src/Pure/tctical.ML
author paulson
Tue Feb 04 10:33:58 1997 +0100 (1997-02-04)
changeset 2580 e3f680709487
parent 2244 dacee519738a
child 2627 4ee01bb55a44
permissions -rw-r--r--
Gradual switching to Basis Library functions nth, drop, etc.
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(*  Title:      tctical
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Tacticals
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*)
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infix 1 THEN THEN';
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infix 0 ORELSE APPEND INTLEAVE ORELSE' APPEND' INTLEAVE';
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infix 0 THEN_ELSE;
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signature TACTICAL =
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  sig
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  type tactic  (* = thm -> thm Sequence.seq*)
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  val all_tac           : tactic
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  val ALLGOALS          : (int -> tactic) -> tactic   
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  val APPEND            : tactic * tactic -> tactic
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  val APPEND'           : ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val CHANGED           : tactic -> tactic
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  val COND              : (thm -> bool) -> tactic -> tactic -> tactic   
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  val DETERM            : tactic -> tactic
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  val EVERY             : tactic list -> tactic   
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  val EVERY'            : ('a -> tactic) list -> 'a -> tactic
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  val EVERY1            : (int -> tactic) list -> tactic
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  val FILTER            : (thm -> bool) -> tactic -> tactic
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  val FIRST             : tactic list -> tactic   
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  val FIRST'            : ('a -> tactic) list -> 'a -> tactic
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  val FIRST1            : (int -> tactic) list -> tactic
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  val FIRSTGOAL         : (int -> tactic) -> tactic
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  val goals_limit       : int ref
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  val INTLEAVE          : tactic * tactic -> tactic
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  val INTLEAVE'         : ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val METAHYPS          : (thm list -> tactic) -> int -> tactic
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  val no_tac            : tactic
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  val ORELSE            : tactic * tactic -> tactic
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  val ORELSE'           : ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val pause_tac         : tactic
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  val print_tac         : tactic
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  val REPEAT            : tactic -> tactic
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  val REPEAT1           : tactic -> tactic
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  val REPEAT_DETERM_N   : int -> tactic -> tactic
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  val REPEAT_DETERM     : tactic -> tactic
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  val REPEAT_DETERM1    : tactic -> tactic
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  val REPEAT_DETERM_FIRST: (int -> tactic) -> tactic
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  val REPEAT_DETERM_SOME: (int -> tactic) -> tactic
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  val REPEAT_FIRST      : (int -> tactic) -> tactic
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  val REPEAT_SOME       : (int -> tactic) -> tactic
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  val SELECT_GOAL       : tactic -> int -> tactic
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  val SOMEGOAL          : (int -> tactic) -> tactic   
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  val STATE             : (thm -> tactic) -> tactic
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  val strip_context     : term -> (string * typ) list * term list * term
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  val SUBGOAL           : ((term*int) -> tactic) -> int -> tactic
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  val suppress_tracing  : bool ref
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  val THEN              : tactic * tactic -> tactic
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  val THEN'             : ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val THEN_ELSE         : tactic * (tactic*tactic) -> tactic
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  val traced_tac        : (thm -> (thm * thm Sequence.seq) option) -> tactic
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  val tracify           : bool ref -> tactic -> thm -> thm Sequence.seq
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  val trace_REPEAT      : bool ref
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  val TRY               : tactic -> tactic
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  val TRYALL            : (int -> tactic) -> tactic   
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  end;
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structure Tactical : TACTICAL = 
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struct
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(**** Tactics ****)
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(*A tactic maps a proof tree to a sequence of proof trees:
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    if length of sequence = 0 then the tactic does not apply;
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    if length > 1 then backtracking on the alternatives can occur.*)
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type tactic = thm -> thm Sequence.seq;
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(*Makes a tactic from one that uses the components of the state.*)
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fun STATE tacfun st = tacfun st st;
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(*** LCF-style tacticals ***)
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(*the tactical THEN performs one tactic followed by another*)
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fun (tac1 THEN tac2) st = Sequence.flats (Sequence.maps tac2 (tac1 st));
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(*The tactical ORELSE uses the first tactic that returns a nonempty sequence.
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  Like in LCF, ORELSE commits to either tac1 or tac2 immediately.
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  Does not backtrack to tac2 if tac1 was initially chosen. *)
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fun (tac1 ORELSE tac2) st =
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    case Sequence.pull(tac1 st) of
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        None       => tac2 st
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      | sequencecell => Sequence.seqof(fn()=> sequencecell);
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(*The tactical APPEND combines the results of two tactics.
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  Like ORELSE, but allows backtracking on both tac1 and tac2.
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  The tactic tac2 is not applied until needed.*)
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fun (tac1 APPEND tac2) st = 
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  Sequence.append(tac1 st,
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                  Sequence.seqof(fn()=> Sequence.pull (tac2 st)));
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(*Like APPEND, but interleaves results of tac1 and tac2.*)
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fun (tac1 INTLEAVE tac2) st = 
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    Sequence.interleave(tac1 st,
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                        Sequence.seqof(fn()=> Sequence.pull (tac2 st)));
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(*Conditional tactic.
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        tac1 ORELSE tac2 = tac1 THEN_ELSE (all_tac, tac2)
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        tac1 THEN tac2   = tac1 THEN_ELSE (tac2, no_tac)
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*)
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fun (tac THEN_ELSE (tac1, tac2)) st = 
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    case Sequence.pull(tac st) of
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        None    => tac2 st              (*failed; try tactic 2*)
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      | seqcell => Sequence.flats       (*succeeded; use tactic 1*)
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                    (Sequence.maps tac1 (Sequence.seqof(fn()=> seqcell)));
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(*Versions for combining tactic-valued functions, as in
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     SOMEGOAL (resolve_tac rls THEN' assume_tac) *)
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fun (tac1 THEN' tac2) x = tac1 x THEN tac2 x;
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fun (tac1 ORELSE' tac2) x = tac1 x ORELSE tac2 x;
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fun (tac1 APPEND' tac2) x = tac1 x APPEND tac2 x;
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fun (tac1 INTLEAVE' tac2) x = tac1 x INTLEAVE tac2 x;
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(*passes all proofs through unchanged;  identity of THEN*)
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fun all_tac st = Sequence.single st;
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(*passes no proofs through;  identity of ORELSE and APPEND*)
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fun no_tac st  = Sequence.null;
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(*Make a tactic deterministic by chopping the tail of the proof sequence*)
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fun DETERM tac st =  
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      case Sequence.pull (tac st) of
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              None => Sequence.null
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            | Some(x,_) => Sequence.cons(x, Sequence.null);
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(*Conditional tactical: testfun controls which tactic to use next.
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  Beware: due to eager evaluation, both thentac and elsetac are evaluated.*)
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fun COND testfun thenf elsef = (fn prf =>
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    if testfun prf then  thenf prf   else  elsef prf);
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(*Do the tactic or else do nothing*)
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fun TRY tac = tac ORELSE all_tac;
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(*** List-oriented tactics ***)
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(* EVERY [tac1,...,tacn]   equals    tac1 THEN ... THEN tacn   *)
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fun EVERY tacs = foldr (op THEN) (tacs, all_tac);
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(* EVERY' [tac1,...,tacn] i  equals    tac1 i THEN ... THEN tacn i   *)
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fun EVERY' tacs = foldr (op THEN') (tacs, K all_tac);
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(*Apply every tactic to 1*)
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fun EVERY1 tacs = EVERY' tacs 1;
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(* FIRST [tac1,...,tacn]   equals    tac1 ORELSE ... ORELSE tacn   *)
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fun FIRST tacs = foldr (op ORELSE) (tacs, no_tac);
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(* FIRST' [tac1,...,tacn] i  equals    tac1 i ORELSE ... ORELSE tacn i   *)
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fun FIRST' tacs = foldr (op ORELSE') (tacs, K no_tac);
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(*Apply first tactic to 1*)
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fun FIRST1 tacs = FIRST' tacs 1;
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(*** Tracing tactics ***)
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(*Max number of goals to print -- set by user*)
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val goals_limit = ref 10;
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(*Print the current proof state and pass it on.*)
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val print_tac = 
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    (fn st => 
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     (!print_goals_ref (!goals_limit) st;   Sequence.single st));
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(*Pause until a line is typed -- if non-empty then fail. *)
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fun pause_tac st =  
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  (prs"** Press RETURN to continue: ";
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   if TextIO.inputLine TextIO.stdIn = "\n" then Sequence.single st
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   else (prs"Goodbye\n";  Sequence.null));
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exception TRACE_EXIT of thm
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and TRACE_QUIT;
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(*Tracing flags*)
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val trace_REPEAT= ref false
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and suppress_tracing = ref false;
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(*Handle all tracing commands for current state and tactic *)
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fun exec_trace_command flag (tac, st) = 
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   case TextIO.inputLine(TextIO.stdIn) of
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       "\n" => tac st
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     | "f\n" => Sequence.null
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     | "o\n" => (flag:=false;  tac st)
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     | "s\n" => (suppress_tracing:=true;  tac st)
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     | "x\n" => (prs"Exiting now\n";  raise (TRACE_EXIT st))
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     | "quit\n" => raise TRACE_QUIT
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     | _     => (prs
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"Type RETURN to continue or...\n\
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\     f    - to fail here\n\
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\     o    - to switch tracing off\n\
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\     s    - to suppress tracing until next entry to a tactical\n\
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\     x    - to exit at this point\n\
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\     quit - to abort this tracing run\n\
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\** Well? "     ;  exec_trace_command flag (tac, st));
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(*Extract from a tactic, a thm->thm seq function that handles tracing*)
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fun tracify flag tac st =
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  if !flag andalso not (!suppress_tracing)
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           then (!print_goals_ref (!goals_limit) st;  
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                 prs"** Press RETURN to continue: ";
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                 exec_trace_command flag (tac,st))
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  else tac st;
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(*Create a tactic whose outcome is given by seqf, handling TRACE_EXIT*)
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fun traced_tac seqf st = 
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    (suppress_tracing := false;
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     Sequence.seqof (fn()=> seqf st
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                         handle TRACE_EXIT st' => Some(st', Sequence.null)));
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(*Deterministic REPEAT: only retains the first outcome; 
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  uses less space than REPEAT; tail recursive.
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  If non-negative, n bounds the number of repetitions.*)
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fun REPEAT_DETERM_N n tac = 
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  let val tac = tracify trace_REPEAT tac
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      fun drep 0 st = Some(st, Sequence.null)
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        | drep n st =
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           (case Sequence.pull(tac st) of
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                None       => Some(st, Sequence.null)
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              | Some(st',_) => drep (n-1) st')
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  in  traced_tac (drep n)  end;
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(*Allows any number of repetitions*)
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val REPEAT_DETERM = REPEAT_DETERM_N ~1;
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(*General REPEAT: maintains a stack of alternatives; tail recursive*)
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fun REPEAT tac = 
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  let val tac = tracify trace_REPEAT tac
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      fun rep qs st = 
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        case Sequence.pull(tac st) of
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            None       => Some(st, Sequence.seqof(fn()=> repq qs))
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          | Some(st',q) => rep (q::qs) st'
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      and repq [] = None
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        | repq(q::qs) = case Sequence.pull q of
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            None       => repq qs
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          | Some(st,q) => rep (q::qs) st
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  in  traced_tac (rep [])  end;
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(*Repeat 1 or more times*)
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fun REPEAT_DETERM1 tac = DETERM tac THEN REPEAT_DETERM tac;
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fun REPEAT1 tac = tac THEN REPEAT tac;
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(** Filtering tacticals **)
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(*Returns all states satisfying the predicate*)
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fun FILTER pred tac st = Sequence.filters pred (tac st);
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(*Returns all changed states*)
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fun CHANGED tac st = 
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    let fun diff st' = not (eq_thm(st,st'))
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    in  Sequence.filters diff (tac st)  end;
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(*** Tacticals based on subgoal numbering ***)
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(*For n subgoals, performs tac(n) THEN ... THEN tac(1) 
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  Essential to work backwards since tac(i) may add/delete subgoals at i. *)
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fun ALLGOALS tac st = 
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  let fun doall 0 = all_tac
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        | doall n = tac(n) THEN doall(n-1)
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  in  doall(nprems_of st)st  end;
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(*For n subgoals, performs tac(n) ORELSE ... ORELSE tac(1)  *)
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fun SOMEGOAL tac st = 
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  let fun find 0 = no_tac
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        | find n = tac(n) ORELSE find(n-1)
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  in  find(nprems_of st)st  end;
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(*For n subgoals, performs tac(1) ORELSE ... ORELSE tac(n).
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  More appropriate than SOMEGOAL in some cases.*)
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fun FIRSTGOAL tac st = 
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  let fun find (i,n) = if i>n then no_tac else  tac(i) ORELSE find (i+1,n)
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  in  find(1, nprems_of st)st  end;
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(*Repeatedly solve some using tac. *)
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fun REPEAT_SOME tac = REPEAT1 (SOMEGOAL (REPEAT1 o tac));
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fun REPEAT_DETERM_SOME tac = REPEAT_DETERM1 (SOMEGOAL (REPEAT_DETERM1 o tac));
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(*Repeatedly solve the first possible subgoal using tac. *)
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fun REPEAT_FIRST tac = REPEAT1 (FIRSTGOAL (REPEAT1 o tac));
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fun REPEAT_DETERM_FIRST tac = REPEAT_DETERM1 (FIRSTGOAL (REPEAT_DETERM1 o tac));
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(*For n subgoals, tries to apply tac to n,...1  *)
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fun TRYALL tac = ALLGOALS (TRY o tac);
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(*Make a tactic for subgoal i, if there is one.  *)
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fun SUBGOAL goalfun i st = goalfun (List.nth(prems_of st, i-1),  i) st
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                             handle Subscript => Sequence.null;
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(*** SELECT_GOAL ***)
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(*Tactical for restricting the effect of a tactic to subgoal i.
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  Works by making a new state from subgoal i, applying tac to it, and
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  composing the resulting metathm with the original state.
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  The "main goal" of the new state will not be atomic, some tactics may fail!
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  DOES NOT work if tactic affects the main goal other than by instantiation.*)
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(*SELECT_GOAL optimization: replace the conclusion by a variable X,
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  to avoid copying.  Proof states have X==concl as an assuption.*)
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val prop_equals = cterm_of Sign.proto_pure 
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                    (Const("==", propT-->propT-->propT));
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fun mk_prop_equals(t,u) = capply (capply prop_equals t) u;
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(*Like trivial but returns [ct==X] ct==>X instead of ct==>ct, if possible.
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  It is paired with a function to undo the transformation.  If ct contains
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  Vars then it returns ct==>ct.*)
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fun eq_trivial ct =
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  let val xfree = cterm_of Sign.proto_pure (Free (gensym"X", propT))
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      val ct_eq_x = mk_prop_equals (ct, xfree)
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      and refl_ct = reflexive ct
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      fun restore th = 
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          implies_elim 
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            (forall_elim ct (forall_intr xfree (implies_intr ct_eq_x th)))
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            refl_ct
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  in  (equal_elim
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         (combination (combination refl_implies refl_ct) (assume ct_eq_x))
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         (trivial ct),
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       restore)
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  end  (*Fails if there are Vars or TVars*)
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    handle THM _ => (trivial ct, I);
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(*Does the work of SELECT_GOAL. *)
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fun select tac st0 i =
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  let val (eq_cprem, restore) = (*we hope maxidx goes to ~1*)
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	  eq_trivial (adjust_maxidx (List.nth(cprems_of st0, i-1)))
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      fun next st = bicompose false (false, restore st, nprems_of st) i st0
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  in  Sequence.flats (Sequence.maps next (tac eq_cprem))
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  end;
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(* (!!selct. PROP ?V) ==> PROP ?V ;  contains NO TYPE VARIABLES.*)
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val dummy_quant_rl = 
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  read_cterm Sign.proto_pure ("!!selct::prop. PROP V",propT) |>
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  assume |> forall_elim_var 0 |> standard;
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(* Prevent the subgoal's assumptions from becoming additional subgoals in the
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   new proof state by enclosing them by a universal quantification *)
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fun protect_subgoal st i =
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        Sequence.hd (bicompose false (false,dummy_quant_rl,1) i st)
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        handle _ => error"SELECT_GOAL -- impossible error???";
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fun SELECT_GOAL tac i st = 
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  case (i, List.drop(prems_of st, i-1)) of
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      (_,[]) => Sequence.null
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    | (1,[_]) => tac st         (*If i=1 and only one subgoal do nothing!*)
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    | (_, (Const("==>",_)$_$_) :: _) => select tac (protect_subgoal st i) i
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    | (_, _::_) => select tac st i;
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(*Strips assumptions in goal yielding  ( [x1,...,xm], [H1,...,Hn], B )
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    H1,...,Hn are the hypotheses;  x1...xm are variants of the parameters. 
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  Main difference from strip_assums concerns parameters: 
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    it replaces the bound variables by free variables.  *)
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fun strip_context_aux (params, Hs, Const("==>", _) $ H $ B) = 
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        strip_context_aux (params, H::Hs, B)
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  | strip_context_aux (params, Hs, Const("all",_)$Abs(a,T,t)) =
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        let val (b,u) = variant_abs(a,T,t)
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        in  strip_context_aux ((b,T)::params, Hs, u)  end
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  | strip_context_aux (params, Hs, B) = (rev params, rev Hs, B);
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fun strip_context A = strip_context_aux ([],[],A);
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(**** METAHYPS -- tactical for using hypotheses as meta-level assumptions
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       METAHYPS (fn prems => tac prems) i
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converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new
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proof state A==>A, supplying A1,...,An as meta-level assumptions (in
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"prems").  The parameters x1,...,xm become free variables.  If the
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resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An)
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then it is lifted back into the original context, yielding k subgoals.
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Replaces unknowns in the context by Frees having the prefix METAHYP_
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New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm.
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DOES NOT HANDLE TYPE UNKNOWNS.
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****)
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local 
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  (*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
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    Instantiates distinct free variables by terms of same type.*)
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  fun free_instantiate ctpairs = 
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      forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs);
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  fun free_of s ((a,i), T) =
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        Free(s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i),
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             T)
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  fun mk_inst (var as Var(v,T))  = (var,  free_of "METAHYP1_" (v,T))
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in
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fun metahyps_aux_tac tacf (prem,i) state = 
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  let val {sign,maxidx,...} = rep_thm state
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      val cterm = cterm_of sign
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      (*find all vars in the hyps -- should find tvars also!*)
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      val hyps_vars = foldr add_term_vars (Logic.strip_assums_hyp prem, [])
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      val insts = map mk_inst hyps_vars
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      (*replace the hyps_vars by Frees*)
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      val prem' = subst_atomic insts prem
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      val (params,hyps,concl) = strip_context prem'
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      val fparams = map Free params
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      val cparams = map cterm fparams
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      and chyps = map cterm hyps
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      val hypths = map assume chyps
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      fun swap_ctpair (t,u) = (cterm u, cterm t)
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      (*Subgoal variables: make Free; lift type over params*)
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      fun mk_subgoal_inst concl_vars (var as Var(v,T)) = 
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          if var mem concl_vars 
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          then (var, true, free_of "METAHYP2_" (v,T))
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          else (var, false,
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                free_of "METAHYP2_" (v, map #2 params --->T))
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      (*Instantiate subgoal vars by Free applied to params*)
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      fun mk_ctpair (t,in_concl,u) = 
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          if in_concl then (cterm t,  cterm u)
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          else (cterm t,  cterm (list_comb (u,fparams)))
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      (*Restore Vars with higher type and index*)
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      fun mk_subgoal_swap_ctpair 
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                (t as Var((a,i),_), in_concl, u as Free(_,U)) = 
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          if in_concl then (cterm u, cterm t)
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          else (cterm u, cterm(Var((a, i+maxidx), U)))
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      (*Embed B in the original context of params and hyps*)
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      fun embed B = list_all_free (params, Logic.list_implies (hyps, B))
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      (*Strip the context using elimination rules*)
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      fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths
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      (*Embed an ff pair in the original params*)
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      fun embed_ff(t,u) = Logic.mk_flexpair (list_abs_free (params, t), 
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                                             list_abs_free (params, u))
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      (*Remove parameter abstractions from the ff pairs*)
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      fun elim_ff ff = flexpair_abs_elim_list cparams ff
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      (*A form of lifting that discharges assumptions.*)
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      fun relift st = 
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        let val prop = #prop(rep_thm st)
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            val subgoal_vars = (*Vars introduced in the subgoals*)
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                  foldr add_term_vars (Logic.strip_imp_prems prop, [])
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            and concl_vars = add_term_vars (Logic.strip_imp_concl prop, [])
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            val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars
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            val st' = instantiate ([], map mk_ctpair subgoal_insts) st
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            val emBs = map (cterm o embed) (prems_of st')
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            and ffs = map (cterm o embed_ff) (tpairs_of st')
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   462
            val Cth  = implies_elim_list st' 
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                            (map (elim_ff o assume) ffs @
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                             map (elim o assume) emBs)
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        in  (*restore the unknowns to the hypotheses*)
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   466
            free_instantiate (map swap_ctpair insts @
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   467
                              map mk_subgoal_swap_ctpair subgoal_insts)
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                (*discharge assumptions from state in same order*)
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                (implies_intr_list (ffs@emBs)
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   470
                  (forall_intr_list cparams (implies_intr_list chyps Cth)))
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   471
        end
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      val subprems = map (forall_elim_vars 0) hypths
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   473
      and st0 = trivial (cterm concl)
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   474
      (*function to replace the current subgoal*)
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   475
      fun next st = bicompose false (false, relift st, nprems_of st)
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   476
                    i state
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  in  Sequence.flats (Sequence.maps next (tacf subprems st0))
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  end;
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   479
end;
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   480
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   481
fun METAHYPS tacf = SUBGOAL (metahyps_aux_tac tacf);
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   482
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   483
end;
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   484
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   485
open Tactical;