub, Locale.Locale sup)
   394     |> ClassData.map (Graph.add_edge (sub, sup))
   395   end;
   396 
   397 fun intro_classes_tac facts st =
   398   let
   399     val thy = Thm.theory_of_thm st;
   400     val classes = Sign.all_classes thy;
   401     val class_trivs = map (Thm.class_triv thy) classes;
   402     val class_intros = map_filter (try (#intro o AxClass.get_info thy)) classes;
   403     val assm_intros = these_assm_intros thy;
   404   in
   405     Method.intros_tac (class_trivs @ class_intros @ assm_intros) facts st
   406   end;
   407 
   408 fun default_intro_tac ctxt [] =
   409       intro_classes_tac [] ORELSE Locale.intro_locales_tac true ctxt []
   410   | default_intro_tac _ _ = no_tac;
   411 
   412 fun default_tac rules ctxt facts =
   413   HEADGOAL (Method.some_rule_tac rules ctxt facts) ORELSE
   414     default_intro_tac ctxt facts;
   415 
   416 val _ = Context.>> (Context.map_theory
   417   (Method.add_methods
   418    [("intro_classes", Method.no_args (Method.METHOD intro_classes_tac),
   419       "back-chain introduction rules of classes"),
   420     ("default", Method.thms_ctxt_args (Method.METHOD oo default_tac),
   421       "apply some intro/elim rule")]));
   422 
   423 
   424 (** classes and class target **)
   425 
   426 (* class context syntax *)
   427 
   428 fun synchronize_class_syntax sups base_sort ctxt =
   429   let
   430     val thy = ProofContext.theory_of ctxt;
   431     val algebra = Sign.classes_of thy;
   432     val operations = these_operations thy sups;
   433     fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort)));
   434     val primary_constraints =
   435       (map o apsnd) (subst_class_typ base_sort o fst o snd) operations;
   436     val secondary_constraints =
   437       (map o apsnd) (fn (class, (ty, _)) => subst_class_typ [class] ty) operations;
   438     fun declare_const (c, _) =
   439       let val b = Sign.base_name c
   440       in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end;
   441     fun improve (c, ty) = (case AList.lookup (op =) primary_constraints c
   442      of SOME ty' => (case try (Type.raw_match (ty', ty)) Vartab.empty
   443          of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0)
   444              of SOME (_, ty' as TVar (tvar as (vi, sort))) =>
   445                   if TypeInfer.is_param vi
   446                     andalso Sorts.sort_le algebra (base_sort, sort)
   447                       then SOME (ty', TFree (Name.aT, base_sort))
   448                       else NONE
   449               | _ => NONE)
   450           | NONE => NONE)
   451       | NONE => NONE)
   452     fun subst (c, ty) = Option.map snd (AList.lookup (op =) operations c);
   453     val unchecks = map (fn (c, (_, (ty, t))) => (t, Const (c, ty))) operations;
   454   in
   455     ctxt
   456     |> fold declare_const primary_constraints
   457     |> Overloading.map_improvable_syntax (K (((primary_constraints, secondary_constraints),
   458         (((improve, subst), true), unchecks)), false))
   459     |> Overloading.set_primary_constraints
   460   end;
   461 
   462 fun refresh_syntax class ctxt =
   463   let
   464     val thy = ProofContext.theory_of ctxt;
   465     val base_sort = (#base_sort o the_class_data thy) class;
   466   in synchronize_class_syntax [class] base_sort ctxt end;
   467 
   468 fun init_ctxt sups base_sort ctxt =
   469   ctxt
   470   |> Variable.declare_term
   471       (Logic.mk_type (TFree (Name.aT, base_sort)))
   472   |> synchronize_class_syntax sups base_sort
   473   |> Overloading.add_improvable_syntax;
   474 
   475 fun init class thy =
   476   thy
   477   |> Locale.init class
   478   |> init_ctxt [class] ((#base_sort o the_class_data thy) class);
   479 
   480 
   481 (* class target *)
   482 
   483 fun declare class pos ((c, mx), dict) thy =
   484   let
   485     val prfx = class_prefix class;
   486     val thy' = thy |> Sign.add_path prfx;
   487     val phi = morphism thy' class;
   488 
   489     val c' = Sign.full_name thy' c;
   490     val dict' = Morphism.term phi dict;
   491     val dict_def = map_types Logic.unvarifyT dict';
   492     val ty' = Term.fastype_of dict_def;
   493     val ty'' = Type.strip_sorts ty';
   494     val def_eq = Logic.mk_equals (Const (c', ty'), dict_def);
   495     fun get_axiom thy = ((Thm.varifyT o Thm.get_axiom_i thy) c', thy);
   496   in
   497     thy'
   498     |> Sign.declare_const pos (c, ty'', mx) |> snd
   499     |> Thm.add_def false false (c, def_eq)
   500     |>> Thm.symmetric
   501     ||>> get_axiom
   502     |-> (fn (def, def') => class_interpretation class [def] [Thm.prop_of def]
   503       #> register_operation class (c', (dict', SOME (Thm.symmetric def')))
   504       #> PureThy.store_thm (c ^ "_raw", def')
   505       #> snd)
   506     |> Sign.restore_naming thy
   507     |> Sign.add_const_constraint (c', SOME ty')
   508   end;
   509 
   510 fun abbrev class prmode pos ((c, mx), rhs) thy =
   511   let
   512     val prfx = class_prefix class;
   513     val thy' = thy |> Sign.add_path prfx;
   514 
   515     val unchecks = map (fn (c, (_, (ty, t))) => (t, Const (c, ty)))
   516       (these_operations thy [class]);
   517     val c' = Sign.full_name thy' c;
   518     val rhs' = Pattern.rewrite_term thy unchecks [] rhs;
   519     val rhs'' = map_types Logic.varifyT rhs';
   520     val ty' = Term.fastype_of rhs';
   521   in
   522     thy'
   523     |> Sign.add_abbrev (#1 prmode) pos (c, map_types Type.strip_sorts rhs'') |> snd
   524     |> Sign.add_const_constraint (c', SOME ty')
   525     |> Sign.notation true prmode [(Const (c', ty'), mx)]
   526     |> not (#1 prmode = PrintMode.input) ? register_operation class (c', (rhs', NONE))
   527     |> Sign.restore_naming thy
   528   end;
   529 
   530 fun note class kind facts thy =
   531   let
   532     val phi = morphism thy class;
   533     val facts' = facts
   534       |> PureThy.map_facts (Morphism.thm phi) 
   535       |> Attrib.map_facts (Attrib.attribute_i thy);
   536   in
   537     thy
   538     |> Sign.add_path (class_prefix class)
   539     |> PureThy.note_thmss kind facts'
   540     ||> Sign.restore_naming thy
   541   end;
   542 
   543 fun declaration class decl thy =
   544   Context.theory_map (decl (morphism thy class)) thy;
   545 
   546 
   547 (* class definition *)
   548 
   549 local
   550 
   551 fun gen_class_spec prep_class process_expr thy raw_supclasses raw_elems =
   552   let
   553     val supclasses = map (prep_class thy) raw_supclasses;
   554     val supsort = Sign.minimize_sort thy supclasses;
   555     val sups = filter (is_class thy) supsort;
   556     val supparam_names = map fst (these_params thy sups);
   557     val _ = if has_duplicates (op =) supparam_names
   558       then error ("Duplicate parameter(s) in superclasses: "
   559         ^ (commas o map quote o duplicates (op =)) supparam_names)
   560       else ();
   561     val base_sort = if null sups then supsort else
   562       foldr1 (Sorts.inter_sort (Sign.classes_of thy))
   563         (map (#base_sort o the_class_data thy) sups);
   564     val suplocales = map Locale.Locale sups;
   565     val supexpr = Locale.Merge suplocales;
   566     val supparams = (map fst o Locale.parameters_of_expr thy) supexpr;
   567     val mergeexpr = Locale.Merge (suplocales);
   568     val constrain = Element.Constrains ((map o apsnd o map_atyps)
   569       (K (TFree (Name.aT, base_sort))) supparams);
   570     fun fork_syn (Element.Fixes xs) =
   571           fold_map (fn (c, ty, syn) => cons (c, syn) #> pair (c, ty, NoSyn)) xs
   572           #>> Element.Fixes
   573       | fork_syn x = pair x;
   574     fun fork_syntax elems =
   575       let
   576         val (elems', global_syntax) = fold_map fork_syn elems [];
   577       in (constrain :: elems', global_syntax) end;
   578     val (elems, global_syntax) =
   579       ProofContext.init thy
   580       |> Locale.cert_expr supexpr [constrain]
   581       |> snd
   582       |> init_ctxt sups base_sort
   583       |> process_expr Locale.empty raw_elems
   584       |> fst
   585       |> fork_syntax
   586   in (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) end;
   587 
   588 val read_class_spec = gen_class_spec Sign.intern_class Locale.read_expr;
   589 val check_class_spec = gen_class_spec (K I) Locale.cert_expr;
   590 
   591 fun adjungate_axclass bname class base_sort sups supsort supparams global_syntax thy =
   592   let
   593     val supconsts = map fst supparams
   594       |> AList.make (snd o the o AList.lookup (op =) (these_params thy sups))
   595       |> (map o apsnd o apsnd o map_atyps o K o TFree) (Name.aT, [class]);
   596     val all_params = map fst (Locale.parameters_of thy class);
   597     fun add_const (v, raw_ty) thy =
   598       let
   599         val c = Sign.full_name thy v;
   600         val ty = map_atyps (K (TFree (Name.aT, base_sort))) raw_ty;
   601         val ty0 = Type.strip_sorts ty;
   602         val ty' = map_atyps (K (TFree (Name.aT, [class]))) ty0;
   603         val syn = (the_default NoSyn o AList.lookup (op =) global_syntax) v;
   604       in
   605         thy
   606         |> Sign.declare_const [] (v, ty0, syn)
   607         |> snd
   608         |> pair ((v, ty), (c, ty'))
   609       end;
   610     fun add_consts raw_params thy =
   611       thy
   612       |> Sign.add_path (Logic.const_of_class bname)
   613       |> fold_map add_const raw_params
   614       ||> Sign.restore_naming thy
   615       |-> (fn params => pair (supconsts @ (map o apfst) fst params, params));
   616     fun globalize param_map = map_aterms
   617       (fn Free (v, ty) => Const ((fst o the o AList.lookup (op =) param_map) v, ty)
   618         | t => t);
   619     val raw_pred = Locale.intros thy class
   620       |> fst
   621       |> map (Logic.unvarify o Logic.strip_imp_concl o Thm.prop_of);
   622     fun get_axiom thy = case (#axioms o AxClass.get_info thy) class
   623      of [] => NONE
   624       | [thm] => SOME thm;
   625   in
   626     thy
   627     |> add_consts ((snd o chop (length supparams)) all_params)
   628     |-> (fn (param_map, params) => AxClass.define_class (bname, supsort)
   629           (map (fst o snd) params)
   630           [((bname ^ "_" ^ AxClass.axiomsN, []), map (globalize param_map) raw_pred)]
   631     #> snd
   632     #> `get_axiom
   633     #-> (fn assm_axiom => fold (Sign.add_const_constraint o apsnd SOME o snd) params
   634     #> pair (param_map, params, assm_axiom)))
   635   end;
   636 
   637 fun gen_class prep_spec bname raw_supclasses raw_elems thy =
   638   let
   639     val class = Sign.full_name thy bname;
   640     val (((sups, supparams), (supsort, base_sort, mergeexpr)), (elems, global_syntax)) =
   641       prep_spec thy raw_supclasses raw_elems;
   642   in
   643     thy
   644     |> Locale.add_locale_i "" bname mergeexpr elems
   645     |> snd
   646     |> ProofContext.theory_of
   647     |> adjungate_axclass bname class base_sort sups supsort supparams global_syntax
   648     |-> (fn (param_map, params, assm_axiom) =>
   649         calculate sups base_sort assm_axiom param_map class
   650     #-> (fn (morphism, axiom, assm_intro, of_class) =>
   651         add_class_data ((class, sups), (params, base_sort,
   652           map snd param_map, morphism, axiom, assm_intro, of_class))
   653     (*#> `(fn thy => Locale.facts_of thy class)
   654     #-> (fn facts => fold_map (note class Thm.assumptionK) facts
   655     #> snd*)
   656     #> class_interpretation class (the_list axiom) []))
   657     |> init class
   658     |> pair class
   659   end;
   660 
   661 in
   662 
   663 val class_cmd = gen_class read_class_spec;
   664 val class = gen_class check_class_spec;
   665 
   666 end; (*local*)
   667 
   668 
   669 
   670 (** instantiation target **)
   671 
   672 (* bookkeeping *)
   673 
   674 datatype instantiation = Instantiation of {
   675   arities: string list * (string * sort) list * sort,
   676   params: ((string * string) * (string * typ)) list
   677     (*(instantiation parameter, type constructor), (local instantiation parameter, typ)*)
   678 }
   679 
   680 structure Instantiation = ProofDataFun
   681 (
   682   type T = instantiation
   683   fun init _ = Instantiation { arities = ([], [], []), params = [] };
   684 );
   685 
   686 fun mk_instantiation (arities, params) =
   687   Instantiation { arities = arities, params = params };
   688 fun get_instantiation lthy = case Instantiation.get (LocalTheory.target_of lthy)
   689  of Instantiation data => data;
   690 fun map_instantiation f = (LocalTheory.target o Instantiation.map)
   691   (fn Instantiation { arities, params } => mk_instantiation (f (arities, params)));
   692 
   693 fun the_instantiation lthy = case get_instantiation lthy
   694  of { arities = ([], [], []), ... } => error "No instantiation target"
   695   | data => data;
   696 
   697 val instantiation_params = #params o get_instantiation;
   698 
   699 fun instantiation_param lthy v = instantiation_params lthy
   700   |> find_first (fn (_, (v', _)) => v = v')
   701   |> Option.map (fst o fst);
   702 
   703 
   704 (* syntax *)
   705 
   706 fun synchronize_inst_syntax ctxt =
   707   let
   708     val Instantiation { arities = (_, _, sort), params = params } = Instantiation.get ctxt;
   709     val thy = ProofContext.theory_of ctxt;
   710     fun subst (c, ty) = case AxClass.inst_tyco_of thy (c, ty)
   711          of SOME tyco => (case AList.lookup (op =) params (c, tyco)
   712              of SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty)
   713               | NONE => NONE)
   714           | NONE => NONE;
   715     val unchecks =
   716       map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params;
   717   in
   718     ctxt
   719     |> Overloading.map_improvable_syntax
   720          (fn (((primary_constraints, _), (((improve, _), _), _)), _) =>
   721             (((primary_constraints, []), (((improve, subst), false), unchecks)), false))
   722   end;
   723 
   724 
   725 (* target *)
   726 
   727 val sanatize_name = (*FIXME*)
   728   let
   729     fun is_valid s = Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s
   730       orelse s = "'" orelse s = "_";
   731     val is_junk = not o is_valid andf Symbol.is_regular;
   732     val junk = Scan.many is_junk;
   733     val scan_valids = Symbol.scanner "Malformed input"
   734       ((junk |--
   735         (Scan.optional (Scan.one Symbol.is_ascii_letter) "x" ^^ (Scan.many is_valid >> implode)
   736         --| junk))
   737       ::: Scan.repeat ((Scan.many1 is_valid >> implode) --| junk));
   738   in
   739     explode #> scan_valids #> implode
   740   end;
   741 
   742 fun type_name "*" = "prod"
   743   | type_name "+" = "sum"
   744   | type_name s = sanatize_name (NameSpace.base s); (*FIXME*)
   745 
   746 fun resort_terms pp algebra consts constraints ts =
   747   let
   748     fun matchings (Const (c_ty as (c, _))) = (case constraints c
   749          of NONE => I
   750           | SOME sorts => fold2 (curry (Sorts.meet_sort algebra))
   751               (Consts.typargs consts c_ty) sorts)
   752       | matchings _ = I
   753     val tvartab = (fold o fold_aterms) matchings ts Vartab.empty
   754       handle Sorts.CLASS_ERROR e => error (Sorts.class_error pp e);
   755     val inst = map_type_tvar
   756       (fn (vi, sort) => TVar (vi, the_default sort (Vartab.lookup tvartab vi)));
   757   in if Vartab.is_empty tvartab then NONE else SOME ((map o map_types) inst ts) end;
   758 
   759 fun init_instantiation (tycos, vs, sort) thy =
   760   let
   761     val _ = if null tycos then error "At least one arity must be given" else ();
   762     val params = these_params thy sort;
   763     fun get_param tyco (param, (_, (c, ty))) = if can (AxClass.param_of_inst thy) (c, tyco)
   764       then NONE else SOME ((c, tyco),
   765         (param ^ "_" ^ type_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty));
   766     val inst_params = map_product get_param tycos params |> map_filter I;
   767     val primary_constraints = map (apsnd
   768       (map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) params;
   769     val pp = Syntax.pp_global thy;
   770     val algebra = Sign.classes_of thy
   771       |> fold (fn tyco => Sorts.add_arities pp
   772             (tyco, map (fn class => (class, map snd vs)) sort)) tycos;
   773     val consts = Sign.consts_of thy;
   774     val improve_constraints = AList.lookup (op =)
   775       (map (fn (_, (class, (c, _))) => (c, [[class]])) params);
   776     fun resort_check ts ctxt = case resort_terms pp algebra consts improve_constraints ts
   777      of NONE => NONE
   778       | SOME ts' => SOME (ts', ctxt);
   779     fun improve (c, ty) = case AxClass.inst_tyco_of thy (c, ty)
   780      of SOME tyco => (case AList.lookup (op =) inst_params (c, tyco)
   781          of SOME (_, ty') => if Type.raw_instance (ty', ty) then SOME (ty, ty') else NONE
   782           | NONE => NONE)
   783       | NONE => NONE;
   784   in
   785     thy
   786     |> ProofContext.init
   787     |> Instantiation.put (mk_instantiation ((tycos, vs, sort), inst_params))
   788     |> fold (Variable.declare_typ o TFree) vs
   789     |> fold (Variable.declare_names o Free o snd) inst_params
   790     |> (Overloading.map_improvable_syntax o apfst)
   791          (fn ((_, _), ((_, subst), unchecks)) =>
   792             ((primary_constraints, []), (((improve, K NONE), false), [])))
   793     |> Overloading.add_improvable_syntax
   794     |> Context.proof_map (Syntax.add_term_check 0 "resorting" resort_check)
   795     |> synchronize_inst_syntax
   796   end;
   797 
   798 fun confirm_declaration c = (map_instantiation o apsnd)
   799   (filter_out (fn (_, (c', _)) => c' = c))
   800   #> LocalTheory.target synchronize_inst_syntax
   801 
   802 fun gen_instantiation_instance do_proof after_qed lthy =
   803   let
   804     val (tycos, vs, sort) = (#arities o the_instantiation) lthy;
   805     val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos;
   806     fun after_qed' results =
   807       LocalTheory.theory (fold (AxClass.add_arity o Thm.varifyT) results)
   808       #> after_qed;
   809   in
   810     lthy
   811     |> do_proof after_qed' arities_proof
   812   end;
   813 
   814 val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts =>
   815   Proof.theorem_i NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts));
   816 
   817 fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed =>
   818   fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t
   819     (fn {context, ...} => tac context)) ts) lthy) I;
   820 
   821 fun conclude_instantiation lthy =
   822   let
   823     val { arities, params } = the_instantiation lthy;
   824     val (tycos, vs, sort) = arities;
   825     val thy = ProofContext.theory_of lthy;
   826     val _ = map (fn tyco => if Sign.of_sort thy
   827         (Type (tyco, map TFree vs), sort)
   828       then () else error ("Missing instance proof for type " ^ quote (Sign.extern_type thy tyco)))
   829         tycos;
   830   in lthy end;
   831 
   832 fun pretty_instantiation lthy =
   833   let
   834     val { arities, params } = the_instantiation lthy;
   835     val (tycos, vs, sort) = arities;
   836     val thy = ProofContext.theory_of lthy;
   837     fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort);
   838     fun pr_param ((c, _), (v, ty)) =
   839       (Pretty.block o Pretty.breaks) [Pretty.str v, Pretty.str "==",
   840         (Pretty.str o Sign.extern_const thy) c, Pretty.str "::", Syntax.pretty_typ_global thy ty];
   841   in
   842     (Pretty.block o Pretty.fbreaks)
   843       (Pretty.str "instantiation" :: map pr_arity tycos @ map pr_param params)
   844   end;
   845 
   846 end;
   847