src/Pure/axclass.ML
author wenzelm
Sun May 18 15:04:09 2008 +0200 (2008-05-18 ago)
changeset 26939 1035c89b4c02
parent 26516 1bf210ac0a90
child 27397 1d8456c5d53d
permissions -rw-r--r--
moved global pretty/string_of functions from Sign to Syntax;
     1 (*  Title:      Pure/axclass.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Type classes defined as predicates, associated with a record of
     6 parameters.
     7 *)
     8 
     9 signature AX_CLASS =
    10 sig
    11   val define_class: bstring * class list -> string list ->
    12     ((bstring * attribute list) * term list) list -> theory -> class * theory
    13   val add_classrel: thm -> theory -> theory
    14   val add_arity: thm -> theory -> theory
    15   val prove_classrel: class * class -> tactic -> theory -> theory
    16   val prove_arity: string * sort list * sort -> tactic -> theory -> theory
    17   val get_info: theory -> class ->
    18     {def: thm, intro: thm, axioms: thm list, params: (string * typ) list}
    19   val class_intros: theory -> thm list
    20   val class_of_param: theory -> string -> class option
    21   val cert_classrel: theory -> class * class -> class * class
    22   val read_classrel: theory -> xstring * xstring -> class * class
    23   val axiomatize_class: bstring * class list -> theory -> theory
    24   val axiomatize_class_cmd: bstring * xstring list -> theory -> theory
    25   val axiomatize_classrel: (class * class) list -> theory -> theory
    26   val axiomatize_classrel_cmd: (xstring * xstring) list -> theory -> theory
    27   val axiomatize_arity: arity -> theory -> theory
    28   val axiomatize_arity_cmd: xstring * string list * string -> theory -> theory
    29   val instance_name: string * class -> string
    30   val declare_overloaded: string * typ -> theory -> term * theory
    31   val define_overloaded: string -> string * term -> theory -> thm * theory
    32   val inst_tyco_of: theory -> string * typ -> string option
    33   val unoverload: theory -> thm -> thm
    34   val overload: theory -> thm -> thm
    35   val unoverload_conv: theory -> conv
    36   val overload_conv: theory -> conv
    37   val unoverload_const: theory -> string * typ -> string
    38   val param_of_inst: theory -> string * string -> string
    39   val inst_of_param: theory -> string -> (string * string) option
    40   type cache
    41   val of_sort: theory -> typ * sort -> cache -> thm list * cache  (*exception Sorts.CLASS_ERROR*)
    42   val cache: cache
    43   val introN: string
    44   val axiomsN: string
    45 end;
    46 
    47 structure AxClass: AX_CLASS =
    48 struct
    49 
    50 (** theory data **)
    51 
    52 (* class parameters (canonical order) *)
    53 
    54 type param = string * class;
    55 
    56 fun add_param pp ((x, c): param) params =
    57   (case AList.lookup (op =) params x of
    58     NONE => (x, c) :: params
    59   | SOME c' => error ("Duplicate class parameter " ^ quote x ^
    60       " for " ^ Pretty.string_of_sort pp [c] ^
    61       (if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c'])));
    62 
    63 fun merge_params _ ([], qs) = qs
    64   | merge_params pp (ps, qs) =
    65       fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps;
    66 
    67 
    68 (* axclasses *)
    69 
    70 val introN = "intro";
    71 val superN = "super";
    72 val axiomsN = "axioms";
    73 
    74 datatype axclass = AxClass of
    75  {def: thm,
    76   intro: thm,
    77   axioms: thm list,
    78   params: (string * typ) list};
    79 
    80 type axclasses = axclass Symtab.table * param list;
    81 
    82 fun make_axclass ((def, intro, axioms), params) =
    83   AxClass {def = def, intro = intro, axioms = axioms, params = params};
    84 
    85 fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses =
    86   (Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2));
    87 
    88 
    89 (* instances *)
    90 
    91 val classrel_prefix = "classrel_";
    92 val arity_prefix = "arity_";
    93 
    94 type instances =
    95   ((class * class) * thm) list *
    96   ((class * sort list) * thm) list Symtab.table;
    97 
    98 fun merge_instances ((classrel1, arities1): instances, (classrel2, arities2)) =
    99  (merge (eq_fst op =) (classrel1, classrel2),
   100   Symtab.join (K (merge (eq_fst op =))) (arities1, arities2));
   101 
   102 
   103 (* instance parameters *)
   104 
   105 type inst_params =
   106   (string * thm) Symtab.table Symtab.table
   107     (*constant name ~> type constructor ~> (constant name, equation)*)
   108   * (string * string) Symtab.table; (*constant name ~> (constant name, type constructor)*)
   109 
   110 fun merge_inst_params ((const_param1, param_const1), (const_param2, param_const2)) =
   111   (Symtab.join  (K (Symtab.merge (K true))) (const_param1, const_param2),
   112     Symtab.merge (K true) (param_const1, param_const2));
   113 
   114 
   115 (* setup data *)
   116 
   117 structure AxClassData = TheoryDataFun
   118 (
   119   type T = axclasses * (instances * inst_params);
   120   val empty = ((Symtab.empty, []), (([], Symtab.empty), (Symtab.empty, Symtab.empty)));
   121   val copy = I;
   122   val extend = I;
   123   fun merge pp ((axclasses1, (instances1, inst_params1)), (axclasses2, (instances2, inst_params2))) =
   124     (merge_axclasses pp (axclasses1, axclasses2),
   125       (merge_instances (instances1, instances2), merge_inst_params (inst_params1, inst_params2)));
   126 );
   127 
   128 
   129 (* maintain axclasses *)
   130 
   131 val get_axclasses = #1 o AxClassData.get;
   132 val map_axclasses = AxClassData.map o apfst;
   133 
   134 val lookup_def = Symtab.lookup o #1 o get_axclasses;
   135 
   136 fun get_info thy c =
   137   (case lookup_def thy c of
   138     SOME (AxClass info) => info
   139   | NONE => error ("No such axclass: " ^ quote c));
   140 
   141 fun class_intros thy =
   142   let
   143     fun add_intro c =
   144       (case lookup_def thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I);
   145     val classes = Sign.all_classes thy;
   146   in map (Thm.class_triv thy) classes @ fold add_intro classes [] end;
   147 
   148 
   149 fun get_params thy pred =
   150   let val params = #2 (get_axclasses thy);
   151   in fold (fn (x, c) => if pred c then cons x else I) params [] end;
   152 
   153 fun params_of thy c = get_params thy (fn c' => c' = c);
   154 fun all_params_of thy S = get_params thy (fn c => Sign.subsort thy (S, [c]));
   155 
   156 fun class_of_param thy = AList.lookup (op =) (#2 (get_axclasses thy));
   157 
   158 
   159 (* maintain instances *)
   160 
   161 fun instance_name (a, c) = NameSpace.base c ^ "_" ^ NameSpace.base a;
   162 
   163 val get_instances = #1 o #2 o AxClassData.get;
   164 val map_instances = AxClassData.map o apsnd o apfst;
   165 
   166 
   167 fun the_classrel thy (c1, c2) =
   168   (case AList.lookup (op =) (#1 (get_instances thy)) (c1, c2) of
   169     SOME th => Thm.transfer thy th
   170   | NONE => error ("Unproven class relation " ^
   171       Syntax.string_of_classrel (ProofContext.init thy) [c1, c2]));
   172 
   173 fun put_classrel arg = map_instances (fn (classrel, arities) =>
   174   (insert (eq_fst op =) arg classrel, arities));
   175 
   176 
   177 fun the_arity thy a (c, Ss) =
   178   (case AList.lookup (op =) (Symtab.lookup_list (#2 (get_instances thy)) a) (c, Ss) of
   179     SOME th => Thm.transfer thy th
   180   | NONE => error ("Unproven type arity " ^
   181       Syntax.string_of_arity (ProofContext.init thy) (a, Ss, [c])));
   182 
   183 fun put_arity ((t, Ss, c), th) = map_instances (fn (classrel, arities) =>
   184   (classrel, arities |> Symtab.insert_list (eq_fst op =) (t, ((c, Ss), th))));
   185 
   186 
   187 (* maintain instance parameters *)
   188 
   189 val get_inst_params = #2 o #2 o AxClassData.get;
   190 val map_inst_params = AxClassData.map o apsnd o apsnd;
   191 
   192 fun get_inst_param thy (c, tyco) =
   193   (the o Symtab.lookup ((the o Symtab.lookup (fst (get_inst_params thy))) c)) tyco;
   194 
   195 fun add_inst_param (c, tyco) inst = (map_inst_params o apfst
   196       o Symtab.map_default (c, Symtab.empty)) (Symtab.update_new (tyco, inst))
   197   #> (map_inst_params o apsnd) (Symtab.update_new (fst inst, (c, tyco)));
   198 
   199 val inst_of_param = Symtab.lookup o snd o get_inst_params;
   200 val param_of_inst = fst oo get_inst_param;
   201 
   202 fun inst_thms thy = (Symtab.fold (Symtab.fold (cons o snd o snd) o snd) o fst)
   203   (get_inst_params thy) [];
   204 
   205 fun inst_tyco_of thy = try (fst o dest_Type o the_single o Sign.const_typargs thy);
   206 
   207 fun unoverload thy = MetaSimplifier.simplify true (inst_thms thy);
   208 fun overload thy = MetaSimplifier.simplify true (map Thm.symmetric (inst_thms thy));
   209 
   210 fun unoverload_conv thy = MetaSimplifier.rewrite true (inst_thms thy);
   211 fun overload_conv thy = MetaSimplifier.rewrite true (map Thm.symmetric (inst_thms thy));
   212 
   213 fun unoverload_const thy (c_ty as (c, _)) =
   214   case class_of_param thy c
   215    of SOME class => (case inst_tyco_of thy c_ty
   216        of SOME tyco => try (param_of_inst thy) (c, tyco) |> the_default c
   217         | NONE => c)
   218     | NONE => c;
   219 
   220 
   221 (** instances **)
   222 
   223 (* class relations *)
   224 
   225 fun cert_classrel thy raw_rel =
   226   let
   227     val string_of_sort = Syntax.string_of_sort_global thy;
   228     val (c1, c2) = pairself (Sign.certify_class thy) raw_rel;
   229     val _ = Sign.primitive_classrel (c1, c2) (Theory.copy thy);
   230     val _ =
   231       (case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of
   232         [] => ()
   233       | xs => raise TYPE ("Class " ^ string_of_sort [c1] ^ " lacks parameter(s) " ^
   234           commas_quote xs ^ " of " ^ string_of_sort [c2], [], []));
   235   in (c1, c2) end;
   236 
   237 fun read_classrel thy raw_rel =
   238   cert_classrel thy (pairself (Sign.read_class thy) raw_rel)
   239     handle TYPE (msg, _, _) => error msg;
   240 
   241 
   242 (* primitive rules *)
   243 
   244 fun add_classrel th thy =
   245   let
   246     fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]);
   247     val prop = Thm.plain_prop_of (Thm.transfer thy th);
   248     val rel = Logic.dest_classrel prop handle TERM _ => err ();
   249     val (c1, c2) = cert_classrel thy rel handle TYPE _ => err ();
   250   in
   251     thy
   252     |> Sign.primitive_classrel (c1, c2)
   253     |> put_classrel ((c1, c2), Drule.unconstrainTs th)
   254   end;
   255 
   256 fun add_arity th thy =
   257   let
   258     fun err () = raise THM ("add_arity: malformed type arity", 0, [th]);
   259     val prop = Thm.plain_prop_of (Thm.transfer thy th);
   260     val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err ();
   261     val _ = map (Sign.certify_sort thy) Ss = Ss orelse err ();
   262     val _ = case filter_out (fn c => can (get_inst_param thy) (c, t)) (params_of thy c)
   263      of [] => ()
   264       | cs => Output.legacy_feature
   265           ("Missing specifications for overloaded parameters " ^ commas_quote cs)
   266   in
   267     thy
   268     |> Sign.primitive_arity (t, Ss, [c])
   269     |> put_arity ((t, Ss, c), Drule.unconstrainTs th)
   270   end;
   271 
   272 
   273 (* tactical proofs *)
   274 
   275 fun prove_classrel raw_rel tac thy =
   276   let
   277     val ctxt = ProofContext.init thy;
   278     val (c1, c2) = cert_classrel thy raw_rel;
   279     val th = Goal.prove ctxt [] []
   280         (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg =>
   281       cat_error msg ("The error(s) above occurred while trying to prove class relation " ^
   282         quote (Syntax.string_of_classrel ctxt [c1, c2]));
   283   in
   284     thy
   285     |> PureThy.add_thms [((prefix classrel_prefix (Logic.name_classrel (c1, c2)), th), [])]
   286     |-> (fn [th'] => add_classrel th')
   287   end;
   288 
   289 fun prove_arity raw_arity tac thy =
   290   let
   291     val ctxt = ProofContext.init thy;
   292     val arity = Sign.cert_arity thy raw_arity;
   293     val names = map (prefix arity_prefix) (Logic.name_arities arity);
   294     val props = Logic.mk_arities arity;
   295     val ths = Goal.prove_multi ctxt [] [] props
   296       (fn _ => Goal.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg =>
   297         cat_error msg ("The error(s) above occurred while trying to prove type arity " ^
   298           quote (Syntax.string_of_arity ctxt arity));
   299   in
   300     thy
   301     |> PureThy.add_thms (map (rpair []) (names ~~ ths))
   302     |-> fold add_arity
   303   end;
   304 
   305 
   306 (* instance parameters and overloaded definitions *)
   307 
   308 (* declaration and definition of instances of overloaded constants *)
   309 
   310 fun declare_overloaded (c, T) thy =
   311   let
   312     val class = case class_of_param thy c
   313      of SOME class => class
   314       | NONE => error ("Not a class parameter: " ^ quote c);
   315     val tyco = case inst_tyco_of thy (c, T)
   316      of SOME tyco => tyco
   317       | NONE => error ("Illegal type for instantiation of class parameter: "
   318         ^ quote (c ^ " :: " ^ Syntax.string_of_typ_global thy T));
   319     val name_inst = instance_name (tyco, class) ^ "_inst";
   320     val c' = NameSpace.base c ^ "_" ^ NameSpace.base tyco;
   321     val T' = Type.strip_sorts T;
   322   in
   323     thy
   324     |> Sign.sticky_prefix name_inst
   325     |> Sign.no_base_names
   326     |> Sign.declare_const [] (c', T', NoSyn)
   327     |-> (fn const' as Const (c'', _) => Thm.add_def false true
   328           (Thm.def_name c', Logic.mk_equals (Const (c, T'), const'))
   329     #>> Thm.varifyT
   330     #-> (fn thm => add_inst_param (c, tyco) (c'', thm)
   331     #> PureThy.note Thm.internalK (c', thm)
   332     #> snd
   333     #> Sign.restore_naming thy
   334     #> pair (Const (c, T))))
   335   end;
   336 
   337 fun define_overloaded name (c, t) thy =
   338   let
   339     val T = Term.fastype_of t;
   340     val SOME tyco = inst_tyco_of thy (c, T);
   341     val (c', eq) = get_inst_param thy (c, tyco);
   342     val prop = Logic.mk_equals (Const (c', T), t);
   343     val name' = Thm.def_name_optional
   344       (NameSpace.base c ^ "_" ^ NameSpace.base tyco) name;
   345   in
   346     thy
   347     |> Thm.add_def false false (name', prop)
   348     |>> (fn thm =>  Drule.transitive_thm OF [eq, thm])
   349   end;
   350 
   351 
   352 
   353 (** class definitions **)
   354 
   355 fun split_defined n eq =
   356   let
   357     val intro =
   358       (eq RS Drule.equal_elim_rule2)
   359       |> Conjunction.curry_balanced n
   360       |> n = 0 ? Thm.eq_assumption 1;
   361     val dests =
   362       if n = 0 then []
   363       else
   364         (eq RS Drule.equal_elim_rule1)
   365         |> BalancedTree.dest (fn th =>
   366           (th RS Conjunction.conjunctionD1, th RS Conjunction.conjunctionD2)) n;
   367   in (intro, dests) end;
   368 
   369 fun define_class (bclass, raw_super) raw_params raw_specs thy =
   370   let
   371     val ctxt = ProofContext.init thy;
   372     val pp = Syntax.pp ctxt;
   373 
   374 
   375     (* class *)
   376 
   377     val bconst = Logic.const_of_class bclass;
   378     val class = Sign.full_name thy bclass;
   379     val super = Sign.minimize_sort thy (Sign.certify_sort thy raw_super);
   380 
   381     fun check_constraint (a, S) =
   382       if Sign.subsort thy (super, S) then ()
   383       else error ("Sort constraint of type variable " ^
   384         setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^
   385         " needs to be weaker than " ^ Pretty.string_of_sort pp super);
   386 
   387 
   388     (* params *)
   389 
   390     val params = raw_params |> map (fn p =>
   391       let
   392         val T = Sign.the_const_type thy p;
   393         val _ =
   394           (case Term.add_tvarsT T [] of
   395             [((a, _), S)] => check_constraint (a, S)
   396           | _ => error ("Exactly one type variable expected in class parameter " ^ quote p));
   397         val T' = Term.map_type_tvar (fn _ => TFree (Name.aT, [class])) T;
   398       in (p, T') end);
   399 
   400 
   401     (* axioms *)
   402 
   403     fun prep_axiom t =
   404       (case Term.add_tfrees t [] of
   405         [(a, S)] => check_constraint (a, S)
   406       | [] => ()
   407       | _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t);
   408       t
   409       |> Term.map_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U))
   410       |> Logic.close_form);
   411 
   412     val axiomss = map (map (prep_axiom o Sign.cert_prop thy) o snd) raw_specs;
   413     val name_atts = map fst raw_specs;
   414 
   415 
   416     (* definition *)
   417 
   418     val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss;
   419     val class_eq =
   420       Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_balanced conjs);
   421 
   422     val ([def], def_thy) =
   423       thy
   424       |> Sign.primitive_class (bclass, super)
   425       |> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])];
   426     val (raw_intro, (raw_classrel, raw_axioms)) =
   427       split_defined (length conjs) def ||> chop (length super);
   428 
   429 
   430     (* facts *)
   431 
   432     val class_triv = Thm.class_triv def_thy class;
   433     val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) =
   434       def_thy
   435       |> PureThy.note_thmss_qualified "" bconst
   436         [((introN, []), [([Drule.standard raw_intro], [])]),
   437          ((superN, []), [(map Drule.standard raw_classrel, [])]),
   438          ((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])];
   439 
   440 
   441     (* result *)
   442 
   443     val axclass = make_axclass ((def, intro, axioms), params);
   444     val result_thy =
   445       facts_thy
   446       |> fold put_classrel (map (pair class) super ~~ classrel)
   447       |> Sign.add_path bconst
   448       |> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd
   449       |> Sign.restore_naming facts_thy
   450       |> map_axclasses (fn (axclasses, parameters) =>
   451         (Symtab.update (class, axclass) axclasses,
   452           fold (fn (x, _) => add_param pp (x, class)) params parameters));
   453 
   454   in (class, result_thy) end;
   455 
   456 
   457 
   458 (** axiomatizations **)
   459 
   460 local
   461 
   462 fun axiomatize prep mk name add raw_args thy =
   463   let
   464     val args = prep thy raw_args;
   465     val specs = mk args;
   466     val names = name args;
   467   in thy |> PureThy.add_axioms_i (map (rpair []) (names ~~ specs)) |-> fold add end;
   468 
   469 fun ax_classrel prep =
   470   axiomatize (map o prep) (map Logic.mk_classrel)
   471     (map (prefix classrel_prefix o Logic.name_classrel)) add_classrel;
   472 
   473 fun ax_arity prep =
   474   axiomatize prep Logic.mk_arities
   475     (map (prefix arity_prefix) o Logic.name_arities) add_arity;
   476 
   477 fun class_const c =
   478   (Logic.const_of_class c, Term.itselfT (Term.aT []) --> propT);
   479 
   480 fun ax_class prep_class prep_classrel (bclass, raw_super) thy =
   481   let
   482     val class = Sign.full_name thy bclass;
   483     val super = map (prep_class thy) raw_super |> Sign.minimize_sort thy;
   484   in
   485     thy
   486     |> Sign.primitive_class (bclass, super)
   487     |> ax_classrel prep_classrel (map (fn c => (class, c)) super)
   488     |> Theory.add_deps "" (class_const class) (map class_const super)
   489   end;
   490 
   491 in
   492 
   493 val axiomatize_class = ax_class Sign.certify_class cert_classrel;
   494 val axiomatize_class_cmd = ax_class Sign.read_class read_classrel;
   495 val axiomatize_classrel = ax_classrel cert_classrel;
   496 val axiomatize_classrel_cmd = ax_classrel read_classrel;
   497 val axiomatize_arity = ax_arity Sign.cert_arity;
   498 val axiomatize_arity_cmd = ax_arity Sign.read_arity;
   499 
   500 end;
   501 
   502 
   503 
   504 (** explicit derivations -- cached **)
   505 
   506 datatype cache = Types of (class * thm) list Typtab.table;
   507 
   508 local
   509 
   510 fun lookup_type (Types cache) = AList.lookup (op =) o Typtab.lookup_list cache;
   511 fun insert_type T der (Types cache) = Types (Typtab.insert_list (eq_fst op =) (T, der) cache);
   512 
   513 fun derive_type _ (_, []) = []
   514   | derive_type thy (typ, sort) =
   515       let
   516         val vars = Term.fold_atyps
   517             (fn T as TFree (_, S) => insert (eq_fst op =) (T, S)
   518               | T as TVar (_, S) => insert (eq_fst op =) (T, S)
   519               | _ => I) typ [];
   520         val hyps = vars
   521           |> map (fn (T, S) => (T, Drule.sort_triv thy (T, S) ~~ S));
   522         val ths = (typ, sort)
   523           |> Sorts.of_sort_derivation (Syntax.pp_global thy) (Sign.classes_of thy)
   524            {class_relation =
   525               fn (th, c1) => fn c2 => th RS the_classrel thy (c1, c2),
   526             type_constructor =
   527               fn a => fn dom => fn c =>
   528                 let val Ss = map (map snd) dom and ths = maps (map fst) dom
   529                 in ths MRS the_arity thy a (c, Ss) end,
   530             type_variable =
   531               the_default [] o AList.lookup (op =) hyps};
   532       in ths end;
   533 
   534 in
   535 
   536 fun of_sort thy (typ, sort) cache =
   537   let
   538     val sort' = filter (is_none o lookup_type cache typ) sort;
   539     val ths' = derive_type thy (typ, sort')
   540       handle ERROR msg => cat_error msg ("The error(s) above occurred for sort derivation: " ^
   541         Syntax.string_of_typ_global thy typ ^ " :: " ^ Syntax.string_of_sort_global thy sort');
   542     val cache' = cache |> fold (insert_type typ) (sort' ~~ ths');
   543     val ths =
   544       sort |> map (fn c =>
   545         Goal.finish (the (lookup_type cache' typ c) RS
   546           Goal.init (Thm.cterm_of thy (Logic.mk_inclass (typ, c))))
   547         |> Thm.adjust_maxidx_thm ~1);
   548   in (ths, cache') end;
   549 
   550 end;
   551 
   552 val cache = Types Typtab.empty;
   553 
   554 end;