src/Pure/tactic.ML
author wenzelm
Fri Dec 14 11:52:54 2001 +0100 (2001-12-14)
changeset 12498 3b0091bf06e8
parent 12320 6e70d870ddf0
child 12725 7ede865e1fe5
permissions -rw-r--r--
changed Thm.varifyT';
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(*  Title:      Pure/tactic.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1991  University of Cambridge
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Tactics.
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*)
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signature BASIC_TACTIC =
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sig
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  val ares_tac          : thm list -> int -> tactic
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  val asm_rewrite_goal_tac: bool*bool*bool ->
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    (MetaSimplifier.meta_simpset -> tactic) -> MetaSimplifier.meta_simpset -> int -> tactic
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  val assume_tac        : int -> tactic
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  val atac      : int ->tactic
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  val bimatch_from_nets_tac:
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      (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic
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  val bimatch_tac       : (bool*thm)list -> int -> tactic
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  val biresolution_from_nets_tac:
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        ('a list -> (bool * thm) list) ->
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        bool -> 'a Net.net * 'a Net.net -> int -> tactic
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  val biresolve_from_nets_tac:
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      (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic
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  val biresolve_tac     : (bool*thm)list -> int -> tactic
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  val build_net : thm list -> (int*thm) Net.net
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  val build_netpair:    (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net ->
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      (bool*thm)list -> (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net
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  val compose_inst_tac  : (string*string)list -> (bool*thm*int) ->
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                          int -> tactic
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  val compose_tac       : (bool * thm * int) -> int -> tactic
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  val cut_facts_tac     : thm list -> int -> tactic
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  val cut_inst_tac      : (string*string)list -> thm -> int -> tactic
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  val datac             : thm -> int -> int -> tactic
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  val defer_tac         : int -> tactic
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  val distinct_subgoals_tac     : tactic
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  val dmatch_tac        : thm list -> int -> tactic
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  val dresolve_tac      : thm list -> int -> tactic
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  val dres_inst_tac     : (string*string)list -> thm -> int -> tactic
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  val dtac              : thm -> int ->tactic
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  val eatac             : thm -> int -> int -> tactic
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  val etac              : thm -> int ->tactic
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  val eq_assume_tac     : int -> tactic
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  val ematch_tac        : thm list -> int -> tactic
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  val eresolve_tac      : thm list -> int -> tactic
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  val eres_inst_tac     : (string*string)list -> thm -> int -> tactic
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  val fatac             : thm -> int -> int -> tactic
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  val filter_prems_tac  : (term -> bool) -> int -> tactic
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  val filter_thms       : (term*term->bool) -> int*term*thm list -> thm list
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  val filt_resolve_tac  : thm list -> int -> int -> tactic
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  val flexflex_tac      : tactic
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  val fold_goals_tac    : thm list -> tactic
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  val fold_rule         : thm list -> thm -> thm
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  val fold_tac          : thm list -> tactic
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  val forward_tac       : thm list -> int -> tactic
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  val forw_inst_tac     : (string*string)list -> thm -> int -> tactic
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  val ftac              : thm -> int ->tactic
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  val insert_tagged_brl : ('a * (bool * thm)) *
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    (('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net) ->
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      ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net
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  val delete_tagged_brl : (bool * thm) *
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    (('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net) ->
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      ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net
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  val is_fact           : thm -> bool
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  val lessb             : (bool * thm) * (bool * thm) -> bool
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  val lift_inst_rule    : thm * int * (string*string)list * thm -> thm
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  val make_elim         : thm -> thm
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  val match_from_net_tac        : (int*thm) Net.net -> int -> tactic
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  val match_tac : thm list -> int -> tactic
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  val metacut_tac       : thm -> int -> tactic
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  val net_bimatch_tac   : (bool*thm) list -> int -> tactic
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  val net_biresolve_tac : (bool*thm) list -> int -> tactic
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  val net_match_tac     : thm list -> int -> tactic
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  val net_resolve_tac   : thm list -> int -> tactic
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  val norm_hhf          : thm -> thm
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  val norm_hhf_tac      : int -> tactic
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  val PRIMITIVE         : (thm -> thm) -> tactic
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  val PRIMSEQ           : (thm -> thm Seq.seq) -> tactic
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  val prune_params_tac  : tactic
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  val rename_params_tac : string list -> int -> tactic
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  val rename_tac        : string -> int -> tactic
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  val rename_last_tac   : string -> string list -> int -> tactic
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  val resolve_from_net_tac      : (int*thm) Net.net -> int -> tactic
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  val resolve_tac       : thm list -> int -> tactic
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  val res_inst_tac      : (string*string)list -> thm -> int -> tactic
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  val rewrite_goal_tac  : thm list -> int -> tactic
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  val rewrite_goals_rule: thm list -> thm -> thm
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  val rewrite_rule      : thm list -> thm -> thm
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  val rewrite_goals_tac : thm list -> tactic
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  val rewrite_tac       : thm list -> tactic
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  val rewtac            : thm -> tactic
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  val rotate_tac        : int -> int -> tactic
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  val rtac              : thm -> int -> tactic
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  val rule_by_tactic    : tactic -> thm -> thm
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  val solve_tac         : thm list -> int -> tactic
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  val subgoal_tac       : string -> int -> tactic
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  val subgoals_tac      : string list -> int -> tactic
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  val subgoals_of_brl   : bool * thm -> int
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  val term_lift_inst_rule       :
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      thm * int * (indexname*typ)list * ((indexname*typ)*term)list  * thm
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      -> thm
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  val instantiate_tac   : (string * string) list -> tactic
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  val thin_tac          : string -> int -> tactic
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  val trace_goalno_tac  : (int -> tactic) -> int -> tactic
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end;
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signature TACTIC =
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sig
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  include BASIC_TACTIC
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  val innermost_params: int -> thm -> (string * typ) list
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  val untaglist: (int * 'a) list -> 'a list
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  val orderlist: (int * 'a) list -> 'a list
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  val rewrite: bool -> thm list -> cterm -> thm
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  val rewrite_cterm: bool -> thm list -> cterm -> cterm
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  val simplify: bool -> thm list -> thm -> thm
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  val conjunction_tac: tactic
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  val prove: Sign.sg -> string list -> term list -> term -> (thm list -> tactic) -> thm
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  val prove_standard: Sign.sg -> string list -> term list -> term -> (thm list -> tactic) -> thm
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end;
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structure Tactic: TACTIC =
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struct
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(*Discover which goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
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fun trace_goalno_tac tac i st =
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    case Seq.pull(tac i st) of
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        None    => Seq.empty
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      | seqcell => (tracing ("Subgoal " ^ string_of_int i ^ " selected");
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                         Seq.make(fn()=> seqcell));
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(*Makes a rule by applying a tactic to an existing rule*)
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fun rule_by_tactic tac rl =
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  let val (st, thaw) = freeze_thaw (zero_var_indexes rl)
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  in case Seq.pull (tac st)  of
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        None        => raise THM("rule_by_tactic", 0, [rl])
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      | Some(st',_) => Thm.varifyT (thaw st')
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  end;
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(*** Basic tactics ***)
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(*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)
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fun PRIMSEQ thmfun st =  thmfun st handle THM _ => Seq.empty;
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(*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)
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fun PRIMITIVE thmfun = PRIMSEQ (Seq.single o thmfun);
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(*** The following fail if the goal number is out of range:
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     thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
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(*Solve subgoal i by assumption*)
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fun assume_tac i = PRIMSEQ (assumption i);
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(*Solve subgoal i by assumption, using no unification*)
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fun eq_assume_tac i = PRIMITIVE (eq_assumption i);
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(** Resolution/matching tactics **)
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(*The composition rule/state: no lifting or var renaming.
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  The arg = (bires_flg, orule, m) ;  see bicompose for explanation.*)
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fun compose_tac arg i = PRIMSEQ (bicompose false arg i);
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(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
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  like [| P&Q; P==>R |] ==> R *)
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fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
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(*Attack subgoal i by resolution, using flags to indicate elimination rules*)
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fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i);
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(*Resolution: the simple case, works for introduction rules*)
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fun resolve_tac rules = biresolve_tac (map (pair false) rules);
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(*Resolution with elimination rules only*)
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fun eresolve_tac rules = biresolve_tac (map (pair true) rules);
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(*Forward reasoning using destruction rules.*)
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fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;
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(*Like forward_tac, but deletes the assumption after use.*)
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fun dresolve_tac rls = eresolve_tac (map make_elim rls);
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(*Shorthand versions: for resolution with a single theorem*)
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val atac    =   assume_tac;
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fun rtac rl =  resolve_tac [rl];
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fun dtac rl = dresolve_tac [rl];
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fun etac rl = eresolve_tac [rl];
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fun ftac rl =  forward_tac [rl];
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fun datac thm j = EVERY' (dtac thm::replicate j atac);
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fun eatac thm j = EVERY' (etac thm::replicate j atac);
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fun fatac thm j = EVERY' (ftac thm::replicate j atac);
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(*Use an assumption or some rules ... A popular combination!*)
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fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;
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fun solve_tac rules = resolve_tac rules THEN_ALL_NEW assume_tac;
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(*Matching tactics -- as above, but forbid updating of state*)
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fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i);
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fun match_tac rules  = bimatch_tac (map (pair false) rules);
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fun ematch_tac rules = bimatch_tac (map (pair true) rules);
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fun dmatch_tac rls   = ematch_tac (map make_elim rls);
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(*Smash all flex-flex disagreement pairs in the proof state.*)
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val flexflex_tac = PRIMSEQ flexflex_rule;
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(*Remove duplicate subgoals.  By Mark Staples*)
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local
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fun cterm_aconv (a,b) = #t (rep_cterm a) aconv #t (rep_cterm b);
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in
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fun distinct_subgoals_tac state =
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    let val (frozth,thawfn) = freeze_thaw state
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        val froz_prems = cprems_of frozth
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        val assumed = implies_elim_list frozth (map assume froz_prems)
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        val implied = implies_intr_list (gen_distinct cterm_aconv froz_prems)
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                                        assumed;
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    in  Seq.single (thawfn implied)  end
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end;
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(*Determine print names of goal parameters (reversed)*)
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fun innermost_params i st =
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  let val (_, _, Bi, _) = dest_state (st, i)
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  in rename_wrt_term Bi (Logic.strip_params Bi) end;
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(*Lift and instantiate a rule wrt the given state and subgoal number *)
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fun lift_inst_rule (st, i, sinsts, rule) =
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let val {maxidx,sign,...} = rep_thm st
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    val (_, _, Bi, _) = dest_state(st,i)
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    val params = Logic.strip_params Bi          (*params of subgoal i*)
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    val params = rev(rename_wrt_term Bi params) (*as they are printed*)
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    val paramTs = map #2 params
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    and inc = maxidx+1
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    fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> incr_tvar inc T)
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      | liftvar t = raise TERM("Variable expected", [t]);
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    fun liftterm t = list_abs_free (params,
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                                    Logic.incr_indexes(paramTs,inc) t)
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    (*Lifts instantiation pair over params*)
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    fun liftpair (cv,ct) = (cterm_fun liftvar cv, cterm_fun liftterm ct)
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    fun lifttvar((a,i),ctyp) =
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        let val {T,sign} = rep_ctyp ctyp
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        in  ((a,i+inc), ctyp_of sign (incr_tvar inc T)) end
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    val rts = types_sorts rule and (types,sorts) = types_sorts st
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    fun types'(a,~1) = (case assoc(params,a) of None => types(a,~1) | sm => sm)
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      | types'(ixn) = types ixn;
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    val used = add_term_tvarnames
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                  (#prop(rep_thm st) $ #prop(rep_thm rule),[])
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    val (Tinsts,insts) = read_insts sign rts (types',sorts) used sinsts
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in Drule.instantiate (map lifttvar Tinsts, map liftpair insts)
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                     (lift_rule (st,i) rule)
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end;
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(*
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Like lift_inst_rule but takes terms, not strings, where the terms may contain
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Bounds referring to parameters of the subgoal.
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insts: [...,(vj,tj),...]
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The tj may contain references to parameters of subgoal i of the state st
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in the form of Bound k, i.e. the tj may be subterms of the subgoal.
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To saturate the lose bound vars, the tj are enclosed in abstractions
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corresponding to the parameters of subgoal i, thus turning them into
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functions. At the same time, the types of the vj are lifted.
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NB: the types in insts must be correctly instantiated already,
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    i.e. Tinsts is not applied to insts.
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*)
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fun term_lift_inst_rule (st, i, Tinsts, insts, rule) =
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let val {maxidx,sign,...} = rep_thm st
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    val (_, _, Bi, _) = dest_state(st,i)
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    val params = Logic.strip_params Bi          (*params of subgoal i*)
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    val paramTs = map #2 params
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    and inc = maxidx+1
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    fun liftvar ((a,j), T) = Var((a, j+inc), paramTs---> incr_tvar inc T)
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    (*lift only Var, not term, which must be lifted already*)
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    fun liftpair (v,t) = (cterm_of sign (liftvar v), cterm_of sign t)
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    fun liftTpair((a,i),T) = ((a,i+inc), ctyp_of sign (incr_tvar inc T))
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in Drule.instantiate (map liftTpair Tinsts, map liftpair insts)
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                     (lift_rule (st,i) rule)
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end;
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(*** Resolve after lifting and instantation; may refer to parameters of the
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     subgoal.  Fails if "i" is out of range.  ***)
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(*compose version: arguments are as for bicompose.*)
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fun compose_inst_tac sinsts (bires_flg, rule, nsubgoal) i st =
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  if i > nprems_of st then no_tac st
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  else st |>
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    (compose_tac (bires_flg, lift_inst_rule (st, i, sinsts, rule), nsubgoal) i
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     handle TERM (msg,_)   => (warning msg;  no_tac)
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          | THM  (msg,_,_) => (warning msg;  no_tac));
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(*"Resolve" version.  Note: res_inst_tac cannot behave sensibly if the
lcp@761
   292
  terms that are substituted contain (term or type) unknowns from the
lcp@761
   293
  goal, because it is unable to instantiate goal unknowns at the same time.
lcp@761
   294
paulson@2029
   295
  The type checker is instructed not to freeze flexible type vars that
nipkow@952
   296
  were introduced during type inference and still remain in the term at the
nipkow@952
   297
  end.  This increases flexibility but can introduce schematic type vars in
nipkow@952
   298
  goals.
lcp@761
   299
*)
clasohm@0
   300
fun res_inst_tac sinsts rule i =
clasohm@0
   301
    compose_inst_tac sinsts (false, rule, nprems_of rule) i;
clasohm@0
   302
paulson@1501
   303
(*eresolve elimination version*)
clasohm@0
   304
fun eres_inst_tac sinsts rule i =
clasohm@0
   305
    compose_inst_tac sinsts (true, rule, nprems_of rule) i;
clasohm@0
   306
lcp@270
   307
(*For forw_inst_tac and dres_inst_tac.  Preserve Var indexes of rl;
lcp@270
   308
  increment revcut_rl instead.*)
wenzelm@10817
   309
fun make_elim_preserve rl =
lcp@270
   310
  let val {maxidx,...} = rep_thm rl
wenzelm@6390
   311
      fun cvar ixn = cterm_of (Theory.sign_of ProtoPure.thy) (Var(ixn,propT));
wenzelm@10817
   312
      val revcut_rl' =
wenzelm@10805
   313
          instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),
wenzelm@10805
   314
                             (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
clasohm@0
   315
      val arg = (false, rl, nprems_of rl)
wenzelm@4270
   316
      val [th] = Seq.list_of (bicompose false arg 1 revcut_rl')
clasohm@0
   317
  in  th  end
clasohm@0
   318
  handle Bind => raise THM("make_elim_preserve", 1, [rl]);
clasohm@0
   319
lcp@270
   320
(*instantiate and cut -- for a FACT, anyway...*)
lcp@270
   321
fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   322
lcp@270
   323
(*forward tactic applies a RULE to an assumption without deleting it*)
lcp@270
   324
fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac;
lcp@270
   325
lcp@270
   326
(*dresolve tactic applies a RULE to replace an assumption*)
clasohm@0
   327
fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   328
oheimb@10347
   329
(*instantiate variables in the whole state*)
oheimb@10347
   330
val instantiate_tac = PRIMITIVE o read_instantiate;
oheimb@10347
   331
paulson@1951
   332
(*Deletion of an assumption*)
paulson@1951
   333
fun thin_tac s = eres_inst_tac [("V",s)] thin_rl;
paulson@1951
   334
lcp@270
   335
(*** Applications of cut_rl ***)
clasohm@0
   336
clasohm@0
   337
(*Used by metacut_tac*)
clasohm@0
   338
fun bires_cut_tac arg i =
clasohm@1460
   339
    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
clasohm@0
   340
clasohm@0
   341
(*The conclusion of the rule gets assumed in subgoal i,
clasohm@0
   342
  while subgoal i+1,... are the premises of the rule.*)
clasohm@0
   343
fun metacut_tac rule = bires_cut_tac [(false,rule)];
clasohm@0
   344
clasohm@0
   345
(*Recognizes theorems that are not rules, but simple propositions*)
clasohm@0
   346
fun is_fact rl =
clasohm@0
   347
    case prems_of rl of
wenzelm@10805
   348
        [] => true  |  _::_ => false;
clasohm@0
   349
clasohm@0
   350
(*"Cut" all facts from theorem list into the goal as assumptions. *)
clasohm@0
   351
fun cut_facts_tac ths i =
clasohm@0
   352
    EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));
clasohm@0
   353
clasohm@0
   354
(*Introduce the given proposition as a lemma and subgoal*)
wenzelm@10817
   355
fun subgoal_tac sprop i st =
wenzelm@4270
   356
  let val st'    = Seq.hd (res_inst_tac [("psi", sprop)] cut_rl i st)
paulson@4178
   357
      val concl' = Logic.strip_assums_concl (List.nth(prems_of st', i))
wenzelm@10817
   358
  in
paulson@4178
   359
      if null (term_tvars concl') then ()
paulson@4178
   360
      else warning"Type variables in new subgoal: add a type constraint?";
wenzelm@4270
   361
      Seq.single st'
paulson@4178
   362
  end;
clasohm@0
   363
lcp@439
   364
(*Introduce a list of lemmas and subgoals*)
lcp@439
   365
fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops);
lcp@439
   366
clasohm@0
   367
clasohm@0
   368
(**** Indexing and filtering of theorems ****)
clasohm@0
   369
clasohm@0
   370
(*Returns the list of potentially resolvable theorems for the goal "prem",
wenzelm@10805
   371
        using the predicate  could(subgoal,concl).
clasohm@0
   372
  Resulting list is no longer than "limit"*)
clasohm@0
   373
fun filter_thms could (limit, prem, ths) =
clasohm@0
   374
  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
clasohm@0
   375
      fun filtr (limit, []) = []
wenzelm@10805
   376
        | filtr (limit, th::ths) =
wenzelm@10805
   377
            if limit=0 then  []
wenzelm@10805
   378
            else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
wenzelm@10805
   379
            else filtr(limit,ths)
clasohm@0
   380
  in  filtr(limit,ths)  end;
clasohm@0
   381
clasohm@0
   382
clasohm@0
   383
(*** biresolution and resolution using nets ***)
clasohm@0
   384
clasohm@0
   385
(** To preserve the order of the rules, tag them with increasing integers **)
clasohm@0
   386
clasohm@0
   387
(*insert tags*)
clasohm@0
   388
fun taglist k [] = []
clasohm@0
   389
  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
clasohm@0
   390
clasohm@0
   391
(*remove tags and suppress duplicates -- list is assumed sorted!*)
clasohm@0
   392
fun untaglist [] = []
clasohm@0
   393
  | untaglist [(k:int,x)] = [x]
clasohm@0
   394
  | untaglist ((k,x) :: (rest as (k',x')::_)) =
clasohm@0
   395
      if k=k' then untaglist rest
clasohm@0
   396
      else    x :: untaglist rest;
clasohm@0
   397
clasohm@0
   398
(*return list elements in original order*)
wenzelm@10817
   399
fun orderlist kbrls = untaglist (sort (int_ord o pairself fst) kbrls);
clasohm@0
   400
clasohm@0
   401
(*insert one tagged brl into the pair of nets*)
wenzelm@12320
   402
fun insert_tagged_brl (kbrl as (k, (eres, th)), (inet, enet)) =
wenzelm@12320
   403
  if eres then
wenzelm@12320
   404
    (case try Thm.major_prem_of th of
wenzelm@12320
   405
      Some prem => (inet, Net.insert_term ((prem, kbrl), enet, K false))
wenzelm@12320
   406
    | None => error "insert_tagged_brl: elimination rule with no premises")
wenzelm@12320
   407
  else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);
clasohm@0
   408
clasohm@0
   409
(*build a pair of nets for biresolution*)
wenzelm@10817
   410
fun build_netpair netpair brls =
lcp@1077
   411
    foldr insert_tagged_brl (taglist 1 brls, netpair);
clasohm@0
   412
wenzelm@12320
   413
(*delete one kbrl from the pair of nets*)
paulson@1801
   414
local
wenzelm@12320
   415
  fun eq_kbrl ((_, (_, th)), (_, (_, th'))) = eq_thm (th, th')
paulson@1801
   416
in
wenzelm@12320
   417
fun delete_tagged_brl (brl as (eres, th), (inet, enet)) =
wenzelm@12320
   418
  if eres then
wenzelm@12320
   419
    (case try Thm.major_prem_of th of
wenzelm@12320
   420
      Some prem => (inet, Net.delete_term ((prem, ((), brl)), enet, eq_kbrl))
wenzelm@12320
   421
    | None => (inet, enet))  (*no major premise: ignore*)
wenzelm@12320
   422
  else (Net.delete_term ((Thm.concl_of th, ((), brl)), inet, eq_kbrl), enet);
paulson@1801
   423
end;
paulson@1801
   424
paulson@1801
   425
wenzelm@10817
   426
(*biresolution using a pair of nets rather than rules.
paulson@3706
   427
    function "order" must sort and possibly filter the list of brls.
paulson@3706
   428
    boolean "match" indicates matching or unification.*)
paulson@3706
   429
fun biresolution_from_nets_tac order match (inet,enet) =
clasohm@0
   430
  SUBGOAL
clasohm@0
   431
    (fn (prem,i) =>
clasohm@0
   432
      let val hyps = Logic.strip_assums_hyp prem
wenzelm@10817
   433
          and concl = Logic.strip_assums_concl prem
clasohm@0
   434
          val kbrls = Net.unify_term inet concl @
paulson@2672
   435
                      List.concat (map (Net.unify_term enet) hyps)
paulson@3706
   436
      in PRIMSEQ (biresolution match (order kbrls) i) end);
clasohm@0
   437
paulson@3706
   438
(*versions taking pre-built nets.  No filtering of brls*)
paulson@3706
   439
val biresolve_from_nets_tac = biresolution_from_nets_tac orderlist false;
paulson@3706
   440
val bimatch_from_nets_tac   = biresolution_from_nets_tac orderlist true;
clasohm@0
   441
clasohm@0
   442
(*fast versions using nets internally*)
lcp@670
   443
val net_biresolve_tac =
lcp@670
   444
    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);
lcp@670
   445
lcp@670
   446
val net_bimatch_tac =
lcp@670
   447
    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);
clasohm@0
   448
clasohm@0
   449
(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
clasohm@0
   450
clasohm@0
   451
(*insert one tagged rl into the net*)
clasohm@0
   452
fun insert_krl (krl as (k,th), net) =
clasohm@0
   453
    Net.insert_term ((concl_of th, krl), net, K false);
clasohm@0
   454
clasohm@0
   455
(*build a net of rules for resolution*)
wenzelm@10817
   456
fun build_net rls =
clasohm@0
   457
    foldr insert_krl (taglist 1 rls, Net.empty);
clasohm@0
   458
clasohm@0
   459
(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
clasohm@0
   460
fun filt_resolution_from_net_tac match pred net =
clasohm@0
   461
  SUBGOAL
clasohm@0
   462
    (fn (prem,i) =>
clasohm@0
   463
      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
wenzelm@10817
   464
      in
wenzelm@10817
   465
         if pred krls
clasohm@0
   466
         then PRIMSEQ
wenzelm@10805
   467
                (biresolution match (map (pair false) (orderlist krls)) i)
clasohm@0
   468
         else no_tac
clasohm@0
   469
      end);
clasohm@0
   470
clasohm@0
   471
(*Resolve the subgoal using the rules (making a net) unless too flexible,
clasohm@0
   472
   which means more than maxr rules are unifiable.      *)
wenzelm@10817
   473
fun filt_resolve_tac rules maxr =
clasohm@0
   474
    let fun pred krls = length krls <= maxr
clasohm@0
   475
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
clasohm@0
   476
clasohm@0
   477
(*versions taking pre-built nets*)
clasohm@0
   478
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
clasohm@0
   479
val match_from_net_tac = filt_resolution_from_net_tac true (K true);
clasohm@0
   480
clasohm@0
   481
(*fast versions using nets internally*)
clasohm@0
   482
val net_resolve_tac = resolve_from_net_tac o build_net;
clasohm@0
   483
val net_match_tac = match_from_net_tac o build_net;
clasohm@0
   484
clasohm@0
   485
clasohm@0
   486
(*** For Natural Deduction using (bires_flg, rule) pairs ***)
clasohm@0
   487
clasohm@0
   488
(*The number of new subgoals produced by the brule*)
lcp@1077
   489
fun subgoals_of_brl (true,rule)  = nprems_of rule - 1
lcp@1077
   490
  | subgoals_of_brl (false,rule) = nprems_of rule;
clasohm@0
   491
clasohm@0
   492
(*Less-than test: for sorting to minimize number of new subgoals*)
clasohm@0
   493
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
clasohm@0
   494
clasohm@0
   495
clasohm@0
   496
(*** Meta-Rewriting Tactics ***)
clasohm@0
   497
clasohm@0
   498
fun result1 tacf mss thm =
wenzelm@4270
   499
  apsome fst (Seq.pull (tacf mss thm));
clasohm@0
   500
wenzelm@3575
   501
val simple_prover =
wenzelm@11671
   502
  result1 (fn mss => ALLGOALS (resolve_tac (MetaSimplifier.prems_of_mss mss)));
wenzelm@3575
   503
wenzelm@11768
   504
val rewrite = MetaSimplifier.rewrite_aux simple_prover;
wenzelm@11768
   505
val rewrite_cterm = (#2 o Thm.dest_comb o #prop o Thm.crep_thm) ooo rewrite;
wenzelm@11768
   506
val simplify = MetaSimplifier.simplify_aux simple_prover;
wenzelm@11768
   507
val rewrite_rule = simplify true;
berghofe@10415
   508
val rewrite_goals_rule = MetaSimplifier.rewrite_goals_rule_aux simple_prover;
wenzelm@3575
   509
paulson@2145
   510
(*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
paulson@2145
   511
fun asm_rewrite_goal_tac mode prover_tac mss =
wenzelm@11671
   512
  SELECT_GOAL
wenzelm@11671
   513
    (PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (result1 prover_tac) mss 1));
clasohm@0
   514
wenzelm@10444
   515
fun rewrite_goal_tac rews =
wenzelm@10444
   516
  asm_rewrite_goal_tac (true, false, false) (K no_tac) (MetaSimplifier.mss_of rews);
wenzelm@10444
   517
lcp@69
   518
(*Rewrite throughout proof state. *)
lcp@69
   519
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);
clasohm@0
   520
clasohm@0
   521
(*Rewrite subgoals only, not main goal. *)
lcp@69
   522
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
clasohm@1460
   523
fun rewtac def = rewrite_goals_tac [def];
clasohm@0
   524
wenzelm@10817
   525
fun norm_hhf th =
wenzelm@10817
   526
  (if Logic.is_norm_hhf (#prop (Thm.rep_thm th)) then th else rewrite_rule [Drule.norm_hhf_eq] th)
wenzelm@10817
   527
  |> Drule.forall_elim_vars_safe;
wenzelm@10817
   528
wenzelm@10817
   529
val norm_hhf_tac = SUBGOAL (fn (t, i) =>
wenzelm@10817
   530
  if Logic.is_norm_hhf t then all_tac
wenzelm@10817
   531
  else rewrite_goal_tac [Drule.norm_hhf_eq] i);
wenzelm@10805
   532
clasohm@0
   533
paulson@1501
   534
(*** for folding definitions, handling critical pairs ***)
lcp@69
   535
lcp@69
   536
(*The depth of nesting in a term*)
lcp@69
   537
fun term_depth (Abs(a,T,t)) = 1 + term_depth t
paulson@2145
   538
  | term_depth (f$t) = 1 + Int.max(term_depth f, term_depth t)
lcp@69
   539
  | term_depth _ = 0;
lcp@69
   540
lcp@69
   541
val lhs_of_thm = #1 o Logic.dest_equals o #prop o rep_thm;
lcp@69
   542
lcp@69
   543
(*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
lcp@69
   544
  Returns longest lhs first to avoid folding its subexpressions.*)
lcp@69
   545
fun sort_lhs_depths defs =
lcp@69
   546
  let val keylist = make_keylist (term_depth o lhs_of_thm) defs
wenzelm@4438
   547
      val keys = distinct (sort (rev_order o int_ord) (map #2 keylist))
lcp@69
   548
  in  map (keyfilter keylist) keys  end;
lcp@69
   549
wenzelm@7596
   550
val rev_defs = sort_lhs_depths o map symmetric;
lcp@69
   551
wenzelm@7596
   552
fun fold_rule defs thm = foldl (fn (th, ds) => rewrite_rule ds th) (thm, rev_defs defs);
wenzelm@7596
   553
fun fold_tac defs = EVERY (map rewrite_tac (rev_defs defs));
wenzelm@7596
   554
fun fold_goals_tac defs = EVERY (map rewrite_goals_tac (rev_defs defs));
lcp@69
   555
lcp@69
   556
lcp@69
   557
(*** Renaming of parameters in a subgoal
lcp@69
   558
     Names may contain letters, digits or primes and must be
lcp@69
   559
     separated by blanks ***)
clasohm@0
   560
clasohm@0
   561
(*Calling this will generate the warning "Same as previous level" since
clasohm@0
   562
  it affects nothing but the names of bound variables!*)
wenzelm@9535
   563
fun rename_params_tac xs i =
wenzelm@9535
   564
  (if !Logic.auto_rename
wenzelm@10817
   565
    then (warning "Resetting Logic.auto_rename";
wenzelm@10805
   566
        Logic.auto_rename := false)
wenzelm@9535
   567
   else (); PRIMITIVE (rename_params_rule (xs, i)));
wenzelm@9535
   568
wenzelm@10817
   569
fun rename_tac str i =
wenzelm@10817
   570
  let val cs = Symbol.explode str in
wenzelm@4693
   571
  case #2 (take_prefix (Symbol.is_letdig orf Symbol.is_blank) cs) of
wenzelm@9535
   572
      [] => rename_params_tac (scanwords Symbol.is_letdig cs) i
clasohm@0
   573
    | c::_ => error ("Illegal character: " ^ c)
clasohm@0
   574
  end;
clasohm@0
   575
paulson@1501
   576
(*Rename recent parameters using names generated from a and the suffixes,
paulson@1501
   577
  provided the string a, which represents a term, is an identifier. *)
wenzelm@10817
   578
fun rename_last_tac a sufs i =
clasohm@0
   579
  let val names = map (curry op^ a) sufs
clasohm@0
   580
  in  if Syntax.is_identifier a
clasohm@0
   581
      then PRIMITIVE (rename_params_rule (names,i))
clasohm@0
   582
      else all_tac
clasohm@0
   583
  end;
clasohm@0
   584
paulson@2043
   585
(*Prunes all redundant parameters from the proof state by rewriting.
paulson@2043
   586
  DOES NOT rewrite main goal, where quantification over an unused bound
paulson@2043
   587
    variable is sometimes done to avoid the need for cut_facts_tac.*)
paulson@2043
   588
val prune_params_tac = rewrite_goals_tac [triv_forall_equality];
clasohm@0
   589
paulson@1501
   590
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
paulson@1501
   591
  right to left if n is positive, and from left to right if n is negative.*)
paulson@2672
   592
fun rotate_tac 0 i = all_tac
paulson@2672
   593
  | rotate_tac k i = PRIMITIVE (rotate_rule k i);
nipkow@1209
   594
paulson@7248
   595
(*Rotates the given subgoal to be the last.*)
paulson@7248
   596
fun defer_tac i = PRIMITIVE (permute_prems (i-1) 1);
paulson@7248
   597
nipkow@5974
   598
(* remove premises that do not satisfy p; fails if all prems satisfy p *)
nipkow@5974
   599
fun filter_prems_tac p =
nipkow@5974
   600
  let fun Then None tac = Some tac
nipkow@5974
   601
        | Then (Some tac) tac' = Some(tac THEN' tac');
nipkow@5974
   602
      fun thins ((tac,n),H) =
nipkow@5974
   603
        if p H then (tac,n+1)
nipkow@5974
   604
        else (Then tac (rotate_tac n THEN' etac thin_rl),0);
nipkow@5974
   605
  in SUBGOAL(fn (subg,n) =>
nipkow@5974
   606
       let val Hs = Logic.strip_assums_hyp subg
nipkow@5974
   607
       in case fst(foldl thins ((None,0),Hs)) of
nipkow@5974
   608
            None => no_tac | Some tac => tac n
nipkow@5974
   609
       end)
nipkow@5974
   610
  end;
nipkow@5974
   611
wenzelm@11961
   612
wenzelm@12139
   613
(*meta-level conjunction*)
wenzelm@12139
   614
val conj_tac = SUBGOAL (fn (Const ("all", _) $ Abs (_, _, Const ("==>", _) $
wenzelm@12139
   615
      (Const ("==>", _) $ _ $ (Const ("==>", _) $ _ $ Bound 0)) $ Bound 0), i) =>
wenzelm@12139
   616
    (fn st =>
wenzelm@12139
   617
      compose_tac (false, Drule.incr_indexes_wrt [] [] [] [st] Drule.conj_intr_thm, 2) i st)
wenzelm@12139
   618
  | _ => no_tac);
wenzelm@12139
   619
  
wenzelm@12139
   620
val conjunction_tac = ALLGOALS (REPEAT_ALL_NEW conj_tac);
wenzelm@12139
   621
wenzelm@12139
   622
wenzelm@12139
   623
wenzelm@11970
   624
(** minimal goal interface for internal use *)
wenzelm@11961
   625
wenzelm@11970
   626
fun prove sign xs asms prop tac =
wenzelm@11961
   627
  let
wenzelm@11961
   628
    val statement = Logic.list_implies (asms, prop);
wenzelm@11961
   629
    val frees = map Term.dest_Free (Term.term_frees statement);
wenzelm@11970
   630
    val fixed_frees = filter_out (fn (x, _) => x mem_string xs) frees;
wenzelm@11970
   631
    val fixed_tfrees = foldr Term.add_typ_tfree_names (map #2 fixed_frees, []);
wenzelm@11961
   632
    val params = mapfilter (fn x => apsome (pair x) (assoc_string (frees, x))) xs;
wenzelm@11961
   633
wenzelm@12212
   634
    fun err msg = raise ERROR_MESSAGE
wenzelm@12212
   635
      (msg ^ "\nThe error(s) above occurred for the goal statement:\n" ^
wenzelm@12212
   636
        Sign.string_of_term sign (Term.list_all_free (params, statement)));
wenzelm@11961
   637
wenzelm@12170
   638
    fun cert_safe t = Thm.cterm_of sign (Envir.beta_norm t)
wenzelm@11961
   639
      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
wenzelm@11961
   640
wenzelm@11961
   641
    val _ = cert_safe statement;
wenzelm@11974
   642
    val _ = Term.no_dummy_patterns statement handle TERM (msg, _) => err msg;
wenzelm@11961
   643
wenzelm@11974
   644
    val cparams = map (cert_safe o Free) params;
wenzelm@11961
   645
    val casms = map cert_safe asms;
wenzelm@11961
   646
    val prems = map (norm_hhf o Thm.assume) casms;
wenzelm@11961
   647
    val goal = Drule.mk_triv_goal (cert_safe prop);
wenzelm@11961
   648
wenzelm@11961
   649
    val goal' =
wenzelm@11961
   650
      (case Seq.pull (tac prems goal) of Some (goal', _) => goal' | _ => err "Tactic failed.");
wenzelm@11961
   651
    val ngoals = Thm.nprems_of goal';
wenzelm@11961
   652
    val raw_result = goal' RS Drule.rev_triv_goal;
wenzelm@11961
   653
    val prop' = #prop (Thm.rep_thm raw_result);
wenzelm@11961
   654
  in
wenzelm@11961
   655
    if ngoals <> 0 then
wenzelm@11961
   656
      err ("Proof failed.\n" ^ Pretty.string_of (Pretty.chunks (Display.pretty_goals ngoals goal'))
wenzelm@11961
   657
        ^ ("\n" ^ string_of_int ngoals ^ " unsolved goal(s)!"))
wenzelm@11970
   658
    else if not (Pattern.matches (Sign.tsig_of sign) (prop, prop')) then
wenzelm@11970
   659
      err ("Proved a different theorem: " ^ Sign.string_of_term sign prop')
wenzelm@11961
   660
    else
wenzelm@11961
   661
      raw_result
wenzelm@11961
   662
      |> Drule.implies_intr_list casms
wenzelm@11974
   663
      |> Drule.forall_intr_list cparams
wenzelm@11961
   664
      |> norm_hhf
wenzelm@12498
   665
      |> (#1 o Thm.varifyT' fixed_tfrees)
wenzelm@11970
   666
      |> Drule.zero_var_indexes
wenzelm@11961
   667
  end;
wenzelm@11961
   668
wenzelm@11970
   669
fun prove_standard sign xs asms prop tac = Drule.standard (prove sign xs asms prop tac);
wenzelm@11970
   670
clasohm@0
   671
end;
paulson@1501
   672
wenzelm@11774
   673
structure BasicTactic: BASIC_TACTIC = Tactic;
wenzelm@11774
   674
open BasicTactic;