src/Pure/variable.ML
author wenzelm
Wed Jul 26 19:37:43 2006 +0200 (2006-07-26)
changeset 20220 5dc68e9ecd9a
parent 20198 7b385487f22f
child 20240 a7b027328d6e
permissions -rw-r--r--
import(T): result includes fixed types/terms;
focus: tuned interface;
     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: Context.proof -> bool
    11   val set_body: bool -> Context.proof -> Context.proof
    12   val restore_body: Context.proof -> Context.proof -> Context.proof
    13   val names_of: Context.proof -> Name.context
    14   val fixes_of: Context.proof -> (string * string) list
    15   val binds_of: Context.proof -> (typ * term) Vartab.table
    16   val constraints_of: Context.proof -> typ Vartab.table * sort Vartab.table
    17   val is_declared: Context.proof -> string -> bool
    18   val is_fixed: Context.proof -> string -> bool
    19   val newly_fixed: Context.proof -> Context.proof -> string -> bool
    20   val default_type: Context.proof -> string -> typ option
    21   val def_type: Context.proof -> bool -> indexname -> typ option
    22   val def_sort: Context.proof -> indexname -> sort option
    23   val declare_constraints: term -> Context.proof -> Context.proof
    24   val declare_internal: term -> Context.proof -> Context.proof
    25   val declare_term: term -> Context.proof -> Context.proof
    26   val declare_thm: thm -> Context.proof -> Context.proof
    27   val thm_context: thm -> Context.proof
    28   val variant_frees: Context.proof -> term list -> (string * 'a) list -> (string * 'a) list
    29   val add_fixes: string list -> Context.proof -> string list * Context.proof
    30   val invent_fixes: string list -> Context.proof -> string list * Context.proof
    31   val invent_types: sort list -> Context.proof -> (string * sort) list * Context.proof
    32   val export_inst: Context.proof -> Context.proof -> string list * string list
    33   val exportT_inst: Context.proof -> Context.proof -> string list
    34   val export_terms: Context.proof -> Context.proof -> term list -> term list
    35   val exportT_terms: Context.proof -> Context.proof -> term list -> term list
    36   val exportT: Context.proof -> Context.proof -> thm list -> thm list
    37   val export: Context.proof -> Context.proof -> thm list -> thm list
    38   val importT_inst: term list -> Context.proof -> ((indexname * sort) * typ) list * Context.proof
    39   val import_inst: bool -> term list -> Context.proof ->
    40     (((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Context.proof
    41   val importT_terms: term list -> Context.proof -> term list * Context.proof
    42   val import_terms: bool -> term list -> Context.proof -> term list * Context.proof
    43   val importT: thm list -> Context.proof -> (ctyp list * thm list) * Context.proof
    44   val import: bool -> thm list -> Context.proof ->
    45     ((ctyp list * cterm list) * thm list) * Context.proof
    46   val tradeT: Context.proof -> (thm list -> thm list) -> thm list -> thm list
    47   val trade: Context.proof -> (thm list -> thm list) -> thm list -> thm list
    48   val focus: cterm -> Context.proof -> (cterm list * cterm) * Context.proof
    49   val warn_extra_tfrees: Context.proof -> Context.proof -> unit
    50   val polymorphic: Context.proof -> term list -> term list
    51   val hidden_polymorphism: term -> typ -> (indexname * sort) list
    52   val add_binds: (indexname * term option) list -> Context.proof -> Context.proof
    53   val expand_binds: Context.proof -> term -> term
    54 end;
    55 
    56 structure Variable: VARIABLE =
    57 struct
    58 
    59 (** local context data **)
    60 
    61 datatype data = Data of
    62  {is_body: bool,                        (*inner body mode*)
    63   names: Name.context,                  (*type/term variable names*)
    64   fixes: (string * string) list,        (*term fixes -- extern/intern*)
    65   binds: (typ * term) Vartab.table,     (*term bindings*)
    66   type_occs: string list Symtab.table,  (*type variables -- possibly within term variables*)
    67   constraints:
    68     typ Vartab.table *                  (*type constraints*)
    69     sort Vartab.table};                 (*default sorts*)
    70 
    71 fun make_data (is_body, names, fixes, binds, type_occs, constraints) =
    72   Data {is_body = is_body, names = names, fixes = fixes, binds = binds,
    73     type_occs = type_occs, constraints = constraints};
    74 
    75 structure Data = ProofDataFun
    76 (
    77   val name = "Pure/variable";
    78   type T = data;
    79   fun init thy =
    80     make_data (false, Name.context, [], Vartab.empty, Symtab.empty, (Vartab.empty, Vartab.empty));
    81   fun print _ _ = ();
    82 );
    83 
    84 val _ = Context.add_setup Data.init;
    85 
    86 fun map_data f =
    87   Data.map (fn Data {is_body, names, fixes, binds, type_occs, constraints} =>
    88     make_data (f (is_body, names, fixes, binds, type_occs, constraints)));
    89 
    90 fun map_names f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
    91   (is_body, f names, fixes, binds, type_occs, constraints));
    92 
    93 fun map_fixes f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
    94   (is_body, names, f fixes, binds, type_occs, constraints));
    95 
    96 fun map_binds f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
    97   (is_body, names, fixes, f binds, type_occs, constraints));
    98 
    99 fun map_type_occs f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   100   (is_body, names, fixes, binds, f type_occs, constraints));
   101 
   102 fun map_constraints f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   103   (is_body, names, fixes, binds, type_occs, f constraints));
   104 
   105 fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
   106 
   107 val is_body = #is_body o rep_data;
   108 fun set_body b = map_data (fn (_, names, fixes, binds, type_occs, constraints) =>
   109   (b, names, fixes, binds, type_occs, constraints));
   110 fun restore_body ctxt = set_body (is_body ctxt);
   111 
   112 val names_of = #names o rep_data;
   113 val fixes_of = #fixes o rep_data;
   114 val binds_of = #binds o rep_data;
   115 val type_occs_of = #type_occs o rep_data;
   116 val constraints_of = #constraints o rep_data;
   117 
   118 val is_declared = Name.is_declared o names_of;
   119 fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);
   120 fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
   121 
   122 
   123 
   124 (** declarations **)
   125 
   126 (* default sorts and types *)
   127 
   128 fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
   129 
   130 fun def_type ctxt pattern xi =
   131   let val {binds, constraints = (types, _), ...} = rep_data ctxt in
   132     (case Vartab.lookup types xi of
   133       NONE =>
   134         if pattern then NONE
   135         else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)
   136     | some => some)
   137   end;
   138 
   139 val def_sort = Vartab.lookup o #2 o constraints_of;
   140 
   141 
   142 (* names *)
   143 
   144 val declare_type_names = map_names o
   145   fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I));
   146 
   147 fun declare_names t =
   148   declare_type_names t #>
   149   map_names (fold_aterms (fn Free (x, _) => Name.declare x | _ => I) t);
   150 
   151 
   152 (* type occurrences *)
   153 
   154 val declare_type_occs = map_type_occs o fold_term_types
   155   (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
   156     | _ => fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I));
   157 
   158 
   159 (* constraints *)
   160 
   161 fun redeclare_skolems ctxt = ctxt |> map_constraints (apfst (fn types =>
   162   let
   163     fun decl (x, x') =
   164       (case default_type ctxt x' of
   165         SOME T => Vartab.update ((x, ~1), T)
   166       | NONE => I);
   167   in fold_rev decl (fixes_of ctxt) types end));
   168 
   169 fun declare_constraints t = map_constraints (fn (types, sorts) =>
   170   let
   171     val types' = fold_aterms
   172       (fn Free (x, T) => Vartab.update ((x, ~1), T)
   173         | Var v => Vartab.update v
   174         | _ => I) t types;
   175     val sorts' = fold_types (fold_atyps
   176       (fn TFree (x, S) => Vartab.update ((x, ~1), S)
   177         | TVar v => Vartab.update v
   178         | _ => I)) t sorts;
   179   in (types', sorts') end)
   180   #> declare_type_names t
   181   #> redeclare_skolems;
   182 
   183 
   184 (* common declarations *)
   185 
   186 fun declare_internal t =
   187   declare_names t #>
   188   declare_type_occs t;
   189 
   190 fun declare_term t =
   191   declare_internal t #>
   192   declare_constraints t;
   193 
   194 fun declare_thm th = fold declare_internal (Thm.full_prop_of th :: Thm.hyps_of th);
   195 fun thm_context th = declare_thm th (Context.init_proof (Thm.theory_of_thm th));
   196 
   197 
   198 (* renaming term/type frees *)
   199 
   200 fun variant_frees ctxt ts frees =
   201   let
   202     val names = names_of (fold declare_names ts ctxt);
   203     val xs = fst (Name.variants (map #1 frees) names);
   204   in xs ~~ map snd frees end;
   205 
   206 
   207 
   208 (** fixes **)
   209 
   210 local
   211 
   212 fun no_dups [] = ()
   213   | no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);
   214 
   215 fun new_fixes names' xs xs' =
   216   map_names (K names') #>
   217   map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>
   218   fold (declare_constraints o Syntax.free) xs' #>
   219   pair xs';
   220 
   221 in
   222 
   223 fun add_fixes xs ctxt =
   224   let
   225     val _ =
   226       (case filter (can Name.dest_skolem) xs of [] => ()
   227       | bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));
   228     val _ = no_dups (duplicates (op =) xs);
   229     val (ys, zs) = split_list (fixes_of ctxt);
   230     val names = names_of ctxt;
   231     val (xs', names') =
   232       if is_body ctxt then Name.variants xs names |>> map Name.skolem
   233       else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);
   234         (xs, fold Name.declare xs names));
   235   in ctxt |> new_fixes names' xs xs' end;
   236 
   237 fun invent_fixes raw_xs ctxt =
   238   let
   239     val names = names_of ctxt;
   240     val xs = map Name.clean raw_xs;
   241     val (xs', names') = Name.variants xs names |>> map Name.skolem;
   242   in ctxt |> new_fixes names' xs xs' end;
   243 
   244 end;
   245 
   246 fun invent_types Ss ctxt =
   247   let
   248     val tfrees = Name.invents (names_of ctxt) "'a" (length Ss) ~~ Ss;
   249     val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
   250   in (tfrees, ctxt') end;
   251 
   252 
   253 
   254 (** export -- generalize type/term variables **)
   255 
   256 fun export_inst inner outer =
   257   let
   258     val declared_outer = is_declared outer;
   259     val fixes_inner = fixes_of inner;
   260     val fixes_outer = fixes_of outer;
   261 
   262     val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));
   263     val still_fixed = not o member (op =) gen_fixes;
   264     val gen_fixesT =
   265       Symtab.fold (fn (a, xs) =>
   266         if declared_outer a orelse exists still_fixed xs
   267         then I else cons a) (type_occs_of inner) [];
   268   in (gen_fixesT, gen_fixes) end;
   269 
   270 fun exportT_inst inner outer = #1 (export_inst inner outer);
   271 
   272 fun exportT_terms inner outer ts =
   273   map (Term.generalize (exportT_inst (fold declare_type_occs ts inner) outer, [])
   274     (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1)) ts;
   275 
   276 fun export_terms inner outer ts =
   277   map (Term.generalize (export_inst (fold declare_type_occs ts inner) outer)
   278     (fold Term.maxidx_term ts ~1 + 1)) ts;
   279 
   280 fun gen_export inst inner outer ths =
   281   let
   282     val ths' = map Thm.adjust_maxidx_thm ths;
   283     val inner' = fold (declare_type_occs o Thm.full_prop_of) ths' inner;
   284   in map (Thm.generalize (inst inner' outer) (fold Thm.maxidx_thm ths' ~1 + 1)) ths' end;
   285 
   286 val exportT = gen_export (rpair [] oo exportT_inst);
   287 val export = gen_export export_inst;
   288 
   289 
   290 
   291 (** import -- fix schematic type/term variables **)
   292 
   293 fun importT_inst ts ctxt =
   294   let
   295     val tvars = rev (fold Term.add_tvars ts []);
   296     val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
   297   in (tvars ~~ map TFree tfrees, ctxt') end;
   298 
   299 fun import_inst is_open ts ctxt =
   300   let
   301     val ren = if is_open then I else Name.internal;
   302     val (instT, ctxt') = importT_inst ts ctxt;
   303     val vars = map (apsnd (Term.instantiateT instT)) (rev (fold Term.add_vars ts []));
   304     val (xs, ctxt'') = invent_fixes (map (ren o #1 o #1) vars) ctxt';
   305     val inst = vars ~~ map Free (xs ~~ map #2 vars);
   306   in ((instT, inst), ctxt'') end;
   307 
   308 fun importT_terms ts ctxt =
   309   let val (instT, ctxt') = importT_inst ts ctxt
   310   in (map (Term.instantiate (instT, [])) ts, ctxt') end;
   311 
   312 fun import_terms is_open ts ctxt =
   313   let val (inst, ctxt') = import_inst is_open ts ctxt
   314   in (map (Term.instantiate inst) ts, ctxt') end;
   315 
   316 fun importT ths ctxt =
   317   let
   318     val thy = Context.theory_of_proof ctxt;
   319     val certT = Thm.ctyp_of thy;
   320     val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
   321     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   322     val ths' = map (Thm.instantiate (instT', [])) ths;
   323   in ((map #2 instT', ths'), ctxt') end;
   324 
   325 fun import is_open ths ctxt =
   326   let
   327     val thy = Context.theory_of_proof ctxt;
   328     val cert = Thm.cterm_of thy;
   329     val certT = Thm.ctyp_of thy;
   330     val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
   331     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   332     val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;
   333     val ths' = map (Thm.instantiate (instT', inst')) ths;
   334   in (((map #2 instT', map #2 inst'), ths'), ctxt') end;
   335 
   336 
   337 (* import/export *)
   338 
   339 fun gen_trade imp exp ctxt f ths =
   340   let val ((_, ths'), ctxt') = imp ths ctxt
   341   in exp ctxt' ctxt (f ths') end;
   342 
   343 val tradeT = gen_trade importT exportT;
   344 val trade = gen_trade (import true) export;
   345 
   346 
   347 (* focus on outermost parameters *)
   348 
   349 fun forall_elim_prop t prop =
   350   Thm.beta_conversion false (Thm.capply (#2 (Thm.dest_comb prop)) t)
   351   |> Thm.cprop_of |> Thm.dest_comb |> #2;
   352 
   353 fun focus goal ctxt =
   354   let
   355     val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
   356     val t = Thm.term_of goal;
   357     val ps = Term.variant_frees t (Term.strip_all_vars t);   (*as they are printed :-*)
   358     val (xs, Ts) = split_list ps;
   359     val (xs', ctxt') = invent_fixes xs ctxt;
   360     val ps' = ListPair.map (cert o Free) (xs', Ts);
   361     val goal' = fold forall_elim_prop ps' goal;
   362   in ((ps', goal'), ctxt') end;
   363 
   364 
   365 (** implicit polymorphism **)
   366 
   367 (* warn_extra_tfrees *)
   368 
   369 fun warn_extra_tfrees ctxt1 ctxt2 =
   370   let
   371     fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
   372     fun occs_free a x =
   373       (case def_type ctxt1 false (x, ~1) of
   374         SOME T => if occs_typ a T then I else cons (a, x)
   375       | NONE => cons (a, x));
   376 
   377     val occs1 = type_occs_of ctxt1;
   378     val occs2 = type_occs_of ctxt2;
   379     val extras = Symtab.fold (fn (a, xs) =>
   380       if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
   381     val tfrees = map #1 extras |> sort_distinct string_ord;
   382     val frees = map #2 extras |> sort_distinct string_ord;
   383   in
   384     if null extras then ()
   385     else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
   386       space_implode " or " (map quote frees))
   387   end;
   388 
   389 
   390 (* polymorphic terms *)
   391 
   392 fun polymorphic ctxt ts =
   393   let
   394     val ctxt' = fold declare_term ts ctxt;
   395     val occs = type_occs_of ctxt;
   396     val occs' = type_occs_of ctxt';
   397     val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
   398     val idx = fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1;
   399   in map (Term.generalize (types, []) idx) ts end;
   400 
   401 fun hidden_polymorphism t T =
   402   let
   403     val tvarsT = Term.add_tvarsT T [];
   404     val extra_tvars = Term.fold_types (Term.fold_atyps
   405       (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
   406   in extra_tvars end;
   407 
   408 
   409 
   410 (** term bindings **)
   411 
   412 fun add_bind (xi, NONE) = map_binds (Vartab.delete_safe xi)
   413   | add_bind ((x, i), SOME t) =
   414       let
   415         val T = Term.fastype_of t;
   416         val t' =
   417           if null (hidden_polymorphism t T) then t
   418           else Var ((x ^ "_has_extra_type_vars_on_rhs", i), T);
   419       in declare_term t' #> map_binds (Vartab.update ((x, i), (T, t'))) end;
   420 
   421 val add_binds = fold add_bind;
   422 
   423 fun expand_binds ctxt =
   424   let
   425     val binds = binds_of ctxt;
   426     fun expand (t as Var (xi, T)) =
   427           (case Vartab.lookup binds xi of
   428             SOME u => Envir.expand_atom T u
   429           | NONE => t)
   430       | expand t = t;
   431   in Envir.beta_norm o Term.map_aterms expand end;
   432 
   433 end;