src/Pure/tctical.ML

+(*  Title: 	tctical
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Tacticals
+*)
+
+infix 1 THEN THEN' THEN_BEST_FIRST;
+infix 0 ORELSE APPEND INTLEAVE ORELSE' APPEND' INTLEAVE';
+
+
+signature TACTICAL =
+  sig
+  structure Thm : THM
+  local open Thm  in
+  datatype tactic = Tactic of thm -> thm Sequence.seq
+  val all_tac: tactic
+  val ALLGOALS: (int -> tactic) -> tactic   
+  val APPEND: tactic * tactic -> tactic
+  val APPEND': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
+  val BEST_FIRST: (thm -> bool) * (thm -> int) -> tactic -> tactic
+  val BREADTH_FIRST: (thm -> bool) -> tactic -> tactic
+  val CHANGED: tactic -> tactic
+  val COND: (thm -> bool) -> tactic -> tactic -> tactic   
+  val DEPTH_FIRST: (thm -> bool) -> tactic -> tactic
+  val DEPTH_SOLVE: tactic -> tactic
+  val DEPTH_SOLVE_1: tactic -> tactic
+  val DETERM: tactic -> tactic
+  val EVERY: tactic list -> tactic   
+  val EVERY': ('a -> tactic) list -> 'a -> tactic
+  val EVERY1: (int -> tactic) list -> tactic
+  val FILTER: (thm -> bool) -> tactic -> tactic
+  val FIRST: tactic list -> tactic   
+  val FIRST': ('a -> tactic) list -> 'a -> tactic
+  val FIRST1: (int -> tactic) list -> tactic
+  val FIRSTGOAL: (int -> tactic) -> tactic
+  val goals_limit: int ref
+  val has_fewer_prems: int -> thm -> bool   
+  val IF_UNSOLVED: tactic -> tactic
+  val INTLEAVE: tactic * tactic -> tactic
+  val INTLEAVE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
+  val METAHYPS: (thm list -> tactic) -> int -> tactic
+  val no_tac: tactic
+  val ORELSE: tactic * tactic -> tactic
+  val ORELSE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
+  val pause_tac: tactic
+  val print_tac: tactic
+  val REPEAT1: tactic -> tactic
+  val REPEAT: tactic -> tactic
+  val REPEAT_DETERM: tactic -> tactic
+  val REPEAT_FIRST: (int -> tactic) -> tactic
+  val REPEAT_SOME: (int -> tactic) -> tactic
+  val SELECT_GOAL: tactic -> int -> tactic
+  val SOMEGOAL: (int -> tactic) -> tactic   
+  val STATE: (thm -> tactic) -> tactic
+  val strip_context: term -> (string * typ) list * term list * term
+  val SUBGOAL: ((term*int) -> tactic) -> int -> tactic
+  val tapply: tactic * thm -> thm Sequence.seq
+  val THEN: tactic * tactic -> tactic
+  val THEN': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
+  val THEN_BEST_FIRST: tactic * ((thm->bool) * (thm->int) * tactic) -> tactic
+  val traced_tac: (thm -> (thm * thm Sequence.seq) option) -> tactic
+  val tracify: bool ref -> tactic -> thm -> thm Sequence.seq
+  val trace_BEST_FIRST: bool ref
+  val trace_DEPTH_FIRST: bool ref
+  val trace_REPEAT: bool ref
+  val TRY: tactic -> tactic
+  val TRYALL: (int -> tactic) -> tactic   
+  end
+  end;
+
+
+functor TacticalFun (structure Logic: LOGIC and Drule: DRULE) : TACTICAL = 
+struct
+structure Thm = Drule.Thm;
+structure Sequence = Thm.Sequence;
+structure Sign = Thm.Sign;
+local open Drule Thm
+in
+
+(**** Tactics ****)
+
+(*A tactic maps a proof tree to a sequence of proof trees:
+    if length of sequence = 0 then the tactic does not apply;
+    if length > 1 then backtracking on the alternatives can occur.*)
+
+datatype tactic = Tactic of thm -> thm Sequence.seq;
+
+fun tapply(Tactic tf, state) = tf (state);
+
+(*Makes a tactic from one that uses the components of the state.*)
+fun STATE tacfun = Tactic (fn state => tapply(tacfun state, state));
+
+
+(*** LCF-style tacticals ***)
+
+(*the tactical THEN performs one tactic followed by another*)
+fun (Tactic tf1)  THEN  (Tactic tf2) = 
+  Tactic (fn state => Sequence.flats (Sequence.maps tf2 (tf1 state)));
+
+
+(*The tactical ORELSE uses the first tactic that returns a nonempty sequence.
+  Like in LCF, ORELSE commits to either tac1 or tac2 immediately.
+  Does not backtrack to tac2 if tac1 was initially chosen. *)
+fun (Tactic tf1)  ORELSE  (Tactic tf2) = 
+  Tactic (fn state =>  
+    case Sequence.pull(tf1 state) of
+	None       => tf2 state
+      | sequencecell => Sequence.seqof(fn()=> sequencecell));
+
+
+(*The tactical APPEND combines the results of two tactics.
+  Like ORELSE, but allows backtracking on both tac1 and tac2.
+  The tactic tac2 is not applied until needed.*)
+fun (Tactic tf1)  APPEND  (Tactic tf2) = 
+  Tactic (fn state =>  Sequence.append(tf1 state,
+                          Sequence.seqof(fn()=> Sequence.pull (tf2 state))));
+
+(*Like APPEND, but interleaves results of tac1 and tac2.*)
+fun (Tactic tf1)  INTLEAVE  (Tactic tf2) = 
+  Tactic (fn state =>  Sequence.interleave(tf1 state,
+                          Sequence.seqof(fn()=> Sequence.pull (tf2 state))));
+
+(*Versions for combining tactic-valued functions, as in
+     SOMEGOAL (resolve_tac rls THEN' assume_tac) *)
+fun tac1 THEN' tac2 = fn x => tac1 x THEN tac2 x;
+fun tac1 ORELSE' tac2 = fn x => tac1 x ORELSE tac2 x;
+fun tac1 APPEND' tac2 = fn x => tac1 x APPEND tac2 x;
+fun tac1 INTLEAVE' tac2 = fn x => tac1 x INTLEAVE tac2 x;
+
+(*passes all proofs through unchanged;  identity of THEN*)
+val all_tac = Tactic (fn state => Sequence.single state);
+
+(*passes no proofs through;  identity of ORELSE and APPEND*)
+val no_tac  = Tactic (fn state => Sequence.null);
+
+
+(*Make a tactic deterministic by chopping the tail of the proof sequence*)
+fun DETERM (Tactic tf) = Tactic (fn state => 
+      case Sequence.pull (tf state) of
+	      None => Sequence.null
+            | Some(x,_) => Sequence.cons(x, Sequence.null));
+
+
+(*Conditional tactical: testfun controls which tactic to use next.
+  Beware: due to eager evaluation, both thentac and elsetac are evaluated.*)
+fun COND testfun (Tactic thenf) (Tactic elsef) = Tactic (fn prf =>
+    if testfun prf then  thenf prf   else  elsef prf);
+
+(*Do the tactic or else do nothing*)
+fun TRY tac = tac ORELSE all_tac;
+
+
+(*** List-oriented tactics ***)
+
+(* EVERY [tac1,...,tacn]   equals    tac1 THEN ... THEN tacn   *)
+fun EVERY tacs = foldr (op THEN) (tacs, all_tac);
+
+(* EVERY' [tf1,...,tfn] i  equals    tf1 i THEN ... THEN tfn i   *)
+fun EVERY' tfs = foldr (op THEN') (tfs, K all_tac);
+
+(*Apply every tactic to 1*)
+fun EVERY1 tfs = EVERY' tfs 1;
+
+(* FIRST [tac1,...,tacn]   equals    tac1 ORELSE ... ORELSE tacn   *)
+fun FIRST tacs = foldr (op ORELSE) (tacs, no_tac);
+
+(* FIRST' [tf1,...,tfn] i  equals    tf1 i ORELSE ... ORELSE tfn i   *)
+fun FIRST' tfs = foldr (op ORELSE') (tfs, K no_tac);
+
+(*Apply first tactic to 1*)
+fun FIRST1 tfs = FIRST' tfs 1;
+
+
+(*** Tracing tactics ***)
+
+(*Max number of goals to print -- set by user*)
+val goals_limit = ref 10;
+
+(*Print the current proof state and pass it on.*)
+val print_tac = Tactic (fn state => 
+  (print_goals (!goals_limit) state;   Sequence.single state));
+
+(*Pause until a line is typed -- if non-empty then fail. *)
+val pause_tac = Tactic (fn state => 
+  (prs"** Press RETURN to continue: ";
+   if input(std_in,1) = "\n" then Sequence.single state
+   else (prs"Goodbye\n";  Sequence.null)));
+
+exception TRACE_EXIT of thm
+and TRACE_QUIT;
+
+(*Handle all tracing commands for current state and tactic *)
+fun exec_trace_command flag (tf, state) = 
+   case input_line(std_in) of
+       "\n" => tf state
+     | "f\n" => Sequence.null
+     | "o\n" => (flag:=false; tf state)
+     | "x\n" => (prs"Exiting now\n";  raise (TRACE_EXIT state))
+     | "quit\n" => raise TRACE_QUIT
+     | _     => (prs
+"Type RETURN to continue or...\n\
+\     f    - to fail here\n\
+\     o    - to switch tracing off\n\
+\     x    - to exit at this point\n\
+\     quit - to abort this tracing run\n\
+\** Well? "     ;  exec_trace_command flag (tf, state));
+
+
+(*Extract from a tactic, a thm->thm seq function that handles tracing*)
+fun tracify flag (Tactic tf) state =
+  if !flag then (print_goals (!goals_limit) state;  
+		 prs"** Press RETURN to continue: ";
+		 exec_trace_command flag (tf,state))
+  else tf state;
+
+(*Create a tactic whose outcome is given by seqf, handling TRACE_EXIT*)
+fun traced_tac seqf = Tactic (fn st =>
+    Sequence.seqof (fn()=> seqf st
+		           handle TRACE_EXIT st' => Some(st', Sequence.null)));
+
+
+(*Tracing flags*)
+val trace_REPEAT= ref false
+and trace_DEPTH_FIRST = ref false
+and trace_BEST_FIRST = ref false;
+
+(*Deterministic REPEAT: only retains the first outcome; 
+  uses less space than REPEAT; tail recursive*)
+fun REPEAT_DETERM tac = 
+  let val tf = tracify trace_REPEAT tac
+      fun drep st =
+        case Sequence.pull(tf st) of
+  	    None       => Some(st, Sequence.null)
+          | Some(st',_) => drep st'
+  in  traced_tac drep  end;
+
+(*General REPEAT: maintains a stack of alternatives; tail recursive*)
+fun REPEAT tac = 
+  let val tf = tracify trace_REPEAT tac
+      fun rep qs st = 
+	case Sequence.pull(tf st) of
+  	    None       => Some(st, Sequence.seqof(fn()=> repq qs))
+          | Some(st',q) => rep (q::qs) st'
+      and repq [] = None
+        | repq(q::qs) = case Sequence.pull q of
+  	    None       => repq qs
+          | Some(st,q) => rep (q::qs) st
+  in  traced_tac (rep [])  end;
+
+(*Repeat 1 or more times*)
+fun REPEAT1 tac = tac THEN REPEAT tac;
+
+
+(** Search tacticals **)
+
+(*Seaarches "satp" reports proof tree as satisfied*)
+fun DEPTH_FIRST satp tac = 
+ let val tf = tracify trace_DEPTH_FIRST tac
+     fun depth [] = None
+       | depth(q::qs) =
+	  case Sequence.pull q of
+	      None         => depth qs
+	    | Some(st,stq) => 
+		if satp st then Some(st, Sequence.seqof(fn()=> depth(stq::qs)))
+		else depth (tf st :: stq :: qs)
+  in  traced_tac (fn st => depth([Sequence.single st]))  end;
+
+
+(*Predicate: Does the rule have fewer than n premises?*)
+fun has_fewer_prems n rule = (nprems_of rule < n);
+
+(*Apply a tactic if subgoals remain, else do nothing.*)
+val IF_UNSOLVED = COND (has_fewer_prems 1) all_tac;
+
+(*Tactical to reduce the number of premises by 1.
+  If no subgoals then it must fail! *)
+fun DEPTH_SOLVE_1 tac = STATE
+ (fn state => 
+    (case nprems_of state of
+	0 => no_tac
+      | n => DEPTH_FIRST (has_fewer_prems n) tac));
+
+(*Uses depth-first search to solve ALL subgoals*)
+val DEPTH_SOLVE = DEPTH_FIRST (has_fewer_prems 1);
+
+(*** Best-first search ***)
+
+(*Insertion into priority queue of states *)
+fun insert (nth: int*thm, []) = [nth]
+  | insert ((m,th), (n,th')::nths) = 
+      if  n<m then (n,th') :: insert ((m,th), nths)
+      else if  n=m andalso eq_thm(th,th')
+              then (n,th')::nths
+              else (m,th)::(n,th')::nths;
+
+(*For creating output sequence*)
+fun some_of_list []     = None
+  | some_of_list (x::l) = Some (x, Sequence.seqof (fn () => some_of_list l));
+
+
+(* Best-first search for a state that satisfies satp (incl initial state)
+  Function sizef estimates size of problem remaining (smaller means better).
+  tactic tf0 sets up the initial priority queue, which is searched by tac. *)
+fun (Tactic tf0) THEN_BEST_FIRST (satp, sizef, tac) = 
+  let val tf = tracify trace_BEST_FIRST tac
+      fun pairsize th = (sizef th, th);
+      fun bfs (news,nprfs) =
+	   (case  partition satp news  of
+		([],nonsats) => next(foldr insert
+					(map pairsize nonsats, nprfs)) 
+	      | (sats,_)  => some_of_list sats)
+      and next [] = None
+        | next ((n,prf)::nprfs) =
+	    (if !trace_BEST_FIRST 
+	       then writeln("state size = " ^ string_of_int n ^ 
+		         "  queue length =" ^ string_of_int (length nprfs))  
+               else ();
+	     bfs (Sequence.list_of_s (tf prf), nprfs))
+      fun tf st = bfs (Sequence.list_of_s (tf0 st),  [])
+  in traced_tac tf end;
+
+(*Ordinary best-first search, with no initial tactic*)
+fun BEST_FIRST (satp,sizef) tac = all_tac THEN_BEST_FIRST (satp,sizef,tac);
+
+(*Breadth-first search to satisfy satpred (including initial state) 
+  SLOW -- SHOULD NOT USE APPEND!*)
+fun BREADTH_FIRST satpred (Tactic tf) = 
+  let val tacf = Sequence.list_of_s o tf;
+      fun bfs prfs =
+	 (case  partition satpred prfs  of
+	      ([],[]) => []
+	    | ([],nonsats) => 
+		  (prs("breadth=" ^ string_of_int(length nonsats) ^ "\n");
+		   bfs (flat (map tacf nonsats)))
+	    | (sats,_)  => sats)
+  in Tactic (fn state => Sequence.s_of_list (bfs [state])) end;
+
+
+(** Filtering tacticals **)
+
+(*Returns all states satisfying the predicate*)
+fun FILTER pred (Tactic tf) = Tactic
+      (fn state => Sequence.filters pred (tf state));
+
+(*Returns all changed states*)
+fun CHANGED (Tactic tf)  = 
+  Tactic (fn state => 
+    let fun diff st = not (eq_thm(state,st))
+    in  Sequence.filters diff (tf state)
+    end );
+
+
+(*** Tacticals based on subgoal numbering ***)
+
+(*For n subgoals, performs tf(n) THEN ... THEN tf(1) 
+  Essential to work backwards since tf(i) may add/delete subgoals at i. *)
+fun ALLGOALS tf = 
+  let fun tac 0 = all_tac
+	| tac n = tf(n) THEN tac(n-1)
+  in  Tactic(fn state => tapply(tac(nprems_of state), state))  end;
+
+(*For n subgoals, performs tf(n) ORELSE ... ORELSE tf(1)  *)
+fun SOMEGOAL tf = 
+  let fun tac 0 = no_tac
+	| tac n = tf(n) ORELSE tac(n-1)
+  in  Tactic(fn state => tapply(tac(nprems_of state), state))  end;
+
+(*For n subgoals, performs tf(1) ORELSE ... ORELSE tf(n).
+  More appropriate than SOMEGOAL in some cases.*)
+fun FIRSTGOAL tf = 
+  let fun tac (i,n) = if i>n then no_tac else  tf(i) ORELSE tac (i+1,n)
+  in  Tactic(fn state => tapply(tac(1, nprems_of state), state))  end;
+
+(*Repeatedly solve some using tf. *)
+fun REPEAT_SOME tf = REPEAT1 (SOMEGOAL (REPEAT1 o tf));
+
+(*Repeatedly solve the first possible subgoal using tf. *)
+fun REPEAT_FIRST tf = REPEAT1 (FIRSTGOAL (REPEAT1 o tf));
+
+(*For n subgoals, tries to apply tf to n,...1  *)
+fun TRYALL tf = ALLGOALS (TRY o tf);
+
+
+(*Make a tactic for subgoal i, if there is one.  *)
+fun SUBGOAL goalfun i = Tactic(fn state =>
+  case drop(i-1, prems_of state) of
+      [] => Sequence.null
+    | prem::_ => tapply(goalfun (prem,i), state));
+
+(*Tactical for restricting the effect of a tactic to subgoal i.
+  Works by making a new state from subgoal i, applying tf to it, and
+  composing the resulting metathm with the original state.
+  The "main goal" of the new state will not be atomic, some tactics may fail!
+  DOES NOT work if tactic affects the main goal other than by instantiation.*)
+
+(* (!!x. ?V) ==> ?V ;  used by protect_subgoal.*)
+val dummy_quant_rl = 
+  standard (forall_elim_var 0 (assume 
+                  (Sign.read_cterm Sign.pure ("!!x. PROP V",propT))));
+
+(* Prevent the subgoal's assumptions from becoming additional subgoals in the
+   new proof state by enclosing them by a universal quantification *)
+fun protect_subgoal state i =
+  case Sequence.chop (1, bicompose false (false,dummy_quant_rl,1) i state)
+  of
+      ([state'],_) => state'
+    | _ => error"SELECT_GOAL -- impossible error???";
+
+(*Does the work of SELECT_GOAL. *)
+fun select (Tactic tf) state i =
+  let val prem::_ = drop(i-1, prems_of state)
+      val st0 = trivial (Sign.cterm_of (#sign(rep_thm state)) prem);
+      fun next st = bicompose false (false, st, nprems_of st) i state
+  in  Sequence.flats (Sequence.maps next (tf st0))
+  end;
+
+(*If i=1 and there is only one subgoal then do nothing!*)
+fun SELECT_GOAL tac i = Tactic (fn state =>
+  case (i, drop(i-1, prems_of state)) of
+      (_,[]) => Sequence.null
+    | (1,[_]) => tapply(tac,state)
+    | (_, (Const("==>",_)$_$_) :: _) => select tac (protect_subgoal state i) i
+    | (_, _::_) => select tac state i);
+
+
+
+(*Strips assumptions in goal yielding  ( [x1,...,xm], [H1,...,Hn], B )
+    H1,...,Hn are the hypotheses;  x1...xm are variants of the parameters. 
+  Main difference from strip_assums concerns parameters: 
+    it replaces the bound variables by free variables.  *)
+fun strip_context_aux (params, Hs, Const("==>", _) $ H $ B) = 
+	strip_context_aux (params, H::Hs, B)
+  | strip_context_aux (params, Hs, Const("all",_)$Abs(a,T,t)) =
+        let val (b,u) = variant_abs(a,T,t)
+	in  strip_context_aux ((b,T)::params, Hs, u)  end
+  | strip_context_aux (params, Hs, B) = (rev params, rev Hs, B);
+
+fun strip_context A = strip_context_aux ([],[],A);
+
+
+(**** METAHYPS -- tactical for using hypotheses as meta-level assumptions
+       METAHYPS (fn prems => tac (prems)) i
+
+converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new
+proof state A==>A, supplying A1,...,An as meta-level assumptions (in
+"prems").  The parameters x1,...,xm become free variables.  If the
+resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An)
+then it is lifted back into the original context, yielding k subgoals.
+
+Replaces unknowns in the context by Frees having the prefix METAHYP_
+New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm.
+DOES NOT HANDLE TYPE UNKNOWNS.
+****)
+
+local 
+  open Logic 
+
+  (*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
+    Instantiates distinct free variables by terms of same type.*)
+  fun free_instantiate ctpairs = 
+      forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs);
+
+  fun free_of s ((a,i), T) =
+        Free(s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i),
+	     T)
+
+  fun mk_inst (var as Var(v,T))  = (var,  free_of "METAHYP1_" (v,T))
+in
+
+fun metahyps_aux_tac tacf (prem,i) = Tactic (fn state =>
+  let val {sign,maxidx,...} = rep_thm state
+      val cterm = Sign.cterm_of sign
+      (*find all vars in the hyps -- should find tvars also!*)
+      val hyps_vars = foldr add_term_vars (strip_assums_hyp prem, [])
+      val insts = map mk_inst hyps_vars
+      (*replace the hyps_vars by Frees*)
+      val prem' = subst_atomic insts prem
+      val (params,hyps,concl) = strip_context prem'
+      val fparams = map Free params
+      val cparams = map cterm fparams
+      and chyps = map cterm hyps
+      val hypths = map assume chyps
+      fun swap_ctpair (t,u) = (cterm u, cterm t)
+      (*Subgoal variables: make Free; lift type over params*)
+      fun mk_subgoal_inst concl_vars (var as Var(v,T)) = 
+          if var mem concl_vars 
+	  then (var, true, free_of "METAHYP2_" (v,T))
+	  else (var, false,
+		free_of "METAHYP2_" (v, map #2 params --->T))
+      (*Instantiate subgoal vars by Free applied to params*)
+      fun mk_ctpair (t,in_concl,u) = 
+	  if in_concl then (cterm t,  cterm u)
+          else (cterm t,  cterm (list_comb (u,fparams)))
+      (*Restore Vars with higher type and index*)
+      fun mk_subgoal_swap_ctpair 
+		(t as Var((a,i),_), in_concl, u as Free(_,U)) = 
+	  if in_concl then (cterm u, cterm t)
+          else (cterm u, cterm(Var((a, i+maxidx), U)))
+      (*Embed B in the original context of params and hyps*)
+      fun embed B = list_all_free (params, list_implies (hyps, B))
+      (*Strip the context using elimination rules*)
+      fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths
+      (*Embed an ff pair in the original params*)
+      fun embed_ff(t,u) = 
+	  mk_flexpair (list_abs_free (params, t), list_abs_free (params, u))
+      (*Remove parameter abstractions from the ff pairs*)
+      fun elim_ff ff = flexpair_abs_elim_list cparams ff
+      (*A form of lifting that discharges assumptions.*)
+      fun relift st = 
+	let val prop = #prop(rep_thm st)
+	    val subgoal_vars = (*Vars introduced in the subgoals*)
+		  foldr add_term_vars (strip_imp_prems prop, [])
+	    and concl_vars = add_term_vars (strip_imp_concl prop, [])
+	    val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars
+	    val st' = instantiate ([], map mk_ctpair subgoal_insts) st
+	    val emBs = map (cterm o embed) (prems_of st')
+            and ffs = map (cterm o embed_ff) (tpairs_of st')
+	    val Cth  = implies_elim_list st' 
+			    (map (elim_ff o assume) ffs @
+			     map (elim o assume) emBs)
+	in  (*restore the unknowns to the hypotheses*)
+	    free_instantiate (map swap_ctpair insts @
+			      map mk_subgoal_swap_ctpair subgoal_insts)
+		(*discharge assumptions from state in same order*)
+		(implies_intr_list (ffs@emBs)
+		  (forall_intr_list cparams (implies_intr_list chyps Cth)))
+	end
+      val subprems = map (forall_elim_vars 0) hypths
+      and st0 = trivial (cterm concl)
+      (*function to replace the current subgoal*)
+      fun next st = bicompose false (false, relift st, nprems_of st)
+	            i state
+  in  Sequence.flats (Sequence.maps next (tapply(tacf subprems, st0)))
+  end);
+end;
+
+fun METAHYPS tacf = SUBGOAL (metahyps_aux_tac tacf);
+
+end;
+end;