src/Pure/tactic.ML

+(*  Title: 	tactic
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1991  University of Cambridge
+
+Tactics 
+*)
+
+signature TACTIC =
+sig
+  structure Tactical: TACTICAL and Net: NET
+  local open Tactical Tactical.Thm Net
+  in
+  val ares_tac: thm list -> int -> tactic
+  val asm_rewrite_goal_tac:
+        (meta_simpset -> tactic) -> meta_simpset -> int -> tactic
+  val assume_tac: int -> tactic
+  val atac: int ->tactic
+  val bimatch_from_nets_tac: (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
+  val bimatch_tac: (bool*thm)list -> int -> tactic
+  val biresolve_from_nets_tac: (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
+  val biresolve_tac: (bool*thm)list -> int -> tactic
+  val build_net: thm list -> (int*thm) net
+  val build_netpair: (bool*thm)list -> (int*(bool*thm)) net * (int*(bool*thm)) net
+  val compose_inst_tac: (string*string)list -> (bool*thm*int) -> int -> tactic
+  val compose_tac: (bool * thm * int) -> int -> tactic 
+  val cut_facts_tac: thm list -> int -> tactic
+  val dmatch_tac: thm list -> int -> tactic
+  val dresolve_tac: thm list -> int -> tactic
+  val dres_inst_tac: (string*string)list -> thm -> int -> tactic   
+  val dtac: thm -> int ->tactic
+  val etac: thm -> int ->tactic
+  val eq_assume_tac: int -> tactic   
+  val ematch_tac: thm list -> int -> tactic
+  val eresolve_tac: thm list -> int -> tactic
+  val eres_inst_tac: (string*string)list -> thm -> int -> tactic   
+  val filter_thms: (term*term->bool) -> int*term*thm list -> thm list
+  val filt_resolve_tac: thm list -> int -> int -> tactic
+  val flexflex_tac: tactic
+  val fold_goals_tac: thm list -> tactic
+  val fold_tac: thm list -> tactic
+  val forward_tac: thm list -> int -> tactic   
+  val forw_inst_tac: (string*string)list -> thm -> int -> tactic
+  val is_fact: thm -> bool
+  val lessb: (bool * thm) * (bool * thm) -> bool
+  val lift_inst_rule: thm * int * (string*string)list * thm -> thm
+  val make_elim: thm -> thm
+  val match_from_net_tac: (int*thm) net -> int -> tactic
+  val match_tac: thm list -> int -> tactic
+  val metacut_tac: thm -> int -> tactic   
+  val net_bimatch_tac: (bool*thm) list -> int -> tactic
+  val net_biresolve_tac: (bool*thm) list -> int -> tactic
+  val net_match_tac: thm list -> int -> tactic
+  val net_resolve_tac: thm list -> int -> tactic
+  val PRIMITIVE: (thm -> thm) -> tactic  
+  val PRIMSEQ: (thm -> thm Sequence.seq) -> tactic  
+  val prune_params_tac: tactic
+  val rename_tac: string -> int -> tactic
+  val rename_last_tac: string -> string list -> int -> tactic
+  val resolve_from_net_tac: (int*thm) net -> int -> tactic
+  val resolve_tac: thm list -> int -> tactic
+  val res_inst_tac: (string*string)list -> thm -> int -> tactic   
+  val rewrite_goals_tac: thm list -> tactic
+  val rewrite_tac: thm list -> tactic
+  val rewtac: thm -> tactic
+  val rtac: thm -> int -> tactic
+  val rule_by_tactic: tactic -> thm -> thm
+  val subgoals_of_brl: bool * thm -> int
+  val subgoal_tac: string -> int -> tactic
+  val trace_goalno_tac: (int -> tactic) -> int -> tactic
+  end
+end;
+
+
+functor TacticFun (structure Logic: LOGIC and Drule: DRULE and 
+		   Tactical: TACTICAL and Net: NET
+	  sharing Drule.Thm = Tactical.Thm) : TACTIC = 
+struct
+structure Tactical = Tactical;
+structure Thm = Tactical.Thm;
+structure Net = Net;
+structure Sequence = Thm.Sequence;
+structure Sign = Thm.Sign;
+local open Tactical Tactical.Thm Drule
+in
+
+(*Discover what goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
+fun trace_goalno_tac tf i = Tactic (fn state => 
+    case Sequence.pull(tapply(tf i, state)) of
+	None    => Sequence.null
+      | seqcell => (prs("Subgoal " ^ string_of_int i ^ " selected\n"); 
+    			 Sequence.seqof(fn()=> seqcell)));
+
+fun string_of (a,0) = a
+  | string_of (a,i) = a ^ "_" ^ string_of_int i;
+
+(*convert all Vars in a theorem to Frees -- export??*)
+fun freeze th =
+  let val fth = freezeT th
+      val {prop,sign,...} = rep_thm fth
+      fun mk_inst (Var(v,T)) = 
+	  (Sign.cterm_of sign (Var(v,T)),
+	   Sign.cterm_of sign (Free(string_of v, T)))
+      val insts = map mk_inst (term_vars prop)
+  in  instantiate ([],insts) fth  end;
+
+(*Makes a rule by applying a tactic to an existing rule*)
+fun rule_by_tactic (Tactic tf) rl =
+    case Sequence.pull(tf (freeze (standard rl))) of
+	None        => raise THM("rule_by_tactic", 0, [rl])
+      | Some(rl',_) => standard rl';
+ 
+(*** Basic tactics ***)
+
+(*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)
+fun PRIMSEQ thmfun = Tactic (fn state => thmfun state
+			                 handle THM _ => Sequence.null);
+
+(*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)
+fun PRIMITIVE thmfun = PRIMSEQ (Sequence.single o thmfun);
+
+(*** The following fail if the goal number is out of range:
+     thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
+
+(*Solve subgoal i by assumption*)
+fun assume_tac i = PRIMSEQ (assumption i);
+
+(*Solve subgoal i by assumption, using no unification*)
+fun eq_assume_tac i = PRIMITIVE (eq_assumption i);
+
+(** Resolution/matching tactics **)
+
+(*The composition rule/state: no lifting or var renaming.
+  The arg = (bires_flg, orule, m) ;  see bicompose for explanation.*)
+fun compose_tac arg i = PRIMSEQ (bicompose false arg i);
+
+(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
+  like [| P&Q; P==>R |] ==> R *)
+fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
+
+(*Attack subgoal i by resolution, using flags to indicate elimination rules*)
+fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i);
+
+(*Resolution: the simple case, works for introduction rules*)
+fun resolve_tac rules = biresolve_tac (map (pair false) rules);
+
+(*Resolution with elimination rules only*)
+fun eresolve_tac rules = biresolve_tac (map (pair true) rules);
+
+(*Forward reasoning using destruction rules.*)
+fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;
+
+(*Like forward_tac, but deletes the assumption after use.*)
+fun dresolve_tac rls = eresolve_tac (map make_elim rls);
+
+(*Shorthand versions: for resolution with a single theorem*)
+fun rtac rl = resolve_tac [rl];
+fun etac rl = eresolve_tac [rl];
+fun dtac rl = dresolve_tac [rl];
+val atac = assume_tac;
+
+(*Use an assumption or some rules ... A popular combination!*)
+fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;
+
+(*Matching tactics -- as above, but forbid updating of state*)
+fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i);
+fun match_tac rules  = bimatch_tac (map (pair false) rules);
+fun ematch_tac rules = bimatch_tac (map (pair true) rules);
+fun dmatch_tac rls   = ematch_tac (map make_elim rls);
+
+(*Smash all flex-flex disagreement pairs in the proof state.*)
+val flexflex_tac = PRIMSEQ flexflex_rule;
+
+(*Lift and instantiate a rule wrt the given state and subgoal number *)
+fun lift_inst_rule (state, i, sinsts, rule) =
+let val {maxidx,sign,...} = rep_thm state
+    val (_, _, Bi, _) = dest_state(state,i)
+    val params = Logic.strip_params Bi	        (*params of subgoal i*)
+    val params = rev(rename_wrt_term Bi params) (*as they are printed*)
+    val paramTs = map #2 params
+    and inc = maxidx+1
+    fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> incr_tvar inc T)
+      | liftvar t = raise TERM("Variable expected", [t]);
+    fun liftterm t = list_abs_free (params, 
+				    Logic.incr_indexes(paramTs,inc) t)
+    (*Lifts instantiation pair over params*)
+    fun liftpair (cv,ct) = (Sign.cfun liftvar cv, Sign.cfun liftterm ct)
+    fun lifttvar((a,i),ctyp) =
+	let val {T,sign} = Sign.rep_ctyp ctyp
+	in  ((a,i+inc), Sign.ctyp_of sign (incr_tvar inc T)) end
+    val rts = types_sorts rule and (types,sorts) = types_sorts state
+    fun types'(a,~1) = (case assoc(params,a) of None => types(a,~1) | sm => sm)
+      | types'(ixn) = types ixn;
+    val (Tinsts,insts) = Sign.read_insts sign rts (types',sorts) sinsts
+in instantiate (map lifttvar Tinsts, map liftpair insts)
+		(lift_rule (state,i) rule)
+end;
+
+
+(*** Resolve after lifting and instantation; may refer to parameters of the
+     subgoal.  Fails if "i" is out of range.  ***)
+
+(*compose version: arguments are as for bicompose.*)
+fun compose_inst_tac sinsts (bires_flg, rule, nsubgoal) i =
+  STATE ( fn state => 
+	   compose_tac (bires_flg, lift_inst_rule (state, i, sinsts, rule),
+			nsubgoal) i
+	   handle TERM (msg,_) => (writeln msg;  no_tac)
+		| THM _ => no_tac );
+
+(*Resolve version*)
+fun res_inst_tac sinsts rule i =
+    compose_inst_tac sinsts (false, rule, nprems_of rule) i;
+
+(*eresolve (elimination) version*)
+fun eres_inst_tac sinsts rule i =
+    compose_inst_tac sinsts (true, rule, nprems_of rule) i;
+
+(*For forw_inst_tac and dres_inst_tac: preserve Var indexes of rl.
+  Fails if rl's major premise contains !! or ==> ; it should not anyway!*)
+fun make_elim_preserve rl = 
+  let val revcut_rl' = lift_rule (rl,1) revcut_rl
+      val arg = (false, rl, nprems_of rl)
+      val [th] = Sequence.list_of_s (bicompose false arg 1 revcut_rl')
+  in  th  end
+  handle Bind => raise THM("make_elim_preserve", 1, [rl]);
+
+(*forward version*)
+fun forw_inst_tac sinsts rule =
+    res_inst_tac sinsts (make_elim_preserve rule) THEN' assume_tac;
+
+(*dresolve version*)
+fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
+
+(*** Applications of cut_rl -- forward reasoning ***)
+
+(*Used by metacut_tac*)
+fun bires_cut_tac arg i =
+    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
+
+(*The conclusion of the rule gets assumed in subgoal i,
+  while subgoal i+1,... are the premises of the rule.*)
+fun metacut_tac rule = bires_cut_tac [(false,rule)];
+
+(*Recognizes theorems that are not rules, but simple propositions*)
+fun is_fact rl =
+    case prems_of rl of
+	[] => true  |  _::_ => false;
+
+(*"Cut" all facts from theorem list into the goal as assumptions. *)
+fun cut_facts_tac ths i =
+    EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));
+
+(*Introduce the given proposition as a lemma and subgoal*)
+fun subgoal_tac sprop = res_inst_tac [("psi", sprop)] cut_rl;
+
+
+(**** Indexing and filtering of theorems ****)
+
+(*Returns the list of potentially resolvable theorems for the goal "prem",
+	using the predicate  could(subgoal,concl).
+  Resulting list is no longer than "limit"*)
+fun filter_thms could (limit, prem, ths) =
+  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
+      fun filtr (limit, []) = []
+	| filtr (limit, th::ths) =
+	    if limit=0 then  []
+	    else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
+	    else filtr(limit,ths)
+  in  filtr(limit,ths)  end;
+
+
+(*** biresolution and resolution using nets ***)
+
+(** To preserve the order of the rules, tag them with increasing integers **)
+
+(*insert tags*)
+fun taglist k [] = []
+  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
+
+(*remove tags and suppress duplicates -- list is assumed sorted!*)
+fun untaglist [] = []
+  | untaglist [(k:int,x)] = [x]
+  | untaglist ((k,x) :: (rest as (k',x')::_)) =
+      if k=k' then untaglist rest
+      else    x :: untaglist rest;
+
+(*return list elements in original order*)
+val orderlist = untaglist o sort (fn(x,y)=> #1 x < #1 y); 
+
+(*insert one tagged brl into the pair of nets*)
+fun insert_kbrl (kbrl as (k,(eres,th)), (inet,enet)) =
+    if eres then 
+	case prems_of th of
+	    prem::_ => (inet, Net.insert_term ((prem,kbrl), enet, K false))
+	  | [] => error"insert_kbrl: elimination rule with no premises"
+    else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);
+
+(*build a pair of nets for biresolution*)
+fun build_netpair brls = 
+    foldr insert_kbrl (taglist 1 brls, (Net.empty,Net.empty));
+
+(*biresolution using a pair of nets rather than rules*)
+fun biresolution_from_nets_tac match (inet,enet) =
+  SUBGOAL
+    (fn (prem,i) =>
+      let val hyps = Logic.strip_assums_hyp prem
+          and concl = Logic.strip_assums_concl prem 
+          val kbrls = Net.unify_term inet concl @
+                      flat (map (Net.unify_term enet) hyps)
+      in PRIMSEQ (biresolution match (orderlist kbrls) i) end);
+
+(*versions taking pre-built nets*)
+val biresolve_from_nets_tac = biresolution_from_nets_tac false;
+val bimatch_from_nets_tac = biresolution_from_nets_tac true;
+
+(*fast versions using nets internally*)
+val net_biresolve_tac = biresolve_from_nets_tac o build_netpair;
+val net_bimatch_tac = bimatch_from_nets_tac o build_netpair;
+
+(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
+
+(*insert one tagged rl into the net*)
+fun insert_krl (krl as (k,th), net) =
+    Net.insert_term ((concl_of th, krl), net, K false);
+
+(*build a net of rules for resolution*)
+fun build_net rls = 
+    foldr insert_krl (taglist 1 rls, Net.empty);
+
+(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
+fun filt_resolution_from_net_tac match pred net =
+  SUBGOAL
+    (fn (prem,i) =>
+      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
+      in 
+	 if pred krls  
+         then PRIMSEQ
+		(biresolution match (map (pair false) (orderlist krls)) i)
+         else no_tac
+      end);
+
+(*Resolve the subgoal using the rules (making a net) unless too flexible,
+   which means more than maxr rules are unifiable.      *)
+fun filt_resolve_tac rules maxr = 
+    let fun pred krls = length krls <= maxr
+    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
+
+(*versions taking pre-built nets*)
+val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
+val match_from_net_tac = filt_resolution_from_net_tac true (K true);
+
+(*fast versions using nets internally*)
+val net_resolve_tac = resolve_from_net_tac o build_net;
+val net_match_tac = match_from_net_tac o build_net;
+
+
+(*** For Natural Deduction using (bires_flg, rule) pairs ***)
+
+(*The number of new subgoals produced by the brule*)
+fun subgoals_of_brl (true,rule) = length (prems_of rule) - 1
+  | subgoals_of_brl (false,rule) = length (prems_of rule);
+
+(*Less-than test: for sorting to minimize number of new subgoals*)
+fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
+
+
+(*** Meta-Rewriting Tactics ***)
+
+fun result1 tacf mss thm =
+  case Sequence.pull(tapply(tacf mss,thm)) of
+    None => None
+  | Some(thm,_) => Some(thm);
+
+(*Rewrite subgoal i only *)
+fun asm_rewrite_goal_tac prover_tac mss i =
+      PRIMITIVE(rewrite_goal_rule (result1 prover_tac) mss i);
+
+(*Rewrite or fold throughout proof state. *)
+fun rewrite_tac thms = PRIMITIVE(rewrite_rule thms);
+fun fold_tac rths = rewrite_tac (map symmetric rths);
+
+(*Rewrite subgoals only, not main goal. *)
+fun rewrite_goals_tac thms = PRIMITIVE (rewrite_goals_rule thms);
+fun fold_goals_tac rths = rewrite_goals_tac (map symmetric rths);
+
+fun rewtac rth = rewrite_goals_tac [rth];
+
+
+(** Renaming of parameters in a subgoal
+    Names may contain letters, digits or primes and must be
+    separated by blanks **)
+
+(*Calling this will generate the warning "Same as previous level" since
+  it affects nothing but the names of bound variables!*)
+fun rename_tac str i = 
+  let val cs = explode str 
+  in  
+  if !Logic.auto_rename 
+  then (writeln"Note: setting Logic.auto_rename := false"; 
+	Logic.auto_rename := false)
+  else ();
+  case #2 (take_prefix (is_letdig orf is_blank) cs) of
+      [] => PRIMITIVE (rename_params_rule (scanwords is_letdig cs, i))
+    | c::_ => error ("Illegal character: " ^ c)
+  end;
+
+(*Rename recent parameters using names generated from (a) and the suffixes,
+  provided the string (a), which represents a term, is an identifier. *)
+fun rename_last_tac a sufs i = 
+  let val names = map (curry op^ a) sufs
+  in  if Syntax.is_identifier a
+      then PRIMITIVE (rename_params_rule (names,i))
+      else all_tac
+  end;
+
+(*Prunes all redundant parameters from the proof state by rewriting*)
+val prune_params_tac = rewrite_tac [triv_forall_equality];
+
+end;
+end;