(* Title: Pure/tactic.ML Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Fundamental tactics.
*)
signature TACTIC = sig val trace_goalno_tac: (int -> tactic) -> int -> tactic val rule_by_tactic: Proof.context -> tactic -> thm -> thm val assume_tac: Proof.context -> int -> tactic val eq_assume_tac: int -> tactic val compose_tac: Proof.context -> (bool * thm * int) -> int -> tactic val make_elim: thm -> thm val biresolve0_tac: (bool * thm) list -> int -> tactic val biresolve_tac: Proof.context -> (bool * thm) list -> int -> tactic val resolve0_tac: thm list -> int -> tactic val resolve_tac: Proof.context -> thm list -> int -> tactic val eresolve0_tac: thm list -> int -> tactic val eresolve_tac: Proof.context -> thm list -> int -> tactic val forward_tac: Proof.context -> thm list -> int -> tactic val dresolve0_tac: thm list -> int -> tactic val dresolve_tac: Proof.context -> thm list -> int -> tactic val ares_tac: Proof.context -> thm list -> int -> tactic val solve_tac: Proof.context -> thm list -> int -> tactic val bimatch_tac: Proof.context -> (bool * thm) list -> int -> tactic val match_tac: Proof.context -> thm list -> int -> tactic val ematch_tac: Proof.context -> thm list -> int -> tactic val dmatch_tac: Proof.context -> thm list -> int -> tactic val flexflex_tac: Proof.context -> tactic val distinct_subgoals_tac: tactic val cut_tac: thm -> int -> tactic val cut_rules_tac: thm list -> int -> tactic val cut_facts_tac: thm list -> int -> tactic val filter_thms: (term * term -> bool) -> int * term * thm list -> thm list val rename_tac: stringlist -> int -> tactic val rotate_tac: int -> int -> tactic val defer_tac: int -> tactic val prefer_tac: int -> tactic val filter_prems_tac: Proof.context -> (term -> bool) -> int -> tactic end;
structure Tactic: TACTIC = struct
(*Discover which goal is chosen: SOMEGOAL(trace_goalno_tac tac) *) fun trace_goalno_tac tac i st = case Seq.pull(tac i st) of
NONE => Seq.empty
| seqcell => (tracing ("Subgoal " ^ string_of_int i ^ " selected");
Seq.make(fn()=> seqcell));
(*Makes a rule by applying a tactic to an existing rule*) fun rule_by_tactic ctxt tac rl = let val thy = Proof_Context.theory_of ctxt; val ctxt' = Variable.declare_thm rl ctxt; val ((_, [st]), ctxt'') = Variable.import true [Thm.transfer thy rl] ctxt'; in
(case Seq.pull (tac st) of
NONE => raise THM ("rule_by_tactic", 0, [rl])
| SOME (st', _) => zero_var_indexes (singleton (Variable.export ctxt'' ctxt') st')) end;
(*** Basic tactics ***)
(*** The following fail if the goal number is out of range:
thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
(*Solve subgoal i by assumption*) fun assume_tac ctxt i = PRIMSEQ (Thm.assumption (SOME ctxt) i);
(*Solve subgoal i by assumption, using no unification*) fun eq_assume_tac i = PRIMITIVE (Thm.eq_assumption i);
(** Resolution/matching tactics **)
(*The composition rule/state: no lifting or var renaming.
The arg = (bires_flg, orule, m); see Thm.bicompose for explanation.*) fun compose_tac ctxt arg i =
PRIMSEQ (Thm.bicompose (SOME ctxt) {flatten = true, match = false, incremented = false} arg i);
(*Converts a "destruct" rule like P \<and> Q \<Longrightarrow> P to an "elimination" rule
like \<lbrakk>P \<and> Q; P \<Longrightarrow> R\<rbrakk> \<Longrightarrow> R *) fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
(*Attack subgoal i by resolution, using flags to indicate elimination rules*) fun biresolve0_tac brules i = PRIMSEQ (Thm.biresolution NONE false brules i); fun biresolve_tac ctxt brules i = PRIMSEQ (Thm.biresolution (SOME ctxt) false brules i);
(*Resolution: the simple case, works for introduction rules*) fun resolve0_tac rules = biresolve0_tac (map (pair false) rules); fun resolve_tac ctxt rules = biresolve_tac ctxt (map (pair false) rules);
(*Resolution with elimination rules only*) fun eresolve0_tac rules = biresolve0_tac (map (pair true) rules); fun eresolve_tac ctxt rules = biresolve_tac ctxt (map (pair true) rules);
(*Forward reasoning using destruction rules.*) fun forward_tac ctxt rls = resolve_tac ctxt (map make_elim rls) THEN' assume_tac ctxt;
(*Like forward_tac, but deletes the assumption after use.*) fun dresolve0_tac rls = eresolve0_tac (map make_elim rls); fun dresolve_tac ctxt rls = eresolve_tac ctxt (map make_elim rls);
(*Use an assumption or some rules*) fun ares_tac ctxt rules = assume_tac ctxt ORELSE' resolve_tac ctxt rules;
(*Matching tactics -- as above, but forbid updating of state*) fun bimatch_tac ctxt brules i = PRIMSEQ (Thm.biresolution (SOME ctxt) true brules i); fun match_tac ctxt rules = bimatch_tac ctxt (map (pair false) rules); fun ematch_tac ctxt rules = bimatch_tac ctxt (map (pair true) rules); fun dmatch_tac ctxt rls = ematch_tac ctxt (map make_elim rls);
(*Smash all flex-flex disagreement pairs in the proof state.*) fun flexflex_tac ctxt = PRIMSEQ (Thm.flexflex_rule (SOME ctxt));
(*Remove duplicate subgoals.*) fun distinct_subgoals_tac st = let val subgoals = Thm.cprems_of st; val (tab, n) =
(subgoals, (Ctermtab.empty, 0)) |-> fold (fn ct => fn (tab, i) => if Ctermtab.defined tab ct then (tab, i) else (Ctermtab.update (ct, i) tab, i + 1)); val st' = if n = length subgoals then st else let val thy = Thm.theory_of_thm st; fun cert_prop i = Thm.global_cterm_of thy (Free (Name.bound i, propT));
val As = map (cert_prop o the o Ctermtab.lookup tab) subgoals; val As' = map cert_prop (0 upto (n - 1)); val C = cert_prop n;
val template = Drule.list_implies (As, C); val inst =
Frees.build
(Frees.add (dest_Free (Thm.term_of C), Thm.cconcl_of st) #>
Ctermtab.fold (fn (ct, i) => Frees.add ((Name.bound i, propT), ct)) tab); in
Thm.assume template
|> fold (Thm.elim_implies o Thm.assume) As
|> fold_rev Thm.implies_intr As'
|> Thm.implies_intr template
|> Thm.instantiate_frees (TFrees.empty, inst)
|> Thm.elim_implies st end; in Seq.single st' end;
(*** Applications of cut_rl ***)
(*The conclusion of the rule gets assumed in subgoal i,
while subgoal i+1,... are the premises of the rule.*) fun cut_tac rule i = resolve0_tac [cut_rl] i THEN resolve0_tac [rule] (i + 1);
(*"Cut" a list of rules into the goal. Their premises will become new
subgoals.*) fun cut_rules_tac ths i = EVERY (map (fn th => cut_tac th i) ths);
(*As above, but inserts only facts (unconditional theorems);
generates no additional subgoals. *) fun cut_facts_tac ths = cut_rules_tac (filter Thm.no_prems ths);
(**** Indexing and filtering of theorems ****)
(*Returns the list of potentially resolvable theorems for the goal "prem", using the predicate could(subgoal,concl).
Resulting list is no longer than "limit"*) fun filter_thms could (limit, prem, ths) = letval pb = Logic.strip_assums_concl prem; (*delete assumptions*) fun filtr (limit, []) = []
| filtr (limit, th::ths) = if limit=0 then [] elseif could(pb, Thm.concl_of th) then th :: filtr(limit-1, ths) else filtr(limit,ths) in filtr(limit,ths) end;
(*Renaming of parameters in a subgoal*) fun rename_tac xs i = case find_first (not o Symbol_Pos.is_identifier) xs of
SOME x => error ("Not an identifier: " ^ x)
| NONE => PRIMITIVE (Thm.rename_params_rule (xs, i));
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
right to left if n is positive, and from left to right if n is negative.*) fun rotate_tac 0 i = all_tac
| rotate_tac k i = PRIMITIVE (Thm.rotate_rule k i);
(*Rotate the given subgoal to be the last.*) fun defer_tac i = PRIMITIVE (Thm.permute_prems (i - 1) 1);
(*Rotate the given subgoal to be the first.*) fun prefer_tac i = PRIMITIVE (Thm.permute_prems (i - 1) 1 #> Thm.permute_prems 0 ~1);
(*Remove premises that do not satisfy pred; fails if all prems satisfy pred.*) fun filter_prems_tac ctxt pred = let funThen NONE tac = SOME tac
| Then (SOME tac) tac' = SOME (tac THEN' tac'); fun thins H (tac, n) = if pred H then (tac, n + 1) else (Then tac (rotate_tac n THEN' eresolve_tac ctxt [thin_rl]), 0); in
SUBGOAL (fn (goal, i) => letval Hs = Logic.strip_assums_hyp goal in
(case fst (fold thins Hs (NONE, 0)) of
NONE => no_tac
| SOME tac => tac i) end) end;
end;
open Tactic;
¤ Dauer der Verarbeitung: 0.9 Sekunden
(vorverarbeitet)
¤
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.
