src/Pure/Isar/rule_insts.ML
author haftmann
Thu Dec 04 14:43:33 2008 +0100 (2008-12-04)
changeset 28965 1de908189869
parent 28083 103d9282a946
child 29606 fedb8be05f24
permissions -rw-r--r--
cleaned up binding module and related code
     1 (*  Title:      Pure/Isar/rule_insts.ML
     2     ID:         $Id$
     3     Author:     Makarius
     4 
     5 Rule instantiations -- operations within a rule/subgoal context.
     6 *)
     7 
     8 signature BASIC_RULE_INSTS =
     9 sig
    10   val read_instantiate: Proof.context -> (indexname * string) list -> thm -> thm
    11   val instantiate_tac: Proof.context -> (indexname * string) list -> tactic
    12   val res_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    13   val eres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    14   val cut_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    15   val forw_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    16   val dres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    17   val thin_tac: Proof.context -> string -> int -> tactic
    18   val subgoal_tac: Proof.context -> string -> int -> tactic
    19   val subgoals_tac: Proof.context -> string list -> int -> tactic
    20 end;
    21 
    22 signature RULE_INSTS =
    23 sig
    24   include BASIC_RULE_INSTS
    25   val make_elim_preserve: thm -> thm
    26 end;
    27 
    28 structure RuleInsts: RULE_INSTS =
    29 struct
    30 
    31 structure T = OuterLex;
    32 structure P = OuterParse;
    33 
    34 
    35 (** reading instantiations **)
    36 
    37 local
    38 
    39 fun is_tvar (x, _) = String.isPrefix "'" x;
    40 
    41 fun error_var msg xi = error (msg ^ Term.string_of_vname xi);
    42 
    43 fun the_sort tvars xi = the (AList.lookup (op =) tvars xi)
    44   handle Option.Option => error_var "No such type variable in theorem: " xi;
    45 
    46 fun the_type vars xi = the (AList.lookup (op =) vars xi)
    47   handle Option.Option => error_var "No such variable in theorem: " xi;
    48 
    49 fun unify_vartypes thy vars (xi, u) (unifier, maxidx) =
    50   let
    51     val T = the_type vars xi;
    52     val U = Term.fastype_of u;
    53     val maxidx' = Term.maxidx_term u (Int.max (#2 xi, maxidx));
    54   in
    55     Sign.typ_unify thy (T, U) (unifier, maxidx')
    56       handle Type.TUNIFY => error_var "Incompatible type for instantiation of " xi
    57   end;
    58 
    59 fun instantiate inst =
    60   TermSubst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>
    61   Envir.beta_norm;
    62 
    63 fun make_instT f v =
    64   let
    65     val T = TVar v;
    66     val T' = f T;
    67   in if T = T' then NONE else SOME (T, T') end;
    68 
    69 fun make_inst f v =
    70   let
    71     val t = Var v;
    72     val t' = f t;
    73   in if t aconv t' then NONE else SOME (t, t') end;
    74 
    75 val add_used =
    76   (Thm.fold_terms o fold_types o fold_atyps)
    77     (fn TFree (a, _) => insert (op =) a
    78       | TVar ((a, _), _) => insert (op =) a
    79       | _ => I);
    80 
    81 in
    82 
    83 fun read_termTs ctxt schematic ss Ts =
    84   let
    85     fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
    86     val ts = map2 parse Ts ss;
    87     val ts' =
    88       map2 (TypeInfer.constrain o TypeInfer.paramify_vars) Ts ts
    89       |> Syntax.check_terms ((schematic ? ProofContext.set_mode ProofContext.mode_schematic) ctxt)
    90       |> Variable.polymorphic ctxt;
    91     val Ts' = map Term.fastype_of ts';
    92     val tyenv = fold Type.raw_match (Ts ~~ Ts') Vartab.empty;
    93   in (ts', map (apsnd snd) (Vartab.dest tyenv)) end;
    94 
    95 fun read_insts ctxt mixed_insts (tvars, vars) =
    96   let
    97     val thy = ProofContext.theory_of ctxt;
    98     val cert = Thm.cterm_of thy;
    99     val certT = Thm.ctyp_of thy;
   100 
   101     val (type_insts, term_insts) = List.partition (is_tvar o fst) mixed_insts;
   102     val internal_insts = term_insts |> map_filter
   103       (fn (xi, T.Term t) => SOME (xi, t)
   104         | (_, T.Text _) => NONE
   105         | (xi, _) => error_var "Term argument expected for " xi);
   106     val external_insts = term_insts |> map_filter
   107       (fn (xi, T.Text s) => SOME (xi, s) | _ => NONE);
   108 
   109 
   110     (* mixed type instantiations *)
   111 
   112     fun readT (xi, arg) =
   113       let
   114         val S = the_sort tvars xi;
   115         val T =
   116           (case arg of
   117             T.Text s => Syntax.read_typ ctxt s
   118           | T.Typ T => T
   119           | _ => error_var "Type argument expected for " xi);
   120       in
   121         if Sign.of_sort thy (T, S) then ((xi, S), T)
   122         else error_var "Incompatible sort for typ instantiation of " xi
   123       end;
   124 
   125     val type_insts1 = map readT type_insts;
   126     val instT1 = TermSubst.instantiateT type_insts1;
   127     val vars1 = map (apsnd instT1) vars;
   128 
   129 
   130     (* internal term instantiations *)
   131 
   132     val instT2 = Envir.norm_type
   133       (#1 (fold (unify_vartypes thy vars1) internal_insts (Vartab.empty, 0)));
   134     val vars2 = map (apsnd instT2) vars1;
   135     val internal_insts2 = map (apsnd (map_types instT2)) internal_insts;
   136     val inst2 = instantiate internal_insts2;
   137 
   138 
   139     (* external term instantiations *)
   140 
   141     val (xs, strs) = split_list external_insts;
   142     val Ts = map (the_type vars2) xs;
   143     val (ts, inferred) = read_termTs ctxt false strs Ts;
   144 
   145     val instT3 = Term.typ_subst_TVars inferred;
   146     val vars3 = map (apsnd instT3) vars2;
   147     val internal_insts3 = map (apsnd (map_types instT3)) internal_insts2;
   148     val external_insts3 = xs ~~ ts;
   149     val inst3 = instantiate external_insts3;
   150 
   151 
   152     (* results *)
   153 
   154     val type_insts3 = map (fn ((a, _), T) => (a, instT3 (instT2 T))) type_insts1;
   155     val term_insts3 = internal_insts3 @ external_insts3;
   156 
   157     val inst_tvars = map_filter (make_instT (instT3 o instT2 o instT1)) tvars;
   158     val inst_vars = map_filter (make_inst (inst3 o inst2)) vars3;
   159   in
   160     ((type_insts3, term_insts3),
   161       (map (pairself certT) inst_tvars, map (pairself cert) inst_vars))
   162   end;
   163 
   164 fun read_instantiate_mixed ctxt mixed_insts thm =
   165   let
   166     val ctxt' = ctxt |> Variable.declare_thm thm
   167       |> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []);  (* FIXME tmp *)
   168     val tvars = Thm.fold_terms Term.add_tvars thm [];
   169     val vars = Thm.fold_terms Term.add_vars thm [];
   170     val ((type_insts, term_insts), insts) = read_insts ctxt' (map snd mixed_insts) (tvars, vars);
   171 
   172     val _ = (*assign internalized values*)
   173       mixed_insts |> List.app (fn (arg, (xi, _)) =>
   174         if is_tvar xi then
   175           T.assign (SOME (T.Typ (the (AList.lookup (op =) type_insts xi)))) arg
   176         else
   177           T.assign (SOME (T.Term (the (AList.lookup (op =) term_insts xi)))) arg);
   178   in
   179     Drule.instantiate insts thm |> RuleCases.save thm
   180   end;
   181 
   182 fun read_instantiate_mixed' ctxt (args, concl_args) thm =
   183   let
   184     fun zip_vars _ [] = []
   185       | zip_vars (_ :: xs) ((_, NONE) :: rest) = zip_vars xs rest
   186       | zip_vars ((x, _) :: xs) ((arg, SOME t) :: rest) = (arg, (x, t)) :: zip_vars xs rest
   187       | zip_vars [] _ = error "More instantiations than variables in theorem";
   188     val insts =
   189       zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
   190       zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;
   191   in read_instantiate_mixed ctxt insts thm end;
   192 
   193 end;
   194 
   195 
   196 (* instantiation of rule or goal state *)
   197 
   198 fun read_instantiate ctxt args thm =
   199   read_instantiate_mixed (ctxt |> ProofContext.set_mode ProofContext.mode_schematic)  (* FIXME !? *)
   200     (map (fn (x, y) => (T.eof, (x, T.Text y))) args) thm;
   201 
   202 fun instantiate_tac ctxt args = PRIMITIVE (read_instantiate ctxt args);
   203 
   204 
   205 
   206 (** attributes **)
   207 
   208 (* where: named instantiation *)
   209 
   210 local
   211 
   212 val value =
   213   Args.internal_typ >> T.Typ ||
   214   Args.internal_term >> T.Term ||
   215   Args.name_source >> T.Text;
   216 
   217 val inst = Args.var -- (Args.$$$ "=" |-- Scan.ahead P.not_eof -- value)
   218   >> (fn (xi, (a, v)) => (a, (xi, v)));
   219 
   220 in
   221 
   222 val where_att = Attrib.syntax (Scan.lift (P.and_list inst) >> (fn args =>
   223   Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args)));
   224 
   225 end;
   226 
   227 
   228 (* of: positional instantiation (terms only) *)
   229 
   230 local
   231 
   232 val value =
   233   Args.internal_term >> T.Term ||
   234   Args.name_source >> T.Text;
   235 
   236 val inst = Scan.ahead P.not_eof -- Args.maybe value;
   237 val concl = Args.$$$ "concl" -- Args.colon;
   238 
   239 val insts =
   240   Scan.repeat (Scan.unless concl inst) --
   241   Scan.optional (concl |-- Scan.repeat inst) [];
   242 
   243 in
   244 
   245 val of_att = Attrib.syntax (Scan.lift insts >> (fn args =>
   246   Thm.rule_attribute (fn context => read_instantiate_mixed' (Context.proof_of context) args)));
   247 
   248 end;
   249 
   250 
   251 (* setup *)
   252 
   253 val _ = Context.>> (Context.map_theory
   254   (Attrib.add_attributes
   255    [("where", where_att, "named instantiation of theorem"),
   256     ("of", of_att, "positional instantiation of theorem")]));
   257 
   258 
   259 
   260 (** tactics **)
   261 
   262 (* resolution after lifting and instantation; may refer to parameters of the subgoal *)
   263 
   264 (* FIXME cleanup this mess!!! *)
   265 
   266 fun bires_inst_tac bires_flag ctxt insts thm =
   267   let
   268     val thy = ProofContext.theory_of ctxt;
   269     (* Separate type and term insts *)
   270     fun has_type_var ((x, _), _) = (case Symbol.explode x of
   271           "'"::cs => true | cs => false);
   272     val Tinsts = List.filter has_type_var insts;
   273     val tinsts = filter_out has_type_var insts;
   274 
   275     (* Tactic *)
   276     fun tac i st =
   277       let
   278         val (_, _, Bi, _) = Thm.dest_state (st, i);
   279         val params = Logic.strip_params Bi;  (*params of subgoal i as string typ pairs*)
   280         val params = rev (Term.rename_wrt_term Bi params)
   281           (*as they are printed: bound variables with*)
   282           (*the same name are renamed during printing*)
   283 
   284         val (param_names, ctxt') = ctxt
   285           |> Variable.declare_thm thm
   286           |> Thm.fold_terms Variable.declare_constraints st
   287           |> ProofContext.add_fixes_i (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params);
   288 
   289         (* Process type insts: Tinsts_env *)
   290         fun absent xi = error
   291               ("No such variable in theorem: " ^ Term.string_of_vname xi);
   292         val (rtypes, rsorts) = Drule.types_sorts thm;
   293         fun readT (xi, s) =
   294             let val S = case rsorts xi of SOME S => S | NONE => absent xi;
   295                 val T = Syntax.read_typ ctxt' s;
   296                 val U = TVar (xi, S);
   297             in if Sign.typ_instance thy (T, U) then (U, T)
   298                else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails")
   299             end;
   300         val Tinsts_env = map readT Tinsts;
   301         (* Preprocess rule: extract vars and their types, apply Tinsts *)
   302         fun get_typ xi =
   303           (case rtypes xi of
   304                SOME T => typ_subst_atomic Tinsts_env T
   305              | NONE => absent xi);
   306         val (xis, ss) = Library.split_list tinsts;
   307         val Ts = map get_typ xis;
   308 
   309         val (ts, envT) = read_termTs ctxt' true ss Ts;
   310         val envT' = map (fn (ixn, T) =>
   311           (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;
   312         val cenv =
   313           map
   314             (fn (xi, t) =>
   315               pairself (Thm.cterm_of thy) (Var (xi, fastype_of t), t))
   316             (distinct
   317               (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
   318               (xis ~~ ts));
   319         (* Lift and instantiate rule *)
   320         val {maxidx, ...} = rep_thm st;
   321         val paramTs = map #2 params
   322         and inc = maxidx+1
   323         fun liftvar (Var ((a,j), T)) =
   324               Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)
   325           | liftvar t = raise TERM("Variable expected", [t]);
   326         fun liftterm t = list_abs_free
   327               (param_names ~~ paramTs, Logic.incr_indexes(paramTs,inc) t)
   328         fun liftpair (cv,ct) =
   329               (cterm_fun liftvar cv, cterm_fun liftterm ct)
   330         val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);
   331         val rule = Drule.instantiate
   332               (map lifttvar envT', map liftpair cenv)
   333               (Thm.lift_rule (Thm.cprem_of st i) thm)
   334       in
   335         if i > nprems_of st then no_tac st
   336         else st |>
   337           compose_tac (bires_flag, rule, nprems_of thm) i
   338       end
   339            handle TERM (msg,_)   => (warning msg; no_tac st)
   340                 | THM  (msg,_,_) => (warning msg; no_tac st);
   341   in tac end;
   342 
   343 val res_inst_tac = bires_inst_tac false;
   344 val eres_inst_tac = bires_inst_tac true;
   345 
   346 
   347 (* forward resolution *)
   348 
   349 fun make_elim_preserve rl =
   350   let
   351     val cert = Thm.cterm_of (Thm.theory_of_thm rl);
   352     val maxidx = Thm.maxidx_of rl;
   353     fun cvar xi = cert (Var (xi, propT));
   354     val revcut_rl' =
   355       instantiate ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),
   356         (cvar ("W", 0), cvar ("W", maxidx + 1))]) Drule.revcut_rl;
   357   in
   358     (case Seq.list_of (bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of
   359       [th] => th
   360     | _ => raise THM ("make_elim_preserve", 1, [rl]))
   361   end;
   362 
   363 (*instantiate and cut -- for atomic fact*)
   364 fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule);
   365 
   366 (*forward tactic applies a rule to an assumption without deleting it*)
   367 fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac;
   368 
   369 (*dresolve tactic applies a rule to replace an assumption*)
   370 fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve rule);
   371 
   372 
   373 (* derived tactics *)
   374 
   375 (*deletion of an assumption*)
   376 fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl;
   377 
   378 (*Introduce the given proposition as lemma and subgoal*)
   379 fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl;
   380 fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As);
   381 
   382 
   383 
   384 (** methods **)
   385 
   386 (* rule_tac etc. -- refer to dynamic goal state! *)
   387 
   388 local
   389 
   390 fun gen_inst _ tac _ (quant, ([], thms)) =
   391       Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac thms))
   392   | gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =
   393       Method.METHOD (fn facts =>
   394         quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm))
   395   | gen_inst _ _ _ _ = error "Cannot have instantiations with multiple rules";
   396 
   397 in
   398 
   399 val res_inst_meth = gen_inst res_inst_tac Tactic.resolve_tac;
   400 val eres_inst_meth = gen_inst eres_inst_tac Tactic.eresolve_tac;
   401 val cut_inst_meth = gen_inst cut_inst_tac Tactic.cut_rules_tac;
   402 val dres_inst_meth = gen_inst dres_inst_tac Tactic.dresolve_tac;
   403 val forw_inst_meth = gen_inst forw_inst_tac Tactic.forward_tac;
   404 
   405 end;
   406 
   407 
   408 (* method syntax *)
   409 
   410 val insts =
   411   Scan.optional (Scan.lift
   412     (P.and_list1 (Args.name -- (Args.$$$ "=" |-- P.!!! Args.name_source)) --| Args.$$$ "in")) []
   413     -- Attrib.thms;
   414 
   415 fun inst_args f src ctxt =
   416   f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));
   417 
   418 val insts_var =
   419   Scan.optional (Scan.lift
   420     (P.and_list1 (Args.var -- (Args.$$$ "=" |-- P.!!! Args.name_source)) --| Args.$$$ "in")) []
   421     -- Attrib.thms;
   422 
   423 fun inst_args_var f src ctxt =
   424   f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));
   425 
   426 
   427 (* setup *)
   428 
   429 val _ = Context.>> (Context.map_theory
   430   (Method.add_methods
   431    [("rule_tac", inst_args_var res_inst_meth,
   432       "apply rule (dynamic instantiation)"),
   433     ("erule_tac", inst_args_var eres_inst_meth,
   434       "apply rule in elimination manner (dynamic instantiation)"),
   435     ("drule_tac", inst_args_var dres_inst_meth,
   436       "apply rule in destruct manner (dynamic instantiation)"),
   437     ("frule_tac", inst_args_var forw_inst_meth,
   438       "apply rule in forward manner (dynamic instantiation)"),
   439     ("cut_tac", inst_args_var cut_inst_meth,
   440       "cut rule (dynamic instantiation)"),
   441     ("subgoal_tac", Method.goal_args_ctxt (Scan.repeat1 Args.name_source) subgoals_tac,
   442       "insert subgoal (dynamic instantiation)"),
   443     ("thin_tac", Method.goal_args_ctxt Args.name_source thin_tac,
   444       "remove premise (dynamic instantiation)")]));
   445 
   446 end;
   447 
   448 structure BasicRuleInsts: BASIC_RULE_INSTS = RuleInsts;
   449 open BasicRuleInsts;