src/Pure/Isar/rule_insts.ML
author wenzelm
Sun Mar 15 15:59:44 2009 +0100 (2009-03-15)
changeset 30528 7173bf123335
parent 30515 bca05b17b618
child 30545 8209a7196389
permissions -rw-r--r--
simplified attribute setup;
     1 (*  Title:      Pure/Isar/rule_insts.ML
     2     Author:     Makarius
     3 
     4 Rule instantiations -- operations within a rule/subgoal context.
     5 *)
     6 
     7 signature BASIC_RULE_INSTS =
     8 sig
     9   val read_instantiate: Proof.context -> (indexname * string) list -> thm -> thm
    10   val instantiate_tac: Proof.context -> (indexname * string) list -> tactic
    11   val res_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    12   val eres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    13   val cut_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    14   val forw_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    15   val dres_inst_tac: Proof.context -> (indexname * string) list -> thm -> int -> tactic
    16   val thin_tac: Proof.context -> string -> int -> tactic
    17   val subgoal_tac: Proof.context -> string -> int -> tactic
    18   val subgoals_tac: Proof.context -> string list -> int -> tactic
    19 end;
    20 
    21 signature RULE_INSTS =
    22 sig
    23   include BASIC_RULE_INSTS
    24   val make_elim_preserve: thm -> thm
    25 end;
    26 
    27 structure RuleInsts: RULE_INSTS =
    28 struct
    29 
    30 structure T = OuterLex;
    31 structure P = OuterParse;
    32 
    33 
    34 (** reading instantiations **)
    35 
    36 local
    37 
    38 fun is_tvar (x, _) = String.isPrefix "'" x;
    39 
    40 fun error_var msg xi = error (msg ^ Term.string_of_vname xi);
    41 
    42 fun the_sort tvars xi = the (AList.lookup (op =) tvars xi)
    43   handle Option.Option => error_var "No such type variable in theorem: " xi;
    44 
    45 fun the_type vars xi = the (AList.lookup (op =) vars xi)
    46   handle Option.Option => error_var "No such variable in theorem: " xi;
    47 
    48 fun unify_vartypes thy vars (xi, u) (unifier, maxidx) =
    49   let
    50     val T = the_type vars xi;
    51     val U = Term.fastype_of u;
    52     val maxidx' = Term.maxidx_term u (Int.max (#2 xi, maxidx));
    53   in
    54     Sign.typ_unify thy (T, U) (unifier, maxidx')
    55       handle Type.TUNIFY => error_var "Incompatible type for instantiation of " xi
    56   end;
    57 
    58 fun instantiate inst =
    59   TermSubst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>
    60   Envir.beta_norm;
    61 
    62 fun make_instT f v =
    63   let
    64     val T = TVar v;
    65     val T' = f T;
    66   in if T = T' then NONE else SOME (T, T') end;
    67 
    68 fun make_inst f v =
    69   let
    70     val t = Var v;
    71     val t' = f t;
    72   in if t aconv t' then NONE else SOME (t, t') end;
    73 
    74 val add_used =
    75   (Thm.fold_terms o fold_types o fold_atyps)
    76     (fn TFree (a, _) => insert (op =) a
    77       | TVar ((a, _), _) => insert (op =) a
    78       | _ => I);
    79 
    80 in
    81 
    82 fun read_termTs ctxt schematic ss Ts =
    83   let
    84     fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
    85     val ts = map2 parse Ts ss;
    86     val ts' =
    87       map2 (TypeInfer.constrain o TypeInfer.paramify_vars) Ts ts
    88       |> Syntax.check_terms ((schematic ? ProofContext.set_mode ProofContext.mode_schematic) ctxt)
    89       |> Variable.polymorphic ctxt;
    90     val Ts' = map Term.fastype_of ts';
    91     val tyenv = fold Type.raw_match (Ts ~~ Ts') Vartab.empty;
    92   in (ts', map (apsnd snd) (Vartab.dest tyenv)) end;
    93 
    94 fun read_insts ctxt mixed_insts (tvars, vars) =
    95   let
    96     val thy = ProofContext.theory_of ctxt;
    97     val cert = Thm.cterm_of thy;
    98     val certT = Thm.ctyp_of thy;
    99 
   100     val (type_insts, term_insts) = List.partition (is_tvar o fst) mixed_insts;
   101     val internal_insts = term_insts |> map_filter
   102       (fn (xi, T.Term t) => SOME (xi, t)
   103         | (_, T.Text _) => NONE
   104         | (xi, _) => error_var "Term argument expected for " xi);
   105     val external_insts = term_insts |> map_filter
   106       (fn (xi, T.Text s) => SOME (xi, s) | _ => NONE);
   107 
   108 
   109     (* mixed type instantiations *)
   110 
   111     fun readT (xi, arg) =
   112       let
   113         val S = the_sort tvars xi;
   114         val T =
   115           (case arg of
   116             T.Text s => Syntax.read_typ ctxt s
   117           | T.Typ T => T
   118           | _ => error_var "Type argument expected for " xi);
   119       in
   120         if Sign.of_sort thy (T, S) then ((xi, S), T)
   121         else error_var "Incompatible sort for typ instantiation of " xi
   122       end;
   123 
   124     val type_insts1 = map readT type_insts;
   125     val instT1 = TermSubst.instantiateT type_insts1;
   126     val vars1 = map (apsnd instT1) vars;
   127 
   128 
   129     (* internal term instantiations *)
   130 
   131     val instT2 = Envir.norm_type
   132       (#1 (fold (unify_vartypes thy vars1) internal_insts (Vartab.empty, 0)));
   133     val vars2 = map (apsnd instT2) vars1;
   134     val internal_insts2 = map (apsnd (map_types instT2)) internal_insts;
   135     val inst2 = instantiate internal_insts2;
   136 
   137 
   138     (* external term instantiations *)
   139 
   140     val (xs, strs) = split_list external_insts;
   141     val Ts = map (the_type vars2) xs;
   142     val (ts, inferred) = read_termTs ctxt false strs Ts;
   143 
   144     val instT3 = Term.typ_subst_TVars inferred;
   145     val vars3 = map (apsnd instT3) vars2;
   146     val internal_insts3 = map (apsnd (map_types instT3)) internal_insts2;
   147     val external_insts3 = xs ~~ ts;
   148     val inst3 = instantiate external_insts3;
   149 
   150 
   151     (* results *)
   152 
   153     val type_insts3 = map (fn ((a, _), T) => (a, instT3 (instT2 T))) type_insts1;
   154     val term_insts3 = internal_insts3 @ external_insts3;
   155 
   156     val inst_tvars = map_filter (make_instT (instT3 o instT2 o instT1)) tvars;
   157     val inst_vars = map_filter (make_inst (inst3 o inst2)) vars3;
   158   in
   159     ((type_insts3, term_insts3),
   160       (map (pairself certT) inst_tvars, map (pairself cert) inst_vars))
   161   end;
   162 
   163 fun read_instantiate_mixed ctxt mixed_insts thm =
   164   let
   165     val ctxt' = ctxt |> Variable.declare_thm thm
   166       |> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []);  (* FIXME tmp *)
   167     val tvars = Thm.fold_terms Term.add_tvars thm [];
   168     val vars = Thm.fold_terms Term.add_vars thm [];
   169     val ((type_insts, term_insts), insts) = read_insts ctxt' (map snd mixed_insts) (tvars, vars);
   170 
   171     val _ = (*assign internalized values*)
   172       mixed_insts |> List.app (fn (arg, (xi, _)) =>
   173         if is_tvar xi then
   174           T.assign (SOME (T.Typ (the (AList.lookup (op =) type_insts xi)))) arg
   175         else
   176           T.assign (SOME (T.Term (the (AList.lookup (op =) term_insts xi)))) arg);
   177   in
   178     Drule.instantiate insts thm |> RuleCases.save thm
   179   end;
   180 
   181 fun read_instantiate_mixed' ctxt (args, concl_args) thm =
   182   let
   183     fun zip_vars _ [] = []
   184       | zip_vars (_ :: xs) ((_, NONE) :: rest) = zip_vars xs rest
   185       | zip_vars ((x, _) :: xs) ((arg, SOME t) :: rest) = (arg, (x, t)) :: zip_vars xs rest
   186       | zip_vars [] _ = error "More instantiations than variables in theorem";
   187     val insts =
   188       zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
   189       zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;
   190   in read_instantiate_mixed ctxt insts thm end;
   191 
   192 end;
   193 
   194 
   195 (* instantiation of rule or goal state *)
   196 
   197 fun read_instantiate ctxt args thm =
   198   read_instantiate_mixed (ctxt |> ProofContext.set_mode ProofContext.mode_schematic)  (* FIXME !? *)
   199     (map (fn (x, y) => (T.eof, (x, T.Text y))) args) thm;
   200 
   201 fun instantiate_tac ctxt args = PRIMITIVE (read_instantiate ctxt args);
   202 
   203 
   204 
   205 (** attributes **)
   206 
   207 (* where: named instantiation *)
   208 
   209 local
   210 
   211 val value =
   212   Args.internal_typ >> T.Typ ||
   213   Args.internal_term >> T.Term ||
   214   Args.name_source >> T.Text;
   215 
   216 val inst = Args.var -- (Args.$$$ "=" |-- Scan.ahead P.not_eof -- value)
   217   >> (fn (xi, (a, v)) => (a, (xi, v)));
   218 
   219 in
   220 
   221 fun where_att x = (Scan.lift (P.and_list inst) >> (fn args =>
   222   Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args))) x;
   223 
   224 end;
   225 
   226 
   227 (* of: positional instantiation (terms only) *)
   228 
   229 local
   230 
   231 val value =
   232   Args.internal_term >> T.Term ||
   233   Args.name_source >> T.Text;
   234 
   235 val inst = Scan.ahead P.not_eof -- Args.maybe value;
   236 val concl = Args.$$$ "concl" -- Args.colon;
   237 
   238 val insts =
   239   Scan.repeat (Scan.unless concl inst) --
   240   Scan.optional (concl |-- Scan.repeat inst) [];
   241 
   242 in
   243 
   244 fun of_att x = (Scan.lift insts >> (fn args =>
   245   Thm.rule_attribute (fn context => read_instantiate_mixed' (Context.proof_of context) args))) x;
   246 
   247 end;
   248 
   249 
   250 (* setup *)
   251 
   252 val _ = Context.>> (Context.map_theory
   253  (Attrib.setup (Binding.name "where") where_att "named instantiation of theorem" #>
   254   Attrib.setup (Binding.name "of") of_att "positional instantiation of theorem"));
   255 
   256 
   257 
   258 (** tactics **)
   259 
   260 (* resolution after lifting and instantation; may refer to parameters of the subgoal *)
   261 
   262 (* FIXME cleanup this mess!!! *)
   263 
   264 fun bires_inst_tac bires_flag ctxt insts thm =
   265   let
   266     val thy = ProofContext.theory_of ctxt;
   267     (* Separate type and term insts *)
   268     fun has_type_var ((x, _), _) = (case Symbol.explode x of
   269           "'"::cs => true | cs => false);
   270     val Tinsts = List.filter has_type_var insts;
   271     val tinsts = filter_out has_type_var insts;
   272 
   273     (* Tactic *)
   274     fun tac i st =
   275       let
   276         val (_, _, Bi, _) = Thm.dest_state (st, i);
   277         val params = Logic.strip_params Bi;  (*params of subgoal i as string typ pairs*)
   278         val params = rev (Term.rename_wrt_term Bi params)
   279           (*as they are printed: bound variables with*)
   280           (*the same name are renamed during printing*)
   281 
   282         val (param_names, ctxt') = ctxt
   283           |> Variable.declare_thm thm
   284           |> Thm.fold_terms Variable.declare_constraints st
   285           |> ProofContext.add_fixes_i (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) params);
   286 
   287         (* Process type insts: Tinsts_env *)
   288         fun absent xi = error
   289               ("No such variable in theorem: " ^ Term.string_of_vname xi);
   290         val (rtypes, rsorts) = Drule.types_sorts thm;
   291         fun readT (xi, s) =
   292             let val S = case rsorts xi of SOME S => S | NONE => absent xi;
   293                 val T = Syntax.read_typ ctxt' s;
   294                 val U = TVar (xi, S);
   295             in if Sign.typ_instance thy (T, U) then (U, T)
   296                else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails")
   297             end;
   298         val Tinsts_env = map readT Tinsts;
   299         (* Preprocess rule: extract vars and their types, apply Tinsts *)
   300         fun get_typ xi =
   301           (case rtypes xi of
   302                SOME T => typ_subst_atomic Tinsts_env T
   303              | NONE => absent xi);
   304         val (xis, ss) = Library.split_list tinsts;
   305         val Ts = map get_typ xis;
   306 
   307         val (ts, envT) = read_termTs ctxt' true ss Ts;
   308         val envT' = map (fn (ixn, T) =>
   309           (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;
   310         val cenv =
   311           map
   312             (fn (xi, t) =>
   313               pairself (Thm.cterm_of thy) (Var (xi, fastype_of t), t))
   314             (distinct
   315               (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
   316               (xis ~~ ts));
   317         (* Lift and instantiate rule *)
   318         val {maxidx, ...} = rep_thm st;
   319         val paramTs = map #2 params
   320         and inc = maxidx+1
   321         fun liftvar (Var ((a,j), T)) =
   322               Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)
   323           | liftvar t = raise TERM("Variable expected", [t]);
   324         fun liftterm t = list_abs_free
   325               (param_names ~~ paramTs, Logic.incr_indexes(paramTs,inc) t)
   326         fun liftpair (cv,ct) =
   327               (cterm_fun liftvar cv, cterm_fun liftterm ct)
   328         val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);
   329         val rule = Drule.instantiate
   330               (map lifttvar envT', map liftpair cenv)
   331               (Thm.lift_rule (Thm.cprem_of st i) thm)
   332       in
   333         if i > nprems_of st then no_tac st
   334         else st |>
   335           compose_tac (bires_flag, rule, nprems_of thm) i
   336       end
   337            handle TERM (msg,_)   => (warning msg; no_tac st)
   338                 | THM  (msg,_,_) => (warning msg; no_tac st);
   339   in tac end;
   340 
   341 val res_inst_tac = bires_inst_tac false;
   342 val eres_inst_tac = bires_inst_tac true;
   343 
   344 
   345 (* forward resolution *)
   346 
   347 fun make_elim_preserve rl =
   348   let
   349     val cert = Thm.cterm_of (Thm.theory_of_thm rl);
   350     val maxidx = Thm.maxidx_of rl;
   351     fun cvar xi = cert (Var (xi, propT));
   352     val revcut_rl' =
   353       instantiate ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),
   354         (cvar ("W", 0), cvar ("W", maxidx + 1))]) Drule.revcut_rl;
   355   in
   356     (case Seq.list_of (bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of
   357       [th] => th
   358     | _ => raise THM ("make_elim_preserve", 1, [rl]))
   359   end;
   360 
   361 (*instantiate and cut -- for atomic fact*)
   362 fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule);
   363 
   364 (*forward tactic applies a rule to an assumption without deleting it*)
   365 fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac;
   366 
   367 (*dresolve tactic applies a rule to replace an assumption*)
   368 fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve rule);
   369 
   370 
   371 (* derived tactics *)
   372 
   373 (*deletion of an assumption*)
   374 fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl;
   375 
   376 (*Introduce the given proposition as lemma and subgoal*)
   377 fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl;
   378 fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As);
   379 
   380 
   381 
   382 (** methods **)
   383 
   384 (* rule_tac etc. -- refer to dynamic goal state! *)
   385 
   386 local
   387 
   388 fun inst_meth inst_tac tac =
   389   Args.goal_spec --
   390   Scan.optional (Scan.lift
   391     (P.and_list1 (Args.var -- (Args.$$$ "=" |-- P.!!! Args.name_source)) --| Args.$$$ "in")) [] --
   392   Attrib.thms >>
   393   (fn ((quant, insts), thms) => fn ctxt => METHOD (fn facts =>
   394     if null insts then quant (Method.insert_tac facts THEN' tac thms)
   395     else
   396       (case thms of
   397         [thm] => quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm)
   398       | _ => error "Cannot have instantiations with multiple rules")));
   399 
   400 in
   401 
   402 val res_inst_meth = inst_meth res_inst_tac Tactic.resolve_tac;
   403 val eres_inst_meth = inst_meth eres_inst_tac Tactic.eresolve_tac;
   404 val cut_inst_meth = inst_meth cut_inst_tac Tactic.cut_rules_tac;
   405 val dres_inst_meth = inst_meth dres_inst_tac Tactic.dresolve_tac;
   406 val forw_inst_meth = inst_meth forw_inst_tac Tactic.forward_tac;
   407 
   408 end;
   409 
   410 
   411 (* setup *)
   412 
   413 val _ = Context.>> (Context.map_theory
   414  (Method.setup (Binding.name "rule_tac") res_inst_meth "apply rule (dynamic instantiation)" #>
   415   Method.setup (Binding.name "erule_tac") eres_inst_meth
   416     "apply rule in elimination manner (dynamic instantiation)" #>
   417   Method.setup (Binding.name "drule_tac") dres_inst_meth
   418     "apply rule in destruct manner (dynamic instantiation)" #>
   419   Method.setup (Binding.name "frule_tac") forw_inst_meth
   420     "apply rule in forward manner (dynamic instantiation)" #>
   421   Method.setup (Binding.name "cut_tac") cut_inst_meth "cut rule (dynamic instantiation)" #>
   422   Method.setup (Binding.name "subgoal_tac")
   423     (Args.goal_spec -- Scan.lift (Scan.repeat1 Args.name_source) >>
   424       (fn (quant, props) => fn ctxt => SIMPLE_METHOD'' quant (subgoals_tac ctxt props)))
   425     "insert subgoal (dynamic instantiation)" #>
   426   Method.setup (Binding.name "thin_tac")
   427     (Args.goal_spec -- Scan.lift Args.name_source >>
   428       (fn (quant, prop) => fn ctxt => SIMPLE_METHOD'' quant (thin_tac ctxt prop)))
   429       "remove premise (dynamic instantiation)"));
   430 
   431 end;
   432 
   433 structure BasicRuleInsts: BASIC_RULE_INSTS = RuleInsts;
   434 open BasicRuleInsts;