src/Pure/variable.ML
author wenzelm
Tue Nov 28 00:35:28 2006 +0100 (2006-11-28)
changeset 21571 6096c956a11f
parent 21522 bd641d927437
child 21683 b90fa6c8e062
permissions -rw-r--r--
added add_fixed;
     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 constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table
    17   val is_declared: Proof.context -> string -> bool
    18   val is_fixed: Proof.context -> string -> bool
    19   val newly_fixed: Proof.context -> Proof.context -> string -> bool
    20   val add_fixed: Proof.context -> term -> (string * typ) list -> (string * typ) list
    21   val default_type: Proof.context -> string -> typ option
    22   val def_type: Proof.context -> bool -> indexname -> typ option
    23   val def_sort: Proof.context -> indexname -> sort option
    24   val declare_constraints: term -> Proof.context -> Proof.context
    25   val declare_internal: term -> Proof.context -> Proof.context
    26   val declare_term: term -> Proof.context -> Proof.context
    27   val declare_prf: Proofterm.proof -> Proof.context -> Proof.context
    28   val declare_thm: thm -> Proof.context -> Proof.context
    29   val thm_context: thm -> Proof.context
    30   val variant_frees: Proof.context -> term list -> (string * 'a) list -> (string * 'a) list
    31   val hidden_polymorphism: term -> typ -> (indexname * sort) list
    32   val add_binds: (indexname * term option) list -> Proof.context -> Proof.context
    33   val expand_binds: Proof.context -> term -> term
    34   val add_fixes: string list -> Proof.context -> string list * Proof.context
    35   val add_fixes_direct: string list -> Proof.context -> Proof.context
    36   val auto_fixes: term -> Proof.context -> Proof.context
    37   val variant_fixes: string list -> Proof.context -> string list * Proof.context
    38   val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context
    39   val export_inst: Proof.context -> Proof.context -> string list * string list
    40   val exportT_inst: Proof.context -> Proof.context -> string list
    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: 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: 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: Proof.context -> term list -> term list
    62 end;
    63 
    64 structure Variable: VARIABLE =
    65 struct
    66 
    67 (** local context data **)
    68 
    69 datatype data = Data of
    70  {is_body: bool,                        (*inner body mode*)
    71   names: Name.context,                  (*type/term variable names*)
    72   fixes: (string * string) list,        (*term fixes -- extern/intern*)
    73   binds: (typ * term) Vartab.table,     (*term bindings*)
    74   type_occs: string list Symtab.table,  (*type variables -- possibly within term variables*)
    75   constraints:
    76     typ Vartab.table *                  (*type constraints*)
    77     sort Vartab.table};                 (*default sorts*)
    78 
    79 fun make_data (is_body, names, fixes, binds, type_occs, constraints) =
    80   Data {is_body = is_body, names = names, fixes = fixes, binds = binds,
    81     type_occs = type_occs, constraints = constraints};
    82 
    83 structure Data = ProofDataFun
    84 (
    85   val name = "Pure/variable";
    86   type T = data;
    87   fun init thy =
    88     make_data (false, Name.context, [], Vartab.empty, Symtab.empty, (Vartab.empty, Vartab.empty));
    89   fun print _ _ = ();
    90 );
    91 
    92 val _ = Context.add_setup Data.init;
    93 
    94 fun map_data f =
    95   Data.map (fn Data {is_body, names, fixes, binds, type_occs, constraints} =>
    96     make_data (f (is_body, names, fixes, binds, type_occs, constraints)));
    97 
    98 fun map_names f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
    99   (is_body, f names, fixes, binds, type_occs, constraints));
   100 
   101 fun map_fixes f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   102   (is_body, names, f fixes, binds, type_occs, constraints));
   103 
   104 fun map_binds f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   105   (is_body, names, fixes, f binds, type_occs, constraints));
   106 
   107 fun map_type_occs f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   108   (is_body, names, fixes, binds, f type_occs, constraints));
   109 
   110 fun map_constraints f = map_data (fn (is_body, names, fixes, binds, type_occs, constraints) =>
   111   (is_body, names, fixes, binds, type_occs, f constraints));
   112 
   113 fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
   114 
   115 val is_body = #is_body o rep_data;
   116 fun set_body b = map_data (fn (_, names, fixes, binds, type_occs, constraints) =>
   117   (b, names, fixes, binds, type_occs, constraints));
   118 fun restore_body ctxt = set_body (is_body ctxt);
   119 
   120 val names_of = #names o rep_data;
   121 val fixes_of = #fixes o rep_data;
   122 val binds_of = #binds o rep_data;
   123 val type_occs_of = #type_occs o rep_data;
   124 val constraints_of = #constraints o rep_data;
   125 
   126 val is_declared = Name.is_declared o names_of;
   127 fun is_fixed ctxt x = exists (fn (_, y) => x = y) (fixes_of ctxt);
   128 fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
   129 
   130 fun add_fixed ctxt = Term.fold_aterms
   131   (fn Free (x, T) => if is_fixed ctxt x then insert (op =) (x, T) else I | _ => I);
   132 
   133 
   134 
   135 (** declarations **)
   136 
   137 (* default sorts and types *)
   138 
   139 fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
   140 
   141 fun def_type ctxt pattern xi =
   142   let val {binds, constraints = (types, _), ...} = rep_data ctxt in
   143     (case Vartab.lookup types xi of
   144       NONE =>
   145         if pattern then NONE
   146         else Vartab.lookup binds xi |> Option.map (TypeInfer.polymorphicT o #1)
   147     | some => some)
   148   end;
   149 
   150 val def_sort = Vartab.lookup o #2 o constraints_of;
   151 
   152 
   153 (* names *)
   154 
   155 val declare_type_names = map_names o
   156   fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I));
   157 
   158 fun declare_names t =
   159   declare_type_names t #>
   160   map_names (fold_aterms (fn Free (x, _) => Name.declare x | _ => I) t);
   161 
   162 
   163 (* type occurrences *)
   164 
   165 val declare_type_occs = map_type_occs o fold_term_types
   166   (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
   167     | _ => fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I));
   168 
   169 
   170 (* constraints *)
   171 
   172 fun redeclare_skolems ctxt = ctxt |> map_constraints (apfst (fn types =>
   173   let
   174     fun decl (x, x') =
   175       (case default_type ctxt x' of
   176         SOME T => Vartab.update ((x, ~1), T)
   177       | NONE => I);
   178   in fold_rev decl (fixes_of ctxt) types end));
   179 
   180 fun constrain_tvar (xi, S) =
   181   if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);
   182 
   183 fun declare_constraints t = map_constraints (fn (types, sorts) =>
   184   let
   185     val types' = fold_aterms
   186       (fn Free (x, T) => Vartab.update ((x, ~1), T)
   187         | Var v => Vartab.update v
   188         | _ => I) t types;
   189     val sorts' = fold_types (fold_atyps
   190       (fn TFree (x, S) => constrain_tvar ((x, ~1), S)
   191         | TVar v => constrain_tvar v
   192         | _ => I)) t sorts;
   193   in (types', sorts') end)
   194   #> declare_type_names t
   195   #> redeclare_skolems;
   196 
   197 
   198 (* common declarations *)
   199 
   200 fun declare_internal t =
   201   declare_names t #>
   202   declare_type_occs t;
   203 
   204 fun declare_term t =
   205   declare_internal t #>
   206   declare_constraints t;
   207 
   208 val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);
   209 
   210 val declare_thm = Drule.fold_terms declare_internal;
   211 fun thm_context th = declare_thm th (ProofContext.init (Thm.theory_of_thm th));
   212 
   213 
   214 (* renaming term/type frees *)
   215 
   216 fun variant_frees ctxt ts frees =
   217   let
   218     val names = names_of (fold declare_names ts ctxt);
   219     val xs = fst (Name.variants (map #1 frees) names);
   220   in xs ~~ map snd frees end;
   221 
   222 
   223 
   224 (** term bindings **)
   225 
   226 fun hidden_polymorphism t T =
   227   let
   228     val tvarsT = Term.add_tvarsT T [];
   229     val extra_tvars = Term.fold_types (Term.fold_atyps
   230       (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
   231   in extra_tvars end;
   232 
   233 fun add_bind (xi, NONE) = map_binds (Vartab.delete_safe xi)
   234   | add_bind ((x, i), SOME t) =
   235       let
   236         val T = Term.fastype_of t;
   237         val t' =
   238           if null (hidden_polymorphism t T) then t
   239           else Var ((x ^ "_has_extra_type_vars_on_rhs", i), T);
   240       in declare_term t' #> map_binds (Vartab.update ((x, i), (T, t'))) end;
   241 
   242 val add_binds = fold add_bind;
   243 
   244 fun expand_binds ctxt =
   245   let
   246     val binds = binds_of ctxt;
   247     fun expand (t as Var (xi, T)) =
   248           (case Vartab.lookup binds xi of
   249             SOME u => Envir.expand_atom T u
   250           | NONE => t)
   251       | expand t = t;
   252   in Envir.beta_norm o Term.map_aterms expand end;
   253 
   254 
   255 
   256 (** fixes **)
   257 
   258 local
   259 
   260 fun no_dups [] = ()
   261   | no_dups dups = error ("Duplicate fixed variable(s): " ^ commas_quote dups);
   262 
   263 fun new_fixes names' xs xs' =
   264   map_names (K names') #>
   265   map_fixes (fn fixes => (rev (xs ~~ xs') @ fixes)) #>
   266   fold (declare_constraints o Syntax.free) xs' #>
   267   pair xs';
   268 
   269 in
   270 
   271 fun add_fixes xs ctxt =
   272   let
   273     val _ =
   274       (case filter (can Name.dest_skolem) xs of [] => ()
   275       | bads => error ("Illegal internal Skolem constant(s): " ^ commas_quote bads));
   276     val _ = no_dups (duplicates (op =) xs);
   277     val (ys, zs) = split_list (fixes_of ctxt);
   278     val names = names_of ctxt;
   279     val (xs', names') =
   280       if is_body ctxt then Name.variants xs names |>> map Name.skolem
   281       else (no_dups (xs inter_string ys); no_dups (xs inter_string zs);
   282         (xs, fold Name.declare xs names));
   283   in ctxt |> new_fixes names' xs xs' end;
   284 
   285 fun variant_fixes raw_xs ctxt =
   286   let
   287     val names = names_of ctxt;
   288     val xs = map Name.clean raw_xs;
   289     val (xs', names') = Name.variants xs names |>> map Name.skolem;
   290   in ctxt |> new_fixes names' xs xs' end;
   291 
   292 end;
   293 
   294 
   295 fun add_fixes_direct xs ctxt = ctxt
   296   |> set_body false
   297   |> (snd o add_fixes xs)
   298   |> restore_body ctxt;
   299 
   300 fun fix_frees t ctxt = ctxt
   301   |> add_fixes_direct
   302       (rev (fold_aterms (fn Free (x, _) =>
   303         if is_fixed ctxt x then I else insert (op =) x | _ => I) t []));
   304 
   305 fun auto_fixes t ctxt =
   306   (if is_body ctxt then ctxt else fix_frees t ctxt)
   307   |> declare_term t;
   308 
   309 fun invent_types Ss ctxt =
   310   let
   311     val tfrees = Name.invents (names_of ctxt) "'a" (length Ss) ~~ Ss;
   312     val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
   313   in (tfrees, ctxt') end;
   314 
   315 
   316 
   317 (** export -- generalize type/term variables **)
   318 
   319 fun export_inst inner outer =
   320   let
   321     val declared_outer = is_declared outer;
   322     val fixes_inner = fixes_of inner;
   323     val fixes_outer = fixes_of outer;
   324 
   325     val gen_fixes = map #2 (Library.take (length fixes_inner - length fixes_outer, fixes_inner));
   326     val still_fixed = not o member (op =) gen_fixes;
   327     val gen_fixesT =
   328       Symtab.fold (fn (a, xs) =>
   329         if declared_outer a orelse exists still_fixed xs
   330         then I else cons a) (type_occs_of inner) [];
   331   in (gen_fixesT, gen_fixes) end;
   332 
   333 fun exportT_inst inner outer = #1 (export_inst inner outer);
   334 
   335 fun exportT_terms inner outer ts =
   336   map (TermSubst.generalize (exportT_inst (fold declare_type_occs ts inner) outer, [])
   337     (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1)) ts;
   338 
   339 fun export_terms inner outer ts =
   340   map (TermSubst.generalize (export_inst (fold declare_type_occs ts inner) outer)
   341     (fold Term.maxidx_term ts ~1 + 1)) ts;
   342 
   343 fun export_prf inner outer prf =
   344   let
   345     val insts = export_inst (declare_prf prf inner) outer;
   346     val idx = Proofterm.maxidx_proof prf ~1 + 1;
   347     val gen_term = TermSubst.generalize_option insts idx;
   348     val gen_typ = TermSubst.generalizeT_option (#1 insts) idx;
   349   in Proofterm.map_proof_terms_option gen_term gen_typ prf end;
   350 
   351 fun gen_export inst inner outer ths =
   352   let
   353     val inner' = fold (declare_type_occs o Thm.full_prop_of) ths inner;
   354   in map (Thm.generalize (inst inner' outer) (fold Thm.maxidx_thm ths ~1 + 1)) ths end;
   355 
   356 val exportT = gen_export (rpair [] oo exportT_inst);
   357 val export = gen_export export_inst;
   358 
   359 fun export_morphism inner outer =
   360   let
   361     val fact = export inner outer;
   362     val term = singleton (export_terms inner outer);
   363     val typ = Logic.type_map term;
   364   in Morphism.morphism {name = I, var = I, typ = typ, term = term, fact = fact} end;
   365 
   366 
   367 (** import -- fix schematic type/term variables **)
   368 
   369 fun importT_inst ts ctxt =
   370   let
   371     val tvars = rev (fold Term.add_tvars ts []);
   372     val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
   373   in (tvars ~~ map TFree tfrees, ctxt') end;
   374 
   375 fun import_inst is_open ts ctxt =
   376   let
   377     val ren = if is_open then I else Name.internal;
   378     val (instT, ctxt') = importT_inst ts ctxt;
   379     val vars = map (apsnd (TermSubst.instantiateT instT)) (rev (fold Term.add_vars ts []));
   380     val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';
   381     val inst = vars ~~ map Free (xs ~~ map #2 vars);
   382   in ((instT, inst), ctxt'') end;
   383 
   384 fun importT_terms ts ctxt =
   385   let val (instT, ctxt') = importT_inst ts ctxt
   386   in (map (TermSubst.instantiate (instT, [])) ts, ctxt') end;
   387 
   388 fun import_terms is_open ts ctxt =
   389   let val (inst, ctxt') = import_inst is_open ts ctxt
   390   in (map (TermSubst.instantiate inst) ts, ctxt') end;
   391 
   392 fun importT ths ctxt =
   393   let
   394     val thy = ProofContext.theory_of ctxt;
   395     val certT = Thm.ctyp_of thy;
   396     val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
   397     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   398     val ths' = map (Thm.instantiate (instT', [])) ths;
   399   in ((map #2 instT', ths'), ctxt') end;
   400 
   401 fun import_prf is_open prf ctxt =
   402   let
   403     val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);
   404     val (insts, ctxt') = import_inst is_open ts ctxt;
   405   in (Proofterm.instantiate insts prf, ctxt') end;
   406 
   407 fun import is_open ths ctxt =
   408   let
   409     val thy = ProofContext.theory_of ctxt;
   410     val cert = Thm.cterm_of thy;
   411     val certT = Thm.ctyp_of thy;
   412     val ((instT, inst), ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
   413     val instT' = map (fn (v, T) => (certT (TVar v), certT T)) instT;
   414     val inst' = map (fn (v, t) => (cert (Var v), cert t)) inst;
   415     val ths' = map (Thm.instantiate (instT', inst')) ths;
   416   in (((map #2 instT', map #2 inst'), ths'), ctxt') end;
   417 
   418 
   419 (* import/export *)
   420 
   421 fun gen_trade imp exp f ctxt ths =
   422   let val ((_, ths'), ctxt') = imp ths ctxt
   423   in exp ctxt' ctxt (f ctxt' ths') end;
   424 
   425 val tradeT = gen_trade importT exportT;
   426 val trade = gen_trade (import true) export;
   427 
   428 
   429 (* focus on outermost parameters *)
   430 
   431 fun forall_elim_prop t prop =
   432   Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)
   433   |> Thm.cprop_of |> Thm.dest_arg;
   434 
   435 fun focus goal ctxt =
   436   let
   437     val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
   438     val t = Thm.term_of goal;
   439     val ps = Term.variant_frees t (Term.strip_all_vars t);   (*as they are printed :-*)
   440     val (xs, Ts) = split_list ps;
   441     val (xs', ctxt') = variant_fixes xs ctxt;
   442     val ps' = ListPair.map (cert o Free) (xs', Ts);
   443     val goal' = fold forall_elim_prop ps' goal;
   444   in ((ps', goal'), ctxt') end;
   445 
   446 fun focus_subgoal i st =
   447   let
   448     val all_vars = Drule.fold_terms Term.add_vars st [];
   449     val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;
   450   in
   451     add_binds no_binds #>
   452     fold (declare_constraints o Var) all_vars #>
   453     focus (Thm.cprem_of st i)
   454   end;
   455 
   456 
   457 
   458 (** implicit polymorphism **)
   459 
   460 (* warn_extra_tfrees *)
   461 
   462 fun warn_extra_tfrees ctxt1 ctxt2 =
   463   let
   464     fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
   465     fun occs_free a x =
   466       (case def_type ctxt1 false (x, ~1) of
   467         SOME T => if occs_typ a T then I else cons (a, x)
   468       | NONE => cons (a, x));
   469 
   470     val occs1 = type_occs_of ctxt1;
   471     val occs2 = type_occs_of ctxt2;
   472     val extras = Symtab.fold (fn (a, xs) =>
   473       if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
   474     val tfrees = map #1 extras |> sort_distinct string_ord;
   475     val frees = map #2 extras |> sort_distinct string_ord;
   476   in
   477     if null extras then ()
   478     else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
   479       space_implode " or " (map quote frees))
   480   end;
   481 
   482 
   483 (* polymorphic terms *)
   484 
   485 fun polymorphic ctxt ts =
   486   let
   487     val ctxt' = fold declare_term ts ctxt;
   488     val occs = type_occs_of ctxt;
   489     val occs' = type_occs_of ctxt';
   490     val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
   491     val idx = fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1;
   492   in map (TermSubst.generalize (types, []) idx) ts end;
   493 
   494 end;