src/Pure/tactic.ML
author wenzelm
Thu Jul 28 15:19:59 2005 +0200 (2005-07-28)
changeset 16942 c01816b32c04
parent 16876 f57b38cced32
child 17203 29b2563f5c11
permissions -rw-r--r--
norm_hhf_rule: Thm.adjust_maxidx_thm before Drule.gen_all;
removed prove_standard, prove_multi_standard;
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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 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_rules_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_plain    : thm -> thm
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  val norm_hhf_rule     : thm -> thm
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  val norm_hhf_tac      : int -> 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 * sort) * 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 eq_kbrl: ('a * (bool * thm)) * ('a * (bool * thm)) -> bool
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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 simplify: bool -> thm list -> thm -> thm
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  val conjunction_tac: tactic
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  val smart_conjunction_tac: int -> tactic
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  val prove_multi_plain: theory -> string list -> term list -> term list ->
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    (thm list -> tactic) -> thm list
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  val prove_multi: theory -> string list -> term list -> term list ->
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    (thm list -> tactic) -> thm list
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  val prove_plain: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
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  val prove: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
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  val compose_inst_tac' : (indexname * string) list -> (bool * thm * int) ->
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                          int -> tactic
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  val lift_inst_rule'   : thm * int * (indexname * string) list * thm -> thm
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  val eres_inst_tac'    : (indexname * string) list -> thm -> int -> tactic
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  val res_inst_tac'     : (indexname * string) list -> thm -> int -> tactic
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  val instantiate_tac'  : (indexname * string) list -> tactic
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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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(*** 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) = term_of a aconv term_of 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  (*Applying Thm.varifyT to the result of thawfn would (re-)generalize
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          all type variables that appear in the subgoals. Unfortunately, it
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          would also break the function AxClass.intro_classes_tac, even in the
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          trivial case where the type class has no axioms.*)
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        Seq.single (thawfn implied)
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    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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(*params of subgoal i as they are printed*)
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fun params_of_state st i =
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  let val (_, _, Bi, _) = dest_state(st,i)
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      val params = Logic.strip_params Bi
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  in rev(rename_wrt_term Bi params) end;
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(*read instantiations with respect to subgoal i of proof state st*)
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fun read_insts_in_state (st, i, sinsts, rule) =
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  let val thy = Thm.theory_of_thm st
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      and params = params_of_state st i
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      and rts = types_sorts rule and (types,sorts) = types_sorts st
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      fun types'(a, ~1) = (case assoc_string (params, a) of NONE => types (a, ~1) | sm => sm)
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        | types' ixn = types ixn;
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      val used = Drule.add_used rule (Drule.add_used st []);
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  in read_insts thy rts (types',sorts) used sinsts 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 (Tinsts,insts) = read_insts_in_state (st, i, sinsts, rule)
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    and {maxidx,...} = rep_thm st
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    and params = params_of_state st i
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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---> Logic.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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    val lifttvar = pairself (ctyp_fun (Logic.incr_tvar inc))
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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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fun lift_inst_rule (st, i, sinsts, rule) = lift_inst_rule'
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  (st, i, map (apfst Syntax.indexname) sinsts, rule);
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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,thy,...} = rep_thm st
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    val paramTs = map #2 (params_of_state st i)
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    and inc = maxidx+1
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    fun liftvar ((a,j), T) = Var((a, j+inc), paramTs---> Logic.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 thy (liftvar v), cterm_of thy t)
berghofe@15797
   291
    fun liftTpair (((a, i), S), T) =
wenzelm@16425
   292
      (ctyp_of thy (TVar ((a, i + inc), S)),
wenzelm@16876
   293
       ctyp_of thy (Logic.incr_tvar inc T))
paulson@8129
   294
in Drule.instantiate (map liftTpair Tinsts, map liftpair insts)
paulson@8129
   295
                     (lift_rule (st,i) rule)
nipkow@1966
   296
end;
clasohm@0
   297
clasohm@0
   298
(*** Resolve after lifting and instantation; may refer to parameters of the
clasohm@0
   299
     subgoal.  Fails if "i" is out of range.  ***)
clasohm@0
   300
clasohm@0
   301
(*compose version: arguments are as for bicompose.*)
berghofe@15442
   302
fun gen_compose_inst_tac instf sinsts (bires_flg, rule, nsubgoal) i st =
paulson@8977
   303
  if i > nprems_of st then no_tac st
paulson@8977
   304
  else st |>
berghofe@15442
   305
    (compose_tac (bires_flg, instf (st, i, sinsts, rule), nsubgoal) i
wenzelm@12262
   306
     handle TERM (msg,_)   => (warning msg;  no_tac)
wenzelm@12262
   307
          | THM  (msg,_,_) => (warning msg;  no_tac));
clasohm@0
   308
berghofe@15442
   309
val compose_inst_tac = gen_compose_inst_tac lift_inst_rule;
berghofe@15442
   310
val compose_inst_tac' = gen_compose_inst_tac lift_inst_rule';
berghofe@15442
   311
lcp@761
   312
(*"Resolve" version.  Note: res_inst_tac cannot behave sensibly if the
lcp@761
   313
  terms that are substituted contain (term or type) unknowns from the
lcp@761
   314
  goal, because it is unable to instantiate goal unknowns at the same time.
lcp@761
   315
paulson@2029
   316
  The type checker is instructed not to freeze flexible type vars that
nipkow@952
   317
  were introduced during type inference and still remain in the term at the
nipkow@952
   318
  end.  This increases flexibility but can introduce schematic type vars in
nipkow@952
   319
  goals.
lcp@761
   320
*)
clasohm@0
   321
fun res_inst_tac sinsts rule i =
clasohm@0
   322
    compose_inst_tac sinsts (false, rule, nprems_of rule) i;
clasohm@0
   323
berghofe@15442
   324
fun res_inst_tac' sinsts rule i =
berghofe@15442
   325
    compose_inst_tac' sinsts (false, rule, nprems_of rule) i;
berghofe@15442
   326
paulson@1501
   327
(*eresolve elimination version*)
clasohm@0
   328
fun eres_inst_tac sinsts rule i =
clasohm@0
   329
    compose_inst_tac sinsts (true, rule, nprems_of rule) i;
clasohm@0
   330
berghofe@15464
   331
fun eres_inst_tac' sinsts rule i =
berghofe@15464
   332
    compose_inst_tac' sinsts (true, rule, nprems_of rule) i;
berghofe@15464
   333
lcp@270
   334
(*For forw_inst_tac and dres_inst_tac.  Preserve Var indexes of rl;
lcp@270
   335
  increment revcut_rl instead.*)
wenzelm@10817
   336
fun make_elim_preserve rl =
lcp@270
   337
  let val {maxidx,...} = rep_thm rl
wenzelm@16425
   338
      fun cvar ixn = cterm_of ProtoPure.thy (Var(ixn,propT));
wenzelm@10817
   339
      val revcut_rl' =
wenzelm@10805
   340
          instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),
wenzelm@10805
   341
                             (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
clasohm@0
   342
      val arg = (false, rl, nprems_of rl)
wenzelm@4270
   343
      val [th] = Seq.list_of (bicompose false arg 1 revcut_rl')
clasohm@0
   344
  in  th  end
clasohm@0
   345
  handle Bind => raise THM("make_elim_preserve", 1, [rl]);
clasohm@0
   346
lcp@270
   347
(*instantiate and cut -- for a FACT, anyway...*)
lcp@270
   348
fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   349
lcp@270
   350
(*forward tactic applies a RULE to an assumption without deleting it*)
lcp@270
   351
fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac;
lcp@270
   352
lcp@270
   353
(*dresolve tactic applies a RULE to replace an assumption*)
clasohm@0
   354
fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   355
oheimb@10347
   356
(*instantiate variables in the whole state*)
oheimb@10347
   357
val instantiate_tac = PRIMITIVE o read_instantiate;
oheimb@10347
   358
berghofe@15797
   359
val instantiate_tac' = PRIMITIVE o Drule.read_instantiate';
berghofe@15797
   360
paulson@1951
   361
(*Deletion of an assumption*)
paulson@1951
   362
fun thin_tac s = eres_inst_tac [("V",s)] thin_rl;
paulson@1951
   363
lcp@270
   364
(*** Applications of cut_rl ***)
clasohm@0
   365
clasohm@0
   366
(*Used by metacut_tac*)
clasohm@0
   367
fun bires_cut_tac arg i =
clasohm@1460
   368
    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
clasohm@0
   369
clasohm@0
   370
(*The conclusion of the rule gets assumed in subgoal i,
clasohm@0
   371
  while subgoal i+1,... are the premises of the rule.*)
clasohm@0
   372
fun metacut_tac rule = bires_cut_tac [(false,rule)];
clasohm@0
   373
clasohm@0
   374
(*Recognizes theorems that are not rules, but simple propositions*)
clasohm@0
   375
fun is_fact rl =
clasohm@0
   376
    case prems_of rl of
wenzelm@10805
   377
        [] => true  |  _::_ => false;
clasohm@0
   378
paulson@13650
   379
(*"Cut" a list of rules into the goal.  Their premises will become new
paulson@13650
   380
  subgoals.*)
paulson@13650
   381
fun cut_rules_tac ths i = EVERY (map (fn th => metacut_tac th i) ths);
paulson@13650
   382
paulson@13650
   383
(*As above, but inserts only facts (unconditional theorems);
paulson@13650
   384
  generates no additional subgoals. *)
skalberg@15570
   385
fun cut_facts_tac ths = cut_rules_tac  (List.filter is_fact ths);
clasohm@0
   386
clasohm@0
   387
(*Introduce the given proposition as a lemma and subgoal*)
wenzelm@12847
   388
fun subgoal_tac sprop =
wenzelm@12847
   389
  DETERM o res_inst_tac [("psi", sprop)] cut_rl THEN' SUBGOAL (fn (prop, _) =>
wenzelm@12847
   390
    let val concl' = Logic.strip_assums_concl prop in
paulson@4178
   391
      if null (term_tvars concl') then ()
paulson@4178
   392
      else warning"Type variables in new subgoal: add a type constraint?";
wenzelm@12847
   393
      all_tac
wenzelm@12847
   394
  end);
clasohm@0
   395
lcp@439
   396
(*Introduce a list of lemmas and subgoals*)
lcp@439
   397
fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops);
lcp@439
   398
clasohm@0
   399
clasohm@0
   400
(**** Indexing and filtering of theorems ****)
clasohm@0
   401
clasohm@0
   402
(*Returns the list of potentially resolvable theorems for the goal "prem",
wenzelm@10805
   403
        using the predicate  could(subgoal,concl).
clasohm@0
   404
  Resulting list is no longer than "limit"*)
clasohm@0
   405
fun filter_thms could (limit, prem, ths) =
clasohm@0
   406
  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
clasohm@0
   407
      fun filtr (limit, []) = []
wenzelm@10805
   408
        | filtr (limit, th::ths) =
wenzelm@10805
   409
            if limit=0 then  []
wenzelm@10805
   410
            else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
wenzelm@10805
   411
            else filtr(limit,ths)
clasohm@0
   412
  in  filtr(limit,ths)  end;
clasohm@0
   413
clasohm@0
   414
clasohm@0
   415
(*** biresolution and resolution using nets ***)
clasohm@0
   416
clasohm@0
   417
(** To preserve the order of the rules, tag them with increasing integers **)
clasohm@0
   418
clasohm@0
   419
(*insert tags*)
clasohm@0
   420
fun taglist k [] = []
clasohm@0
   421
  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
clasohm@0
   422
clasohm@0
   423
(*remove tags and suppress duplicates -- list is assumed sorted!*)
clasohm@0
   424
fun untaglist [] = []
clasohm@0
   425
  | untaglist [(k:int,x)] = [x]
clasohm@0
   426
  | untaglist ((k,x) :: (rest as (k',x')::_)) =
clasohm@0
   427
      if k=k' then untaglist rest
clasohm@0
   428
      else    x :: untaglist rest;
clasohm@0
   429
clasohm@0
   430
(*return list elements in original order*)
wenzelm@10817
   431
fun orderlist kbrls = untaglist (sort (int_ord o pairself fst) kbrls);
clasohm@0
   432
clasohm@0
   433
(*insert one tagged brl into the pair of nets*)
wenzelm@12320
   434
fun insert_tagged_brl (kbrl as (k, (eres, th)), (inet, enet)) =
wenzelm@12320
   435
  if eres then
wenzelm@12320
   436
    (case try Thm.major_prem_of th of
wenzelm@16809
   437
      SOME prem => (inet, Net.insert_term (K false) (prem, kbrl) enet)
skalberg@15531
   438
    | NONE => error "insert_tagged_brl: elimination rule with no premises")
wenzelm@16809
   439
  else (Net.insert_term (K false) (concl_of th, kbrl) inet, enet);
clasohm@0
   440
clasohm@0
   441
(*build a pair of nets for biresolution*)
wenzelm@10817
   442
fun build_netpair netpair brls =
skalberg@15574
   443
    foldr insert_tagged_brl netpair (taglist 1 brls);
clasohm@0
   444
wenzelm@12320
   445
(*delete one kbrl from the pair of nets*)
wenzelm@16809
   446
fun eq_kbrl ((_, (_, th)), (_, (_, th'))) = Drule.eq_thm_prop (th, th')
wenzelm@16809
   447
wenzelm@12320
   448
fun delete_tagged_brl (brl as (eres, th), (inet, enet)) =
paulson@13925
   449
  (if eres then
wenzelm@12320
   450
    (case try Thm.major_prem_of th of
wenzelm@16809
   451
      SOME prem => (inet, Net.delete_term eq_kbrl (prem, ((), brl)) enet)
skalberg@15531
   452
    | NONE => (inet, enet))  (*no major premise: ignore*)
wenzelm@16809
   453
  else (Net.delete_term eq_kbrl (Thm.concl_of th, ((), brl)) inet, enet))
paulson@13925
   454
  handle Net.DELETE => (inet,enet);
paulson@1801
   455
paulson@1801
   456
wenzelm@10817
   457
(*biresolution using a pair of nets rather than rules.
paulson@3706
   458
    function "order" must sort and possibly filter the list of brls.
paulson@3706
   459
    boolean "match" indicates matching or unification.*)
paulson@3706
   460
fun biresolution_from_nets_tac order match (inet,enet) =
clasohm@0
   461
  SUBGOAL
clasohm@0
   462
    (fn (prem,i) =>
clasohm@0
   463
      let val hyps = Logic.strip_assums_hyp prem
wenzelm@10817
   464
          and concl = Logic.strip_assums_concl prem
clasohm@0
   465
          val kbrls = Net.unify_term inet concl @
paulson@2672
   466
                      List.concat (map (Net.unify_term enet) hyps)
paulson@3706
   467
      in PRIMSEQ (biresolution match (order kbrls) i) end);
clasohm@0
   468
paulson@3706
   469
(*versions taking pre-built nets.  No filtering of brls*)
paulson@3706
   470
val biresolve_from_nets_tac = biresolution_from_nets_tac orderlist false;
paulson@3706
   471
val bimatch_from_nets_tac   = biresolution_from_nets_tac orderlist true;
clasohm@0
   472
clasohm@0
   473
(*fast versions using nets internally*)
lcp@670
   474
val net_biresolve_tac =
lcp@670
   475
    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);
lcp@670
   476
lcp@670
   477
val net_bimatch_tac =
lcp@670
   478
    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);
clasohm@0
   479
clasohm@0
   480
(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
clasohm@0
   481
clasohm@0
   482
(*insert one tagged rl into the net*)
clasohm@0
   483
fun insert_krl (krl as (k,th), net) =
wenzelm@16809
   484
    Net.insert_term (K false) (concl_of th, krl) net;
clasohm@0
   485
clasohm@0
   486
(*build a net of rules for resolution*)
wenzelm@10817
   487
fun build_net rls =
skalberg@15574
   488
    foldr insert_krl Net.empty (taglist 1 rls);
clasohm@0
   489
clasohm@0
   490
(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
clasohm@0
   491
fun filt_resolution_from_net_tac match pred net =
clasohm@0
   492
  SUBGOAL
clasohm@0
   493
    (fn (prem,i) =>
clasohm@0
   494
      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
wenzelm@10817
   495
      in
wenzelm@10817
   496
         if pred krls
clasohm@0
   497
         then PRIMSEQ
wenzelm@10805
   498
                (biresolution match (map (pair false) (orderlist krls)) i)
clasohm@0
   499
         else no_tac
clasohm@0
   500
      end);
clasohm@0
   501
clasohm@0
   502
(*Resolve the subgoal using the rules (making a net) unless too flexible,
clasohm@0
   503
   which means more than maxr rules are unifiable.      *)
wenzelm@10817
   504
fun filt_resolve_tac rules maxr =
clasohm@0
   505
    let fun pred krls = length krls <= maxr
clasohm@0
   506
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
clasohm@0
   507
clasohm@0
   508
(*versions taking pre-built nets*)
clasohm@0
   509
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
clasohm@0
   510
val match_from_net_tac = filt_resolution_from_net_tac true (K true);
clasohm@0
   511
clasohm@0
   512
(*fast versions using nets internally*)
clasohm@0
   513
val net_resolve_tac = resolve_from_net_tac o build_net;
clasohm@0
   514
val net_match_tac = match_from_net_tac o build_net;
clasohm@0
   515
clasohm@0
   516
clasohm@0
   517
(*** For Natural Deduction using (bires_flg, rule) pairs ***)
clasohm@0
   518
clasohm@0
   519
(*The number of new subgoals produced by the brule*)
lcp@1077
   520
fun subgoals_of_brl (true,rule)  = nprems_of rule - 1
lcp@1077
   521
  | subgoals_of_brl (false,rule) = nprems_of rule;
clasohm@0
   522
clasohm@0
   523
(*Less-than test: for sorting to minimize number of new subgoals*)
clasohm@0
   524
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
clasohm@0
   525
clasohm@0
   526
clasohm@0
   527
(*** Meta-Rewriting Tactics ***)
clasohm@0
   528
wenzelm@3575
   529
val simple_prover =
wenzelm@15021
   530
  SINGLE o (fn ss => ALLGOALS (resolve_tac (MetaSimplifier.prems_of_ss ss)));
wenzelm@3575
   531
wenzelm@11768
   532
val rewrite = MetaSimplifier.rewrite_aux simple_prover;
wenzelm@11768
   533
val simplify = MetaSimplifier.simplify_aux simple_prover;
wenzelm@11768
   534
val rewrite_rule = simplify true;
berghofe@10415
   535
val rewrite_goals_rule = MetaSimplifier.rewrite_goals_rule_aux simple_prover;
wenzelm@3575
   536
wenzelm@10444
   537
fun rewrite_goal_tac rews =
wenzelm@15021
   538
  MetaSimplifier.asm_rewrite_goal_tac (true, false, false) (K no_tac)
wenzelm@15021
   539
    (MetaSimplifier.empty_ss addsimps rews);
wenzelm@10444
   540
lcp@69
   541
(*Rewrite throughout proof state. *)
lcp@69
   542
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);
clasohm@0
   543
clasohm@0
   544
(*Rewrite subgoals only, not main goal. *)
lcp@69
   545
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
clasohm@1460
   546
fun rewtac def = rewrite_goals_tac [def];
clasohm@0
   547
ballarin@15696
   548
fun norm_hhf_plain th =
wenzelm@16942
   549
  if Drule.is_norm_hhf (Thm.prop_of th) then th
ballarin@15696
   550
  else rewrite_rule [Drule.norm_hhf_eq] th;
ballarin@15696
   551
wenzelm@16942
   552
val norm_hhf_rule =
wenzelm@16942
   553
  norm_hhf_plain
wenzelm@16942
   554
  #> Thm.adjust_maxidx_thm
wenzelm@16942
   555
  #> Drule.gen_all;
wenzelm@10817
   556
wenzelm@12782
   557
val norm_hhf_tac =
wenzelm@12782
   558
  rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
wenzelm@12782
   559
  THEN' SUBGOAL (fn (t, i) =>
wenzelm@12801
   560
    if Drule.is_norm_hhf t then all_tac
wenzelm@12782
   561
    else rewrite_goal_tac [Drule.norm_hhf_eq] i);
wenzelm@10805
   562
clasohm@0
   563
paulson@1501
   564
(*** for folding definitions, handling critical pairs ***)
lcp@69
   565
lcp@69
   566
(*The depth of nesting in a term*)
lcp@69
   567
fun term_depth (Abs(a,T,t)) = 1 + term_depth t
paulson@2145
   568
  | term_depth (f$t) = 1 + Int.max(term_depth f, term_depth t)
lcp@69
   569
  | term_depth _ = 0;
lcp@69
   570
wenzelm@12801
   571
val lhs_of_thm = #1 o Logic.dest_equals o prop_of;
lcp@69
   572
lcp@69
   573
(*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
lcp@69
   574
  Returns longest lhs first to avoid folding its subexpressions.*)
lcp@69
   575
fun sort_lhs_depths defs =
lcp@69
   576
  let val keylist = make_keylist (term_depth o lhs_of_thm) defs
wenzelm@4438
   577
      val keys = distinct (sort (rev_order o int_ord) (map #2 keylist))
lcp@69
   578
  in  map (keyfilter keylist) keys  end;
lcp@69
   579
wenzelm@7596
   580
val rev_defs = sort_lhs_depths o map symmetric;
lcp@69
   581
skalberg@15570
   582
fun fold_rule defs thm = Library.foldl (fn (th, ds) => rewrite_rule ds th) (thm, rev_defs defs);
wenzelm@7596
   583
fun fold_tac defs = EVERY (map rewrite_tac (rev_defs defs));
wenzelm@7596
   584
fun fold_goals_tac defs = EVERY (map rewrite_goals_tac (rev_defs defs));
lcp@69
   585
lcp@69
   586
lcp@69
   587
(*** Renaming of parameters in a subgoal
lcp@69
   588
     Names may contain letters, digits or primes and must be
lcp@69
   589
     separated by blanks ***)
clasohm@0
   590
clasohm@0
   591
(*Calling this will generate the warning "Same as previous level" since
clasohm@0
   592
  it affects nothing but the names of bound variables!*)
wenzelm@9535
   593
fun rename_params_tac xs i =
wenzelm@14673
   594
  case Library.find_first (not o Syntax.is_identifier) xs of
skalberg@15531
   595
      SOME x => error ("Not an identifier: " ^ x)
wenzelm@16425
   596
    | NONE =>
paulson@13559
   597
       (if !Logic.auto_rename
wenzelm@16425
   598
         then (warning "Resetting Logic.auto_rename";
wenzelm@16425
   599
             Logic.auto_rename := false)
wenzelm@16425
   600
        else (); PRIMITIVE (rename_params_rule (xs, i)));
wenzelm@9535
   601
wenzelm@10817
   602
fun rename_tac str i =
wenzelm@10817
   603
  let val cs = Symbol.explode str in
wenzelm@4693
   604
  case #2 (take_prefix (Symbol.is_letdig orf Symbol.is_blank) cs) of
wenzelm@9535
   605
      [] => rename_params_tac (scanwords Symbol.is_letdig cs) i
clasohm@0
   606
    | c::_ => error ("Illegal character: " ^ c)
clasohm@0
   607
  end;
clasohm@0
   608
paulson@1501
   609
(*Rename recent parameters using names generated from a and the suffixes,
paulson@1501
   610
  provided the string a, which represents a term, is an identifier. *)
wenzelm@10817
   611
fun rename_last_tac a sufs i =
clasohm@0
   612
  let val names = map (curry op^ a) sufs
clasohm@0
   613
  in  if Syntax.is_identifier a
clasohm@0
   614
      then PRIMITIVE (rename_params_rule (names,i))
clasohm@0
   615
      else all_tac
clasohm@0
   616
  end;
clasohm@0
   617
paulson@2043
   618
(*Prunes all redundant parameters from the proof state by rewriting.
paulson@2043
   619
  DOES NOT rewrite main goal, where quantification over an unused bound
paulson@2043
   620
    variable is sometimes done to avoid the need for cut_facts_tac.*)
paulson@2043
   621
val prune_params_tac = rewrite_goals_tac [triv_forall_equality];
clasohm@0
   622
paulson@1501
   623
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
paulson@1501
   624
  right to left if n is positive, and from left to right if n is negative.*)
paulson@2672
   625
fun rotate_tac 0 i = all_tac
paulson@2672
   626
  | rotate_tac k i = PRIMITIVE (rotate_rule k i);
nipkow@1209
   627
paulson@7248
   628
(*Rotates the given subgoal to be the last.*)
paulson@7248
   629
fun defer_tac i = PRIMITIVE (permute_prems (i-1) 1);
paulson@7248
   630
nipkow@5974
   631
(* remove premises that do not satisfy p; fails if all prems satisfy p *)
nipkow@5974
   632
fun filter_prems_tac p =
skalberg@15531
   633
  let fun Then NONE tac = SOME tac
skalberg@15531
   634
        | Then (SOME tac) tac' = SOME(tac THEN' tac');
nipkow@5974
   635
      fun thins ((tac,n),H) =
nipkow@5974
   636
        if p H then (tac,n+1)
nipkow@5974
   637
        else (Then tac (rotate_tac n THEN' etac thin_rl),0);
nipkow@5974
   638
  in SUBGOAL(fn (subg,n) =>
nipkow@5974
   639
       let val Hs = Logic.strip_assums_hyp subg
skalberg@15570
   640
       in case fst(Library.foldl thins ((NONE,0),Hs)) of
skalberg@15531
   641
            NONE => no_tac | SOME tac => tac n
nipkow@5974
   642
       end)
nipkow@5974
   643
  end;
nipkow@5974
   644
wenzelm@11961
   645
wenzelm@12139
   646
(*meta-level conjunction*)
wenzelm@12139
   647
val conj_tac = SUBGOAL (fn (Const ("all", _) $ Abs (_, _, Const ("==>", _) $
wenzelm@12139
   648
      (Const ("==>", _) $ _ $ (Const ("==>", _) $ _ $ Bound 0)) $ Bound 0), i) =>
wenzelm@12139
   649
    (fn st =>
wenzelm@12139
   650
      compose_tac (false, Drule.incr_indexes_wrt [] [] [] [st] Drule.conj_intr_thm, 2) i st)
wenzelm@12139
   651
  | _ => no_tac);
wenzelm@16425
   652
wenzelm@12139
   653
val conjunction_tac = ALLGOALS (REPEAT_ALL_NEW conj_tac);
wenzelm@12139
   654
wenzelm@15874
   655
fun smart_conjunction_tac 0 = assume_tac 1
wenzelm@15874
   656
  | smart_conjunction_tac _ = TRY conjunction_tac;
wenzelm@15874
   657
wenzelm@12139
   658
wenzelm@12139
   659
wenzelm@15874
   660
(** minimal goal interface for programmed proofs *)
wenzelm@11961
   661
wenzelm@16425
   662
fun gen_prove_multi finish_thm thy xs asms props tac =
wenzelm@11961
   663
  let
wenzelm@15874
   664
    val prop = Logic.mk_conjunction_list props;
wenzelm@11961
   665
    val statement = Logic.list_implies (asms, prop);
wenzelm@11961
   666
    val frees = map Term.dest_Free (Term.term_frees statement);
wenzelm@11970
   667
    val fixed_frees = filter_out (fn (x, _) => x mem_string xs) frees;
berghofe@15797
   668
    val fixed_tfrees = foldr Term.add_typ_tfrees [] (map #2 fixed_frees);
skalberg@15570
   669
    val params = List.mapPartial (fn x => Option.map (pair x) (assoc_string (frees, x))) xs;
wenzelm@11961
   670
wenzelm@12212
   671
    fun err msg = raise ERROR_MESSAGE
wenzelm@12212
   672
      (msg ^ "\nThe error(s) above occurred for the goal statement:\n" ^
wenzelm@16425
   673
        Sign.string_of_term thy (Term.list_all_free (params, statement)));
wenzelm@11961
   674
wenzelm@16425
   675
    fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm t)
wenzelm@11961
   676
      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
wenzelm@11961
   677
wenzelm@11961
   678
    val _ = cert_safe statement;
wenzelm@11974
   679
    val _ = Term.no_dummy_patterns statement handle TERM (msg, _) => err msg;
wenzelm@11961
   680
wenzelm@11974
   681
    val cparams = map (cert_safe o Free) params;
wenzelm@11961
   682
    val casms = map cert_safe asms;
wenzelm@12801
   683
    val prems = map (norm_hhf_rule o Thm.assume) casms;
wenzelm@11961
   684
    val goal = Drule.mk_triv_goal (cert_safe prop);
wenzelm@11961
   685
wenzelm@11961
   686
    val goal' =
skalberg@15531
   687
      (case Seq.pull (tac prems goal) of SOME (goal', _) => goal' | _ => err "Tactic failed.");
wenzelm@11961
   688
    val ngoals = Thm.nprems_of goal';
wenzelm@15874
   689
    val _ = conditional (ngoals <> 0) (fn () =>
wenzelm@15874
   690
      err ("Proof failed.\n" ^
wenzelm@15874
   691
        Pretty.string_of (Pretty.chunks (Display.pretty_goals ngoals goal')) ^
wenzelm@15874
   692
        ("\n" ^ string_of_int ngoals ^ " unsolved goal(s)!")));
wenzelm@15874
   693
wenzelm@11961
   694
    val raw_result = goal' RS Drule.rev_triv_goal;
wenzelm@12801
   695
    val prop' = prop_of raw_result;
wenzelm@16425
   696
    val _ = conditional (not (Pattern.matches (Sign.tsig_of thy) (prop, prop'))) (fn () =>
wenzelm@16425
   697
      err ("Proved a different theorem: " ^ Sign.string_of_term thy prop'));
wenzelm@11961
   698
  in
wenzelm@15874
   699
    Drule.conj_elim_precise (length props) raw_result
wenzelm@15874
   700
    |> map (fn res => res
wenzelm@11961
   701
      |> Drule.implies_intr_list casms
wenzelm@11974
   702
      |> Drule.forall_intr_list cparams
ballarin@16325
   703
      |> finish_thm fixed_tfrees)
wenzelm@11961
   704
  end;
wenzelm@11961
   705
wenzelm@16425
   706
fun prove_multi_plain thy xs asms prop tac =
wenzelm@16425
   707
  gen_prove_multi (K norm_hhf_plain) thy xs asms prop tac;
wenzelm@16425
   708
fun prove_multi thy xs asms prop tac =
ballarin@16325
   709
  gen_prove_multi (fn fixed_tfrees => Drule.zero_var_indexes o
ballarin@16325
   710
      (#1 o Thm.varifyT' fixed_tfrees) o norm_hhf_rule)
wenzelm@16425
   711
    thy xs asms prop tac;
wenzelm@15874
   712
wenzelm@16425
   713
fun prove_plain thy xs asms prop tac = hd (prove_multi_plain thy xs asms [prop] tac);
wenzelm@16425
   714
fun prove thy xs asms prop tac = hd (prove_multi thy xs asms [prop] tac);
wenzelm@11970
   715
clasohm@0
   716
end;
paulson@1501
   717
wenzelm@11774
   718
structure BasicTactic: BASIC_TACTIC = Tactic;
wenzelm@11774
   719
open BasicTactic;