1 (* Title: Pure/Isar/rule_insts.ML
5 Rule instantiations -- operations within a rule/subgoal context.
8 signature BASIC_RULE_INSTS =
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
22 signature RULE_INSTS =
24 include BASIC_RULE_INSTS
25 val make_elim_preserve: thm -> thm
28 structure RuleInsts: RULE_INSTS =
32 (** reading instantiations **)
36 fun is_tvar (x, _) = String.isPrefix "'" x;
38 fun error_var msg xi = error (msg ^ Term.string_of_vname xi);
40 fun the_sort tvars xi = the (AList.lookup (op =) tvars xi)
41 handle Option.Option => error_var "No such type variable in theorem: " xi;
43 fun the_type vars xi = the (AList.lookup (op =) vars xi)
44 handle Option.Option => error_var "No such variable in theorem: " xi;
46 fun unify_vartypes thy vars (xi, u) (unifier, maxidx) =
48 val T = the_type vars xi;
49 val U = Term.fastype_of u;
50 val maxidx' = Term.maxidx_term u (Int.max (#2 xi, maxidx));
52 Sign.typ_unify thy (T, U) (unifier, maxidx')
53 handle Type.TUNIFY => error_var "Incompatible type for instantiation of " xi
56 fun instantiate inst =
57 TermSubst.instantiate ([], map (fn (xi, t) => ((xi, Term.fastype_of t), t)) inst) #>
64 in if T = T' then NONE else SOME (T, T') end;
70 in if t aconv t' then NONE else SOME (t, t') end;
73 (Thm.fold_terms o fold_types o fold_atyps)
74 (fn TFree (a, _) => insert (op =) a
75 | TVar ((a, _), _) => insert (op =) a
80 fun read_termTs ctxt schematic ss Ts =
82 fun parse T = if T = propT then Syntax.parse_prop ctxt else Syntax.parse_term ctxt;
83 val ts = map2 parse Ts ss;
85 map2 (TypeInfer.constrain o TypeInfer.paramify_vars) Ts ts
86 |> Syntax.check_terms ((schematic ? ProofContext.set_mode ProofContext.mode_schematic) ctxt)
87 |> Variable.polymorphic ctxt;
88 val Ts' = map Term.fastype_of ts';
89 val tyenv = fold Type.raw_match (Ts ~~ Ts') Vartab.empty;
90 in (ts', map (apsnd snd) (Vartab.dest tyenv)) end;
92 fun read_insts ctxt mixed_insts (tvars, vars) =
94 val thy = ProofContext.theory_of ctxt;
95 val cert = Thm.cterm_of thy;
96 val certT = Thm.ctyp_of thy;
98 val (type_insts, term_insts) = List.partition (is_tvar o fst) mixed_insts;
99 val internal_insts = term_insts |> map_filter
100 (fn (xi, Args.Term t) => SOME (xi, t)
101 | (_, Args.Text _) => NONE
102 | (xi, _) => error_var "Term argument expected for " xi);
103 val external_insts = term_insts |> map_filter
104 (fn (xi, Args.Text s) => SOME (xi, s) | _ => NONE);
107 (* mixed type instantiations *)
109 fun readT (xi, arg) =
111 val S = the_sort tvars xi;
114 Args.Text s => Syntax.read_typ ctxt s
116 | _ => error_var "Type argument expected for " xi);
118 if Sign.of_sort thy (T, S) then ((xi, S), T)
119 else error_var "Incompatible sort for typ instantiation of " xi
122 val type_insts1 = map readT type_insts;
123 val instT1 = TermSubst.instantiateT type_insts1;
124 val vars1 = map (apsnd instT1) vars;
127 (* internal term instantiations *)
129 val instT2 = Envir.norm_type
130 (#1 (fold (unify_vartypes thy vars1) internal_insts (Vartab.empty, 0)));
131 val vars2 = map (apsnd instT2) vars1;
132 val internal_insts2 = map (apsnd (map_types instT2)) internal_insts;
133 val inst2 = instantiate internal_insts2;
136 (* external term instantiations *)
138 val (xs, strs) = split_list external_insts;
139 val Ts = map (the_type vars2) xs;
140 val (ts, inferred) = read_termTs ctxt false strs Ts;
142 val instT3 = Term.typ_subst_TVars inferred;
143 val vars3 = map (apsnd instT3) vars2;
144 val internal_insts3 = map (apsnd (map_types instT3)) internal_insts2;
145 val external_insts3 = xs ~~ ts;
146 val inst3 = instantiate external_insts3;
151 val type_insts3 = map (fn ((a, _), T) => (a, instT3 (instT2 T))) type_insts1;
152 val term_insts3 = internal_insts3 @ external_insts3;
154 val inst_tvars = map_filter (make_instT (instT3 o instT2 o instT1)) tvars;
155 val inst_vars = map_filter (make_inst (inst3 o inst2)) vars3;
157 ((type_insts3, term_insts3),
158 (map (pairself certT) inst_tvars, map (pairself cert) inst_vars))
161 fun read_instantiate_mixed ctxt mixed_insts thm =
163 val ctxt' = ctxt |> Variable.declare_thm thm
164 |> fold (fn a => Variable.declare_names (Logic.mk_type (TFree (a, dummyS)))) (add_used thm []); (* FIXME tmp *)
165 val tvars = Thm.fold_terms Term.add_tvars thm [];
166 val vars = Thm.fold_terms Term.add_vars thm [];
167 val ((type_insts, term_insts), insts) = read_insts ctxt' (map snd mixed_insts) (tvars, vars);
169 val _ = (*assign internalized values*)
170 mixed_insts |> List.app (fn (arg, (xi, _)) =>
172 Args.assign (SOME (Args.Typ (the (AList.lookup (op =) type_insts xi)))) arg
174 Args.assign (SOME (Args.Term (the (AList.lookup (op =) term_insts xi)))) arg);
176 Drule.instantiate insts thm |> RuleCases.save thm
179 fun read_instantiate_mixed' ctxt (args, concl_args) thm =
181 fun zip_vars _ [] = []
182 | zip_vars (_ :: xs) ((_, NONE) :: rest) = zip_vars xs rest
183 | zip_vars ((x, _) :: xs) ((arg, SOME t) :: rest) = (arg, (x, t)) :: zip_vars xs rest
184 | zip_vars [] _ = error "More instantiations than variables in theorem";
186 zip_vars (rev (Term.add_vars (Thm.full_prop_of thm) [])) args @
187 zip_vars (rev (Term.add_vars (Thm.concl_of thm) [])) concl_args;
188 in read_instantiate_mixed ctxt insts thm end;
193 (* instantiation of rule or goal state *)
195 fun read_instantiate ctxt args thm =
196 read_instantiate_mixed (ctxt |> ProofContext.set_mode ProofContext.mode_schematic) (* FIXME !? *)
197 (map (fn (x, y) => (Args.eof, (x, Args.Text y))) args) thm;
199 fun instantiate_tac ctxt args = PRIMITIVE (read_instantiate ctxt args);
205 (* where: named instantiation *)
210 Args.internal_typ >> Args.Typ ||
211 Args.internal_term >> Args.Term ||
212 Args.name >> Args.Text;
214 val inst = Args.var -- (Args.$$$ "=" |-- Args.ahead -- value)
215 >> (fn (xi, (a, v)) => (a, (xi, v)));
219 val where_att = Attrib.syntax (Args.and_list (Scan.lift inst) >> (fn args =>
220 Thm.rule_attribute (fn context => read_instantiate_mixed (Context.proof_of context) args)));
225 (* of: positional instantiation (terms only) *)
230 Args.internal_term >> Args.Term ||
231 Args.name >> Args.Text;
233 val inst = Args.ahead -- Args.maybe value;
234 val concl = Args.$$$ "concl" -- Args.colon;
237 Scan.repeat (Scan.unless concl inst) --
238 Scan.optional (concl |-- Scan.repeat inst) [];
242 val of_att = Attrib.syntax (Scan.lift insts >> (fn args =>
243 Thm.rule_attribute (fn context => read_instantiate_mixed' (Context.proof_of context) args)));
250 val _ = Context.>> (Context.map_theory
251 (Attrib.add_attributes
252 [("where", where_att, "named instantiation of theorem"),
253 ("of", of_att, "positional instantiation of theorem")]));
259 (* resolution after lifting and instantation; may refer to parameters of the subgoal *)
261 (* FIXME cleanup this mess!!! *)
263 fun bires_inst_tac bires_flag ctxt insts thm =
265 val thy = ProofContext.theory_of ctxt;
266 (* Separate type and term insts *)
267 fun has_type_var ((x, _), _) = (case Symbol.explode x of
268 "'"::cs => true | cs => false);
269 val Tinsts = List.filter has_type_var insts;
270 val tinsts = filter_out has_type_var insts;
275 val (_, _, Bi, _) = Thm.dest_state (st, i);
276 val params = Logic.strip_params Bi; (*params of subgoal i as string typ pairs*)
277 val params = rev (Term.rename_wrt_term Bi params)
278 (*as they are printed: bound variables with*)
279 (*the same name are renamed during printing*)
281 val (param_names, ctxt') = ctxt
282 |> Variable.declare_thm thm
283 |> Thm.fold_terms Variable.declare_constraints st
284 |> ProofContext.add_fixes_i (map (fn (x, T) => (x, SOME T, NoSyn)) params);
286 (* Process type insts: Tinsts_env *)
287 fun absent xi = error
288 ("No such variable in theorem: " ^ Term.string_of_vname xi);
289 val (rtypes, rsorts) = Drule.types_sorts thm;
291 let val S = case rsorts xi of SOME S => S | NONE => absent xi;
292 val T = Syntax.read_typ ctxt' s;
293 val U = TVar (xi, S);
294 in if Sign.typ_instance thy (T, U) then (U, T)
295 else error ("Instantiation of " ^ Term.string_of_vname xi ^ " fails")
297 val Tinsts_env = map readT Tinsts;
298 (* Preprocess rule: extract vars and their types, apply Tinsts *)
301 SOME T => typ_subst_atomic Tinsts_env T
302 | NONE => absent xi);
303 val (xis, ss) = Library.split_list tinsts;
304 val Ts = map get_typ xis;
306 val (ts, envT) = read_termTs ctxt' true ss Ts;
307 val envT' = map (fn (ixn, T) =>
308 (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;
312 pairself (Thm.cterm_of thy) (Var (xi, fastype_of t), t))
314 (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
316 (* Lift and instantiate rule *)
317 val {maxidx, ...} = rep_thm st;
318 val paramTs = map #2 params
320 fun liftvar (Var ((a,j), T)) =
321 Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)
322 | liftvar t = raise TERM("Variable expected", [t]);
323 fun liftterm t = list_abs_free
324 (param_names ~~ paramTs, Logic.incr_indexes(paramTs,inc) t)
325 fun liftpair (cv,ct) =
326 (cterm_fun liftvar cv, cterm_fun liftterm ct)
327 val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);
328 val rule = Drule.instantiate
329 (map lifttvar envT', map liftpair cenv)
330 (Thm.lift_rule (Thm.cprem_of st i) thm)
332 if i > nprems_of st then no_tac st
334 compose_tac (bires_flag, rule, nprems_of thm) i
336 handle TERM (msg,_) => (warning msg; no_tac st)
337 | THM (msg,_,_) => (warning msg; no_tac st);
340 val res_inst_tac = bires_inst_tac false;
341 val eres_inst_tac = bires_inst_tac true;
344 (* forward resolution *)
346 fun make_elim_preserve rl =
348 val cert = Thm.cterm_of (Thm.theory_of_thm rl);
349 val maxidx = Thm.maxidx_of rl;
350 fun cvar xi = cert (Var (xi, propT));
352 instantiate ([], [(cvar ("V", 0), cvar ("V", maxidx + 1)),
353 (cvar ("W", 0), cvar ("W", maxidx + 1))]) Drule.revcut_rl;
355 (case Seq.list_of (bicompose false (false, rl, Thm.nprems_of rl) 1 revcut_rl') of
357 | _ => raise THM ("make_elim_preserve", 1, [rl]))
360 (*instantiate and cut -- for atomic fact*)
361 fun cut_inst_tac ctxt insts rule = res_inst_tac ctxt insts (make_elim_preserve rule);
363 (*forward tactic applies a rule to an assumption without deleting it*)
364 fun forw_inst_tac ctxt insts rule = cut_inst_tac ctxt insts rule THEN' assume_tac;
366 (*dresolve tactic applies a rule to replace an assumption*)
367 fun dres_inst_tac ctxt insts rule = eres_inst_tac ctxt insts (make_elim_preserve rule);
370 (* derived tactics *)
372 (*deletion of an assumption*)
373 fun thin_tac ctxt s = eres_inst_tac ctxt [(("V", 0), s)] Drule.thin_rl;
375 (*Introduce the given proposition as lemma and subgoal*)
376 fun subgoal_tac ctxt A = DETERM o res_inst_tac ctxt [(("psi", 0), A)] cut_rl;
377 fun subgoals_tac ctxt As = EVERY' (map (subgoal_tac ctxt) As);
383 (* rule_tac etc. -- refer to dynamic goal state! *)
387 fun gen_inst _ tac _ (quant, ([], thms)) =
388 Method.METHOD (fn facts => quant (Method.insert_tac facts THEN' tac thms))
389 | gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =
390 Method.METHOD (fn facts =>
391 quant (Method.insert_tac facts THEN' inst_tac ctxt insts thm))
392 | gen_inst _ _ _ _ = error "Cannot have instantiations with multiple rules";
396 val res_inst_meth = gen_inst res_inst_tac Tactic.resolve_tac;
397 val eres_inst_meth = gen_inst eres_inst_tac Tactic.eresolve_tac;
398 val cut_inst_meth = gen_inst cut_inst_tac Tactic.cut_rules_tac;
399 val dres_inst_meth = gen_inst dres_inst_tac Tactic.dresolve_tac;
400 val forw_inst_meth = gen_inst forw_inst_tac Tactic.forward_tac;
409 (Args.and_list1 (Scan.lift (Args.name -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
410 Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;
412 fun inst_args f src ctxt =
413 f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));
417 (Args.and_list1 (Scan.lift (Args.var -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
418 Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;
420 fun inst_args_var f src ctxt =
421 f ctxt (fst (Method.syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));
426 val _ = Context.>> (Context.map_theory
428 [("rule_tac", inst_args_var res_inst_meth,
429 "apply rule (dynamic instantiation)"),
430 ("erule_tac", inst_args_var eres_inst_meth,
431 "apply rule in elimination manner (dynamic instantiation)"),
432 ("drule_tac", inst_args_var dres_inst_meth,
433 "apply rule in destruct manner (dynamic instantiation)"),
434 ("frule_tac", inst_args_var forw_inst_meth,
435 "apply rule in forward manner (dynamic instantiation)"),
436 ("cut_tac", inst_args_var cut_inst_meth,
437 "cut rule (dynamic instantiation)"),
438 ("subgoal_tac", Method.goal_args_ctxt (Scan.repeat1 Args.name) subgoals_tac,
439 "insert subgoal (dynamic instantiation)"),
440 ("thin_tac", Method.goal_args_ctxt Args.name thin_tac,
441 "remove premise (dynamic instantiation)")]));
445 structure BasicRuleInsts: BASIC_RULE_INSTS = RuleInsts;