src/Pure/variable.ML
author wenzelm
Tue Nov 06 22:50:34 2007 +0100 (2007-11-06)
changeset 25316 17c183417f93
parent 25051 71cd45fdf332
child 25325 0659c05cc107
permissions -rw-r--r--
added is_const/declare_const for local scope of fixes/consts;
     1 (*  Title:      Pure/variable.ML
     2     ID:         $Id$
     3     Author:     Makarius
     4 
     5 Fixed type/term variables and polymorphic term abbreviations.
     6 *)
     7 
     8 signature VARIABLE =
     9 sig
    10   val is_body: Proof.context -> bool
    11   val set_body: bool -> Proof.context -> Proof.context
    12   val restore_body: Proof.context -> Proof.context -> Proof.context
    13   val names_of: Proof.context -> Name.context
    14   val fixes_of: Proof.context -> (string * string) list
    15   val binds_of: Proof.context -> (typ * term) Vartab.table
    16   val maxidx_of: Proof.context -> int
    17   val constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table
    18   val is_declared: Proof.context -> string -> bool
    19   val is_fixed: Proof.context -> string -> bool
    20   val newly_fixed: Proof.context -> Proof.context -> string -> bool
    21   val add_fixed: Proof.context -> term -> (string * typ) list -> (string * typ) list
    22   val default_type: Proof.context -> string -> typ option
    23   val def_type: Proof.context -> bool -> indexname -> typ option
    24   val def_sort: Proof.context -> indexname -> sort option
    25   val declare_constraints: term -> Proof.context -> Proof.context
    26   val declare_internal: term -> Proof.context -> Proof.context
    27   val declare_term: term -> Proof.context -> Proof.context
    28   val declare_prf: Proofterm.proof -> Proof.context -> Proof.context
    29   val declare_thm: thm -> Proof.context -> Proof.context
    30   val thm_context: thm -> Proof.context
    31   val variant_frees: Proof.context -> term list -> (string * 'a) list -> (string * 'a) list
    32   val add_binds: (indexname * term option) list -> Proof.context -> Proof.context
    33   val expand_binds: Proof.context -> term -> term
    34   val is_const: Proof.context -> string -> bool
    35   val declare_const: string -> Proof.context -> Proof.context
    36   val add_fixes: string list -> Proof.context -> string list * Proof.context
    37   val add_fixes_direct: string list -> Proof.context -> Proof.context
    38   val auto_fixes: term -> Proof.context -> Proof.context
    39   val variant_fixes: string list -> Proof.context -> string list * Proof.context
    40   val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context
    41   val export_terms: Proof.context -> Proof.context -> term list -> term list
    42   val exportT_terms: Proof.context -> Proof.context -> term list -> term list
    43   val exportT: Proof.context -> Proof.context -> thm list -> thm list
    44   val export_prf: Proof.context -> Proof.context -> Proofterm.proof -> Proofterm.proof
    45   val export: Proof.context -> Proof.context -> thm list -> thm list
    46   val export_morphism: Proof.context -> Proof.context -> morphism
    47   val importT_inst: term list -> Proof.context -> ((indexname * sort) * typ) list * Proof.context
    48   val import_inst: bool -> term list -> Proof.context ->
    49     (((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Proof.context
    50   val importT_terms: term list -> Proof.context -> term list * Proof.context
    51   val import_terms: bool -> term list -> Proof.context -> term list * Proof.context
    52   val importT_thms: thm list -> Proof.context -> (ctyp list * thm list) * Proof.context
    53   val import_prf: bool -> Proofterm.proof -> Proof.context -> Proofterm.proof * Proof.context
    54   val import_thms: bool -> thm list -> Proof.context ->
    55     ((ctyp list * cterm list) * thm list) * Proof.context
    56   val tradeT: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
    57   val trade: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
    58   val focus: cterm -> Proof.context -> (cterm list * cterm) * Proof.context
    59   val focus_subgoal: int -> thm -> Proof.context -> (cterm list * cterm) * Proof.context
    60   val warn_extra_tfrees: Proof.context -> Proof.context -> unit
    61   val polymorphic_types: Proof.context -> term list -> (indexname * sort) list * term list
    62   val polymorphic: Proof.context -> term list -> term list
    63 end;
    64 
    65 structure Variable: VARIABLE =
    66 struct
    67 
    68 (** local context data **)
    69 
    70 datatype data = Data of
    71  {is_body: bool,                        (*inner body mode*)
    72   names: Name.context,                  (*type/term variable names*)
    73   scope: bool Symtab.table,             (*local scope of fixes/consts*)
    74   fixes: (string * string) list,        (*term fixes -- extern/intern*)
    75   binds: (typ * term) Vartab.table,     (*term bindings*)
    76   type_occs: string list Symtab.table,  (*type variables -- possibly within term variables*)
    77   maxidx: int,                          (*maximum var index*)
    78   constraints:
    79     typ Vartab.table *                  (*type constraints*)
    80     sort Vartab.table};                 (*default sorts*)
    81 
    82 fun make_data (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =
    83   Data {is_body = is_body, names = names, scope = scope, fixes = fixes, binds = binds,
    84     type_occs = type_occs, maxidx = maxidx, constraints = constraints};
    85 
    86 structure Data = ProofDataFun
    87 (
    88   type T = data;
    89   fun init thy =
    90     make_data (false, Name.context, Symtab.empty, [], Vartab.empty, Symtab.empty,
    91       ~1, (Vartab.empty, Vartab.empty));
    92 );
    93 
    94 fun map_data f =
    95   Data.map (fn Data {is_body, names, scope, fixes, binds, type_occs, maxidx, constraints} =>
    96     make_data (f (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints)));
    97 
    98 fun map_names f =
    99   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   100     (is_body, f names, scope, fixes, binds, type_occs, maxidx, constraints));
   101 
   102 fun map_scope f =
   103   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   104     (is_body, names, f scope, fixes, binds, type_occs, maxidx, constraints));
   105 
   106 fun map_fixes f =
   107   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   108     (is_body, names, scope, f fixes, binds, type_occs, maxidx, constraints));
   109 
   110 fun map_binds f =
   111   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   112     (is_body, names, scope, fixes, f binds, type_occs, maxidx, constraints));
   113 
   114 fun map_type_occs f =
   115   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   116     (is_body, names, scope, fixes, binds, f type_occs, maxidx, constraints));
   117 
   118 fun map_maxidx f =
   119   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   120     (is_body, names, scope, fixes, binds, type_occs, f maxidx, constraints));
   121 
   122 fun map_constraints f =
   123   map_data (fn (is_body, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   124     (is_body, names, scope, fixes, binds, type_occs, maxidx, f constraints));
   125 
   126 fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
   127 
   128 val is_body = #is_body o rep_data;
   129 
   130 fun set_body b = map_data (fn (_, names, scope, fixes, binds, type_occs, maxidx, constraints) =>
   131   (b, names, scope, fixes, binds, type_occs, maxidx, constraints));
   132 
   133 fun restore_body ctxt = set_body (is_body ctxt);
   134 
   135 val names_of = #names o rep_data;
   136 val fixes_of = #fixes o rep_data;
   137 val binds_of = #binds o rep_data;
   138 val type_occs_of = #type_occs o rep_data;
   139 val maxidx_of = #maxidx o rep_data;
   140 val constraints_of = #constraints o rep_data;
   141 
   142 val is_declared = Name.is_declared o names_of;
   143 fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);
   144 fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
   145 
   146 fun add_fixed ctxt = Term.fold_aterms
   147   (fn Free (x, T) => if is_fixed ctxt x then insert (op =) (x, T) else I | _ => I);
   148 
   149 
   150 
   151 (** declarations **)
   152 
   153 (* default sorts and types *)
   154 
   155 fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
   156 
   157 fun def_type ctxt pattern xi =
   158   let val {binds, constraints = (types, _), ...} = rep_data ctxt in
   159     (case Vartab.lookup types xi of
   160       NONE =>
   161         if pattern then NONE
   162         else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)
   163     | some => some)
   164   end;
   165 
   166 val def_sort = Vartab.lookup o #2 o constraints_of;
   167 
   168 
   169 (* names *)
   170 
   171 fun declare_type_names t =
   172   map_names (fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) t) #>
   173   map_maxidx (fold_types Term.maxidx_typ t);
   174 
   175 fun declare_names t =
   176   declare_type_names t #>
   177   map_names (fold_aterms (fn Free (x, _) => Name.declare x | _ => I) t) #>
   178   map_maxidx (Term.maxidx_term t);
   179 
   180 
   181 (* type occurrences *)
   182 
   183 fun decl_type_occsT T = fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I) T;
   184 
   185 val decl_type_occs = fold_term_types
   186   (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
   187     | _ => decl_type_occsT);
   188 
   189 val declare_type_occsT = map_type_occs o fold_types decl_type_occsT;
   190 val declare_type_occs = map_type_occs o decl_type_occs;
   191 
   192 
   193 (* constraints *)
   194 
   195 fun constrain_tvar (xi, S) =
   196   if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);
   197 
   198 fun declare_constraints t = map_constraints (fn (types, sorts) =>
   199   let
   200     val types' = fold_aterms
   201       (fn Free (x, T) => Vartab.update ((x, ~1), T)
   202         | Var v => Vartab.update v
   203         | _ => I) t types;
   204     val sorts' = fold_types (fold_atyps
   205       (fn TFree (x, S) => constrain_tvar ((x, ~1), S)
   206         | TVar v => constrain_tvar v
   207         | _ => I)) t sorts;
   208   in (types', sorts') end)
   209   #> declare_type_occsT t
   210   #> declare_type_names t;
   211 
   212 
   213 (* common declarations *)
   214 
   215 fun declare_internal t =
   216   declare_names t #>
   217   declare_type_occs t;
   218 
   219 fun declare_term t =
   220   declare_internal t #>
   221   declare_constraints t;
   222 
   223 val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);
   224 
   225 val declare_thm = Thm.fold_terms declare_internal;
   226 fun thm_context th = declare_thm th (ProofContext.init (Thm.theory_of_thm th));
   227 
   228 
   229 (* renaming term/type frees *)
   230 
   231 fun variant_frees ctxt ts frees =
   232   let
   233     val names = names_of (fold declare_names ts ctxt);
   234     val xs = fst (Name.variants (map #1 frees) names);
   235   in xs ~~ map snd frees end;
   236 
   237 
   238 
   239 (** term bindings **)
   240 
   241 fun add_bind (xi, NONE) = map_binds (Vartab.delete_safe xi)
   242   | add_bind ((x, i), SOME t) =
   243       let
   244         val u = Term.close_schematic_term t;
   245         val U = Term.fastype_of u;
   246       in declare_term u #> map_binds (Vartab.update ((x, i), (U, u))) end;
   247 
   248 val add_binds = fold add_bind;
   249 
   250 fun expand_binds ctxt =
   251   let
   252     val binds = binds_of ctxt;
   253     val get = fn Var (xi, _) => Vartab.lookup binds xi | _ => NONE;
   254   in Envir.beta_norm o Envir.expand_term get end;
   255 
   256 
   257 
   258 (** local scope **)
   259 
   260 fun is_const ctxt x = the_default false (Symtab.lookup (#scope (rep_data ctxt)) x);
   261 
   262 fun declare_fixed x = map_scope (Symtab.update (x, false));
   263 fun declare_const c = map_scope (Symtab.update (c, true));
   264 
   265 
   266 
   267 (** fixes **)
   268 
   269 local
   270 
   271 fun no_dups [] = ()
   272   | no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);
   273 
   274 fun new_fixes names' xs xs' =
   275   map_names (K names') #>
   276   fold declare_fixed xs #>
   277   map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>
   278   fold (declare_constraints o Syntax.free) xs' #>
   279   pair xs';
   280 
   281 in
   282 
   283 fun add_fixes xs ctxt =
   284   let
   285     val _ =
   286       (case filter (can Name.dest_skolem) xs of [] => ()
   287       | bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));
   288     val _ = no_dups (duplicates (op =) xs);
   289     val (ys, zs) = split_list (fixes_of ctxt);
   290     val names = names_of ctxt;
   291     val (xs', names') =
   292       if is_body ctxt then Name.variants xs names |>> map Name.skolem
   293       else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);
   294         (xs, fold Name.declare xs names));
   295   in ctxt |> new_fixes names' xs xs' end;
   296 
   297 fun variant_fixes raw_xs ctxt =
   298   let
   299     val names = names_of ctxt;
   300     val xs = map Name.clean raw_xs;
   301     val (xs', names') = Name.variants xs names |>> map Name.skolem;
   302   in ctxt |> new_fixes names' xs xs' end;
   303 
   304 end;
   305 
   306 
   307 fun add_fixes_direct xs ctxt = ctxt
   308   |> set_body false
   309   |> (snd o add_fixes xs)
   310   |> restore_body ctxt;
   311 
   312 fun fix_frees t ctxt = ctxt
   313   |> add_fixes_direct
   314       (rev (fold_aterms (fn Free (x, _) =>
   315         if is_fixed ctxt x then I else insert (op =) x | _ => I) t []));
   316 
   317 fun auto_fixes t ctxt =
   318   (if is_body ctxt then ctxt else fix_frees t ctxt)
   319   |> declare_term t;
   320 
   321 fun invent_types Ss ctxt =
   322   let
   323     val tfrees = Name.invents (names_of ctxt) Name.aT (length Ss) ~~ Ss;
   324     val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
   325   in (tfrees, ctxt') end;
   326 
   327 
   328 
   329 (** export -- generalize type/term variables (beware of closure sizes) **)
   330 
   331 fun export_inst inner outer =
   332   let
   333     val declared_outer = is_declared outer;
   334     val fixes_inner = fixes_of inner;
   335     val fixes_outer = fixes_of outer;
   336 
   337     val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));
   338     val still_fixed = not o member (op =) gen_fixes;
   339 
   340     val type_occs_inner = type_occs_of inner;
   341     fun gen_fixesT ts =
   342       Symtab.fold (fn (a, xs) =>
   343         if declared_outer a orelse exists still_fixed xs
   344         then I else cons a) (fold decl_type_occs ts type_occs_inner) [];
   345   in (gen_fixesT, gen_fixes) end;
   346 
   347 fun exportT_inst inner outer = #1 (export_inst inner outer);
   348 
   349 fun exportT_terms inner outer =
   350   let val mk_tfrees = exportT_inst inner outer in
   351     fn ts => ts |> map
   352       (TermSubst.generalize (mk_tfrees ts, [])
   353         (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1))
   354   end;
   355 
   356 fun export_terms inner outer =
   357   let val (mk_tfrees, tfrees) = export_inst inner outer in
   358     fn ts => ts |> map
   359       (TermSubst.generalize (mk_tfrees ts, tfrees)
   360         (fold Term.maxidx_term ts ~1 + 1))
   361   end;
   362 
   363 fun export_prf inner outer prf =
   364   let
   365     val (mk_tfrees, frees) = export_inst (declare_prf prf inner) outer;
   366     val tfrees = mk_tfrees [];
   367     val idx = Proofterm.maxidx_proof prf ~1 + 1;
   368     val gen_term = TermSubst.generalize_option (tfrees, frees) idx;
   369     val gen_typ = TermSubst.generalizeT_option tfrees idx;
   370   in Proofterm.map_proof_terms_option gen_term gen_typ prf end;
   371 
   372 
   373 fun gen_export (mk_tfrees, frees) ths =
   374   let
   375     val tfrees = mk_tfrees (map Thm.full_prop_of ths);
   376     val maxidx = fold Thm.maxidx_thm ths ~1;
   377   in map (Thm.generalize (tfrees, frees) (maxidx + 1)) ths end;
   378 
   379 fun exportT inner outer = gen_export (exportT_inst inner outer, []);
   380 fun export inner outer = gen_export (export_inst inner outer);
   381 
   382 fun export_morphism inner outer =
   383   let
   384     val fact = export inner outer;
   385     val term = singleton (export_terms inner outer);
   386     val typ = Logic.type_map term;
   387   in Morphism.morphism {name = I, var = I, typ = typ, term = term, fact = fact} end;
   388 
   389 
   390 
   391 (** import -- fix schematic type/term variables **)
   392 
   393 fun importT_inst ts ctxt =
   394   let
   395     val tvars = rev (fold Term.add_tvars ts []);
   396     val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
   397   in (tvars ~~ map TFree tfrees, ctxt') end;
   398 
   399 fun import_inst is_open ts ctxt =
   400   let
   401     val ren = if is_open then I else Name.internal;
   402     val (instT, ctxt') = importT_inst ts ctxt;
   403     val vars = map (apsnd (TermSubst.instantiateT instT)) (rev (fold Term.add_vars ts []));
   404     val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';
   405     val inst = vars ~~ map Free (xs ~~ map #2 vars);
   406   in ((instT, inst), ctxt'') end;
   407 
   408 fun importT_terms ts ctxt =
   409   let val (instT, ctxt') = importT_inst ts ctxt
   410   in (map (TermSubst.instantiate (instT, [])) ts, ctxt') end;
   411 
   412 fun import_terms is_open ts ctxt =
   413   let val (inst, ctxt') = import_inst is_open ts ctxt
   414   in (map (TermSubst.instantiate inst) ts, ctxt') end;
   415 
   416 fun importT_thms ths ctxt =
   417   let
   418     val thy = ProofContext.theory_of ctxt;
   419     val certT = Thm.ctyp_of thy;
   420     val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
   421     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   422     val ths' = map (Thm.instantiate (instT', [])) ths;
   423   in ((map #2 instT', ths'), ctxt') end;
   424 
   425 fun import_prf is_open prf ctxt =
   426   let
   427     val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);
   428     val (insts, ctxt') = import_inst is_open ts ctxt;
   429   in (Proofterm.instantiate insts prf, ctxt') end;
   430 
   431 fun import_thms is_open ths ctxt =
   432   let
   433     val thy = ProofContext.theory_of ctxt;
   434     val cert = Thm.cterm_of thy;
   435     val certT = Thm.ctyp_of thy;
   436     val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
   437     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   438     val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;
   439     val ths' = map (Thm.instantiate (instT', inst')) ths;
   440   in (((map #2 instT', map #2 inst'), ths'), ctxt') end;
   441 
   442 
   443 (* import/export *)
   444 
   445 fun gen_trade imp exp f ctxt ths =
   446   let val ((_, ths'), ctxt') = imp ths ctxt
   447   in exp ctxt' ctxt (f ctxt' ths') end;
   448 
   449 val tradeT = gen_trade importT_thms exportT;
   450 val trade = gen_trade (import_thms true) export;
   451 
   452 
   453 (* focus on outermost parameters *)
   454 
   455 fun forall_elim_prop t prop =
   456   Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)
   457   |> Thm.cprop_of |> Thm.dest_arg;
   458 
   459 fun focus goal ctxt =
   460   let
   461     val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
   462     val t = Thm.term_of goal;
   463     val ps = Term.variant_frees t (Term.strip_all_vars t);   (*as they are printed :-*)
   464     val (xs, Ts) = split_list ps;
   465     val (xs', ctxt') = variant_fixes xs ctxt;
   466     val ps' = ListPair.map (cert o Free) (xs', Ts);
   467     val goal' = fold forall_elim_prop ps' goal;
   468   in ((ps', goal'), ctxt') end;
   469 
   470 fun focus_subgoal i st =
   471   let
   472     val all_vars = Thm.fold_terms Term.add_vars st [];
   473     val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;
   474   in
   475     add_binds no_binds #>
   476     fold (declare_constraints o Var) all_vars #>
   477     focus (Thm.cprem_of st i)
   478   end;
   479 
   480 
   481 
   482 (** implicit polymorphism **)
   483 
   484 (* warn_extra_tfrees *)
   485 
   486 fun warn_extra_tfrees ctxt1 ctxt2 =
   487   let
   488     fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
   489     fun occs_free a x =
   490       (case def_type ctxt1 false (x, ~1) of
   491         SOME T => if occs_typ a T then I else cons (a, x)
   492       | NONE => cons (a, x));
   493 
   494     val occs1 = type_occs_of ctxt1;
   495     val occs2 = type_occs_of ctxt2;
   496     val extras = Symtab.fold (fn (a, xs) =>
   497       if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
   498     val tfrees = map #1 extras |> sort_distinct string_ord;
   499     val frees = map #2 extras |> sort_distinct string_ord;
   500   in
   501     if null extras then ()
   502     else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
   503       space_implode " or " (map quote frees))
   504   end;
   505 
   506 
   507 (* polymorphic terms *)
   508 
   509 fun polymorphic_types ctxt ts =
   510   let
   511     val ctxt' = fold declare_term ts ctxt;
   512     val occs = type_occs_of ctxt;
   513     val occs' = type_occs_of ctxt';
   514     val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
   515     val idx = maxidx_of ctxt' + 1;
   516     val Ts' = (fold o fold_types o fold_atyps)
   517       (fn T as TFree _ =>
   518           (case TermSubst.generalizeT types idx T of TVar v => insert (op =) v | _ => I)
   519         | _ => I) ts [];
   520     val ts' = map (TermSubst.generalize (types, []) idx) ts;
   521   in (rev Ts', ts') end;
   522 
   523 fun polymorphic ctxt ts = snd (polymorphic_types ctxt ts);
   524 
   525 end;