src/Pure/tactic.ML
author nipkow
Fri Jul 28 17:24:53 1995 +0200 (1995-07-28)
changeset 1209 03dc596b3a18
parent 1077 c2df11ae8b55
child 1458 fd510875fb71
permissions -rw-r--r--
added rotate_tac.
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(*  Title: 	tactic
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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 TACTIC =
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sig
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  structure Tactical: TACTICAL and Net: NET
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  local open Tactical Tactical.Thm Net
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  in
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  val ares_tac: thm list -> int -> tactic
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  val asm_rewrite_goal_tac:
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        bool*bool -> (meta_simpset -> tactic) -> 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 * (int*(bool*thm)) net -> int -> tactic
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  val bimatch_tac: (bool*thm)list -> int -> tactic
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  val biresolve_from_nets_tac: 
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      (int*(bool*thm)) net * (int*(bool*thm)) 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
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  val build_netpair:    (int*(bool*thm)) net * (int*(bool*thm)) net ->
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      (bool*thm)list -> (int*(bool*thm)) net * (int*(bool*thm)) net
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  val compose_inst_tac: (string*string)list -> (bool*thm*int) -> 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 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 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 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_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 freeze: thm -> thm   
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  val insert_tagged_brl:  ('a*(bool*thm)) * 
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                    (('a*(bool*thm))net * ('a*(bool*thm))net) ->
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                    ('a*(bool*thm))net * ('a*(bool*thm))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 -> 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 PRIMITIVE: (thm -> thm) -> tactic  
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  val PRIMSEQ: (thm -> thm Sequence.seq) -> tactic  
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  val prune_params_tac: 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 -> 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_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 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 trace_goalno_tac: (int -> tactic) -> int -> tactic
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  end
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end;
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functor TacticFun (structure Logic: LOGIC and Drule: DRULE and 
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		   Tactical: TACTICAL and Net: NET
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	  sharing Drule.Thm = Tactical.Thm) : TACTIC = 
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struct
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structure Tactical = Tactical;
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structure Thm = Tactical.Thm;
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structure Net = Net;
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structure Sequence = Thm.Sequence;
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structure Sign = Thm.Sign;
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local open Tactical Tactical.Thm Drule
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in
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(*Discover what goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
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fun trace_goalno_tac tf i = Tactic (fn state => 
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    case Sequence.pull(tapply(tf i, state)) of
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	None    => Sequence.null
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      | seqcell => (prs("Subgoal " ^ string_of_int i ^ " selected\n"); 
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    			 Sequence.seqof(fn()=> seqcell)));
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fun string_of (a,0) = a
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  | string_of (a,i) = a ^ "_" ^ string_of_int i;
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(*convert all Vars in a theorem to Frees*)
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fun freeze th =
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  let val fth = freezeT th
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      val {prop,sign,...} = rep_thm fth
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      fun mk_inst (Var(v,T)) = 
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	  (cterm_of sign (Var(v,T)),
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	   cterm_of sign (Free(string_of v, T)))
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      val insts = map mk_inst (term_vars prop)
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  in  instantiate ([],insts) fth  end;
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(*Makes a rule by applying a tactic to an existing rule*)
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fun rule_by_tactic (Tactic tf) rl =
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    case Sequence.pull(tf (freeze (standard rl))) of
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	None        => raise THM("rule_by_tactic", 0, [rl])
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      | Some(rl',_) => standard rl';
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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 = Tactic (fn state => thmfun state
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			                 handle THM _ => Sequence.null);
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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 (Sequence.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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fun rtac rl = resolve_tac [rl];
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fun etac rl = eresolve_tac [rl];
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fun dtac rl = dresolve_tac [rl];
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val atac = assume_tac;
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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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(*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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(*Lift and instantiate a rule wrt the given state and subgoal number *)
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fun lift_inst_rule (state, i, sinsts, rule) =
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let val {maxidx,sign,...} = rep_thm state
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    val (_, _, Bi, _) = dest_state(state,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 state
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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 state) $ #prop(rep_thm rule),[])
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    val (Tinsts,insts) = read_insts sign rts (types',sorts) used sinsts
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in instantiate (map lifttvar Tinsts, map liftpair insts)
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               (lift_rule (state,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 =
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  STATE ( fn state => 
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	   compose_tac (bires_flg, lift_inst_rule (state, i, sinsts, rule),
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			nsubgoal) i
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	   handle TERM (msg,_) => (writeln msg;  no_tac)
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		| THM  (msg,_,_) => (writeln msg;  no_tac) );
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(*"Resolve" version.  Note: res_inst_tac cannot behave sensibly if the
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  terms that are substituted contain (term or type) unknowns from the
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  goal, because it is unable to instantiate goal unknowns at the same time.
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  The type checker is instructed not to freezes flexible type vars that
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  were introduced during type inference and still remain in the term at the
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  end.  This increases flexibility but can introduce schematic type vars in
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  goals.
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*)
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fun res_inst_tac sinsts rule i =
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    compose_inst_tac sinsts (false, rule, nprems_of rule) i;
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(*eresolve (elimination) version*)
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fun eres_inst_tac sinsts rule i =
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    compose_inst_tac sinsts (true, rule, nprems_of rule) i;
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(*For forw_inst_tac and dres_inst_tac.  Preserve Var indexes of rl;
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  increment revcut_rl instead.*)
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fun make_elim_preserve rl = 
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  let val {maxidx,...} = rep_thm rl
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      fun cvar ixn = cterm_of Sign.proto_pure (Var(ixn,propT));
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      val revcut_rl' = 
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	  instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),
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			     (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
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      val arg = (false, rl, nprems_of rl)
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      val [th] = Sequence.list_of_s (bicompose false arg 1 revcut_rl')
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  in  th  end
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  handle Bind => raise THM("make_elim_preserve", 1, [rl]);
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(*instantiate and cut -- for a FACT, anyway...*)
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fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule);
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(*forward tactic applies a RULE to an assumption without deleting it*)
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fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac;
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(*dresolve tactic applies a RULE to replace an assumption*)
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fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
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(*** Applications of cut_rl ***)
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(*Used by metacut_tac*)
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fun bires_cut_tac arg i =
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    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
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(*The conclusion of the rule gets assumed in subgoal i,
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  while subgoal i+1,... are the premises of the rule.*)
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fun metacut_tac rule = bires_cut_tac [(false,rule)];
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(*Recognizes theorems that are not rules, but simple propositions*)
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fun is_fact rl =
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    case prems_of rl of
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	[] => true  |  _::_ => false;
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(*"Cut" all facts from theorem list into the goal as assumptions. *)
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fun cut_facts_tac ths i =
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    EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));
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(*Introduce the given proposition as a lemma and subgoal*)
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fun subgoal_tac sprop = res_inst_tac [("psi", sprop)] cut_rl;
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(*Introduce a list of lemmas and subgoals*)
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fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops);
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(**** Indexing and filtering of theorems ****)
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(*Returns the list of potentially resolvable theorems for the goal "prem",
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	using the predicate  could(subgoal,concl).
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  Resulting list is no longer than "limit"*)
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fun filter_thms could (limit, prem, ths) =
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  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
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      fun filtr (limit, []) = []
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	| filtr (limit, th::ths) =
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	    if limit=0 then  []
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	    else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
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	    else filtr(limit,ths)
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  in  filtr(limit,ths)  end;
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(*** biresolution and resolution using nets ***)
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(** To preserve the order of the rules, tag them with increasing integers **)
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(*insert tags*)
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fun taglist k [] = []
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  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
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(*remove tags and suppress duplicates -- list is assumed sorted!*)
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   311
fun untaglist [] = []
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  | untaglist [(k:int,x)] = [x]
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  | untaglist ((k,x) :: (rest as (k',x')::_)) =
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      if k=k' then untaglist rest
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      else    x :: untaglist rest;
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   316
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(*return list elements in original order*)
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   318
val orderlist = untaglist o sort (fn(x,y)=> #1 x < #1 y); 
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   319
clasohm@0
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(*insert one tagged brl into the pair of nets*)
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   321
fun insert_tagged_brl (kbrl as (k,(eres,th)), (inet,enet)) =
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    if eres then 
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	case prems_of th of
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	    prem::_ => (inet, Net.insert_term ((prem,kbrl), enet, K false))
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	  | [] => error"insert_tagged_brl: elimination rule with no premises"
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    else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);
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(*build a pair of nets for biresolution*)
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fun build_netpair netpair brls = 
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    foldr insert_tagged_brl (taglist 1 brls, netpair);
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(*biresolution using a pair of nets rather than rules*)
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fun biresolution_from_nets_tac match (inet,enet) =
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  SUBGOAL
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    (fn (prem,i) =>
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      let val hyps = Logic.strip_assums_hyp prem
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          and concl = Logic.strip_assums_concl prem 
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          val kbrls = Net.unify_term inet concl @
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                      flat (map (Net.unify_term enet) hyps)
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      in PRIMSEQ (biresolution match (orderlist kbrls) i) end);
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(*versions taking pre-built nets*)
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val biresolve_from_nets_tac = biresolution_from_nets_tac false;
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val bimatch_from_nets_tac = biresolution_from_nets_tac true;
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   345
clasohm@0
   346
(*fast versions using nets internally*)
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val net_biresolve_tac =
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    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);
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lcp@670
   350
val net_bimatch_tac =
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    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);
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   352
clasohm@0
   353
(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
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   354
clasohm@0
   355
(*insert one tagged rl into the net*)
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   356
fun insert_krl (krl as (k,th), net) =
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   357
    Net.insert_term ((concl_of th, krl), net, K false);
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   358
clasohm@0
   359
(*build a net of rules for resolution*)
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   360
fun build_net rls = 
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    foldr insert_krl (taglist 1 rls, Net.empty);
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   362
clasohm@0
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(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
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   364
fun filt_resolution_from_net_tac match pred net =
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  SUBGOAL
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    (fn (prem,i) =>
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      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
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   368
      in 
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	 if pred krls  
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   370
         then PRIMSEQ
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		(biresolution match (map (pair false) (orderlist krls)) i)
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         else no_tac
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   373
      end);
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   374
clasohm@0
   375
(*Resolve the subgoal using the rules (making a net) unless too flexible,
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   376
   which means more than maxr rules are unifiable.      *)
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   377
fun filt_resolve_tac rules maxr = 
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   378
    let fun pred krls = length krls <= maxr
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   379
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
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   380
clasohm@0
   381
(*versions taking pre-built nets*)
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   382
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
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   383
val match_from_net_tac = filt_resolution_from_net_tac true (K true);
clasohm@0
   384
clasohm@0
   385
(*fast versions using nets internally*)
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   386
val net_resolve_tac = resolve_from_net_tac o build_net;
clasohm@0
   387
val net_match_tac = match_from_net_tac o build_net;
clasohm@0
   388
clasohm@0
   389
clasohm@0
   390
(*** For Natural Deduction using (bires_flg, rule) pairs ***)
clasohm@0
   391
clasohm@0
   392
(*The number of new subgoals produced by the brule*)
lcp@1077
   393
fun subgoals_of_brl (true,rule)  = nprems_of rule - 1
lcp@1077
   394
  | subgoals_of_brl (false,rule) = nprems_of rule;
clasohm@0
   395
clasohm@0
   396
(*Less-than test: for sorting to minimize number of new subgoals*)
clasohm@0
   397
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
clasohm@0
   398
clasohm@0
   399
clasohm@0
   400
(*** Meta-Rewriting Tactics ***)
clasohm@0
   401
clasohm@0
   402
fun result1 tacf mss thm =
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   403
  case Sequence.pull(tapply(tacf mss,thm)) of
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   404
    None => None
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   405
  | Some(thm,_) => Some(thm);
clasohm@0
   406
clasohm@0
   407
(*Rewrite subgoal i only *)
nipkow@214
   408
fun asm_rewrite_goal_tac mode prover_tac mss i =
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   409
      PRIMITIVE(rewrite_goal_rule mode (result1 prover_tac) mss i);
clasohm@0
   410
lcp@69
   411
(*Rewrite throughout proof state. *)
lcp@69
   412
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);
clasohm@0
   413
clasohm@0
   414
(*Rewrite subgoals only, not main goal. *)
lcp@69
   415
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
clasohm@0
   416
lcp@69
   417
fun rewtac def = rewrite_goals_tac [def];
clasohm@0
   418
clasohm@0
   419
lcp@69
   420
(*** Tactic for folding definitions, handling critical pairs ***)
lcp@69
   421
lcp@69
   422
(*The depth of nesting in a term*)
lcp@69
   423
fun term_depth (Abs(a,T,t)) = 1 + term_depth t
lcp@69
   424
  | term_depth (f$t) = 1 + max [term_depth f, term_depth t]
lcp@69
   425
  | term_depth _ = 0;
lcp@69
   426
lcp@69
   427
val lhs_of_thm = #1 o Logic.dest_equals o #prop o rep_thm;
lcp@69
   428
lcp@69
   429
(*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
lcp@69
   430
  Returns longest lhs first to avoid folding its subexpressions.*)
lcp@69
   431
fun sort_lhs_depths defs =
lcp@69
   432
  let val keylist = make_keylist (term_depth o lhs_of_thm) defs
lcp@69
   433
      val keys = distinct (sort op> (map #2 keylist))
lcp@69
   434
  in  map (keyfilter keylist) keys  end;
lcp@69
   435
lcp@69
   436
fun fold_tac defs = EVERY 
lcp@69
   437
    (map rewrite_tac (sort_lhs_depths (map symmetric defs)));
lcp@69
   438
lcp@69
   439
fun fold_goals_tac defs = EVERY 
lcp@69
   440
    (map rewrite_goals_tac (sort_lhs_depths (map symmetric defs)));
lcp@69
   441
lcp@69
   442
lcp@69
   443
(*** Renaming of parameters in a subgoal
lcp@69
   444
     Names may contain letters, digits or primes and must be
lcp@69
   445
     separated by blanks ***)
clasohm@0
   446
clasohm@0
   447
(*Calling this will generate the warning "Same as previous level" since
clasohm@0
   448
  it affects nothing but the names of bound variables!*)
clasohm@0
   449
fun rename_tac str i = 
clasohm@0
   450
  let val cs = explode str 
clasohm@0
   451
  in  
clasohm@0
   452
  if !Logic.auto_rename 
clasohm@0
   453
  then (writeln"Note: setting Logic.auto_rename := false"; 
clasohm@0
   454
	Logic.auto_rename := false)
clasohm@0
   455
  else ();
clasohm@0
   456
  case #2 (take_prefix (is_letdig orf is_blank) cs) of
clasohm@0
   457
      [] => PRIMITIVE (rename_params_rule (scanwords is_letdig cs, i))
clasohm@0
   458
    | c::_ => error ("Illegal character: " ^ c)
clasohm@0
   459
  end;
clasohm@0
   460
clasohm@0
   461
(*Rename recent parameters using names generated from (a) and the suffixes,
clasohm@0
   462
  provided the string (a), which represents a term, is an identifier. *)
clasohm@0
   463
fun rename_last_tac a sufs i = 
clasohm@0
   464
  let val names = map (curry op^ a) sufs
clasohm@0
   465
  in  if Syntax.is_identifier a
clasohm@0
   466
      then PRIMITIVE (rename_params_rule (names,i))
clasohm@0
   467
      else all_tac
clasohm@0
   468
  end;
clasohm@0
   469
clasohm@0
   470
(*Prunes all redundant parameters from the proof state by rewriting*)
clasohm@0
   471
val prune_params_tac = rewrite_tac [triv_forall_equality];
clasohm@0
   472
nipkow@1209
   473
(* rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
nipkow@1209
   474
 * right to left if n is positive, and from left to right if n is negative.
nipkow@1209
   475
 *)
nipkow@1209
   476
fun rotate_tac n =
nipkow@1209
   477
  let fun rot(n) = EVERY'(replicate n (dtac asm_rl));
nipkow@1209
   478
  in if n >= 0 then rot n
nipkow@1209
   479
     else SUBGOAL (fn (t,i) => rot(length(Logic.strip_assums_hyp t)+n) i)
nipkow@1209
   480
  end;
nipkow@1209
   481
clasohm@0
   482
end;
clasohm@0
   483
end;