src/Pure/tactical.ML
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(*  Title:      Pure/tactical.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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Tacticals.
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*)
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infix 1 THEN THEN' THEN_ALL_NEW;
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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 Seq.seq
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  val THEN: tactic * tactic -> tactic
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  val ORELSE: tactic * tactic -> tactic
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  val APPEND: tactic * tactic -> tactic
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  val INTLEAVE: tactic * tactic -> tactic
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  val THEN_ELSE: tactic * (tactic*tactic) -> tactic
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  val THEN': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val ORELSE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val APPEND': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val INTLEAVE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic
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  val all_tac: tactic
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  val no_tac: tactic
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  val DETERM: tactic -> tactic
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  val COND: (thm -> bool) -> tactic -> tactic -> tactic
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  val TRY: 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 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 RANGE: (int -> tactic) list -> int -> tactic
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  val print_tac: string -> tactic
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  val pause_tac: tactic
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  val trace_REPEAT: bool ref
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  val suppress_tracing: bool ref
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  val tracify: bool ref -> tactic -> tactic
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  val traced_tac: (thm -> (thm * thm Seq.seq) option) -> tactic
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  val DETERM_UNTIL: (thm -> bool) -> 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: tactic -> tactic
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  val REPEAT_DETERM1: tactic -> tactic
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  val REPEAT1: tactic -> tactic
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  val FILTER: (thm -> bool) -> tactic -> tactic
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  val CHANGED: tactic -> tactic
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  val CHANGED_PROP: tactic -> tactic
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  val ALLGOALS: (int -> tactic) -> tactic
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  val SOMEGOAL: (int -> tactic) -> tactic
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  val FIRSTGOAL: (int -> tactic) -> tactic
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  val REPEAT_SOME: (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_DETERM_FIRST: (int -> tactic) -> tactic
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  val TRYALL: (int -> tactic) -> tactic
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  val CSUBGOAL: ((cterm * int) -> tactic) -> int -> tactic
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  val SUBGOAL: ((term * int) -> tactic) -> int -> tactic
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  val CHANGED_GOAL: (int -> tactic) -> int -> tactic
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  val THEN_ALL_NEW: (int -> tactic) * (int -> tactic) -> int -> tactic
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  val REPEAT_ALL_NEW: (int -> tactic) -> int -> tactic
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  val PRIMSEQ: (thm -> thm Seq.seq) -> tactic
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  val PRIMITIVE: (thm -> thm) -> tactic
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  val SINGLE: tactic -> thm -> thm option
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  val CONVERSION: conv -> int -> 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 Seq.seq;
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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 = Seq.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 Seq.pull(tac1 st) of
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        NONE       => tac2 st
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      | sequencecell => Seq.make(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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  Seq.append (tac1 st) (Seq.make(fn()=> Seq.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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    Seq.interleave(tac1 st,
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                        Seq.make(fn()=> Seq.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 Seq.pull(tac st) of
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        NONE    => tac2 st                                   (*failed; try tactic 2*)
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      | seqcell => Seq.maps tac1 (Seq.make(fn()=> seqcell)); (*succeeded; use tactic 1*)
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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 = Seq.single st;
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(*passes no proofs through;  identity of ORELSE and APPEND*)
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fun no_tac st  = Seq.empty;
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(*Make a tactic deterministic by chopping the tail of the proof sequence*)
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fun DETERM tac = Seq.DETERM tac;
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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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local
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  (*This version of EVERY avoids backtracking over repeated states*)
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  fun EVY (trail, []) st =
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        Seq.make (fn()=> SOME(st,
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                        Seq.make (fn()=> Seq.pull (evyBack trail))))
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    | EVY (trail, tac::tacs) st =
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          case Seq.pull(tac st) of
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              NONE    => evyBack trail              (*failed: backtrack*)
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            | SOME(st',q) => EVY ((st',q,tacs)::trail, tacs) st'
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  and evyBack [] = Seq.empty (*no alternatives*)
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    | evyBack ((st',q,tacs)::trail) =
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          case Seq.pull q of
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              NONE        => evyBack trail
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            | SOME(st,q') => if Thm.eq_thm (st',st)
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                             then evyBack ((st',q',tacs)::trail)
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                             else EVY ((st,q',tacs)::trail, tacs) st
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in
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(* EVERY [tac1,...,tacn]   equals    tac1 THEN ... THEN tacn   *)
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fun EVERY tacs = EVY ([], tacs);
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end;
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(* EVERY' [tac1,...,tacn] i  equals    tac1 i THEN ... THEN tacn i   *)
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fun EVERY' tacs i = EVERY (map (fn f => f i) tacs);
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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 = fold_rev (curry 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 = fold_rev (curry 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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(*Apply tactics on consecutive subgoals*)
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fun RANGE [] _ = all_tac
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  | RANGE (tac :: tacs) i = RANGE tacs (i + 1) THEN tac i;
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(*** Tracing tactics ***)
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(*Print the current proof state and pass it on.*)
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fun print_tac msg st =
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 (tracing (msg ^ "\n" ^
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    Pretty.string_of (Pretty.chunks
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      (Goal_Display.pretty_goals_without_context (! Goal_Display.goals_limit) st)));
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  Seq.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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  (tracing "** Press RETURN to continue:";
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   if TextIO.inputLine TextIO.stdIn = SOME "\n" then Seq.single st
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   else (tracing "Goodbye";  Seq.empty));
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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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       SOME "\n" => tac st
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     | SOME "f\n" => Seq.empty
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     | SOME "o\n" => (flag:=false;  tac st)
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     | SOME "s\n" => (suppress_tracing:=true;  tac st)
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     | SOME "x\n" => (tracing "Exiting now";  raise (TRACE_EXIT st))
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     | SOME "quit\n" => raise TRACE_QUIT
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     | _     => (tracing
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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) then
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    (tracing (Pretty.string_of (Pretty.chunks
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        (Goal_Display.pretty_goals_without_context (! Goal_Display.goals_limit) st @
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          [Pretty.str "** 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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     Seq.make (fn()=> seqf st
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                         handle TRACE_EXIT st' => SOME(st', Seq.empty)));
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(*Deterministic DO..UNTIL: only retains the first outcome; tail recursive.
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  Forces repitition until predicate on state is fulfilled.*)
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fun DETERM_UNTIL p tac =
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let val tac = tracify trace_REPEAT tac
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    fun drep st = if p st then SOME (st, Seq.empty)
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                          else (case Seq.pull(tac st) of
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                                  NONE        => NONE
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                                | SOME(st',_) => drep st')
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in  traced_tac drep  end;
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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, Seq.empty)
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        | drep n st =
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           (case Seq.pull(tac st) of
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                NONE       => SOME(st, Seq.empty)
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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 Seq.pull(tac st) of
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            NONE       => SOME(st, Seq.make(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 Seq.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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fun FILTER pred tac st = Seq.filter pred (tac st);
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(*Accept only next states that change the theorem somehow*)
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fun CHANGED tac st =
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  let fun diff st' = not (Thm.eq_thm (st, st'));
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  in Seq.filter diff (tac st) end;
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(*Accept only next states that change the theorem's prop field
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  (changes to signature, hyps, etc. don't count)*)
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fun CHANGED_PROP tac st =
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  let fun diff st' = not (Thm.eq_thm_prop (st, st'));
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  in Seq.filter 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 CSUBGOAL goalfun i st =
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  (case SOME (Thm.cprem_of st i) handle THM _ => NONE of
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    SOME goal => goalfun (goal, i) st
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  | NONE => Seq.empty);
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fun SUBGOAL goalfun =
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  CSUBGOAL (fn (goal, i) => goalfun (Thm.term_of goal, i));
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(*Returns all states that have changed in subgoal i, counted from the LAST
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  subgoal.  For stac, for example.*)
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fun CHANGED_GOAL tac i st =
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    let val np = Thm.nprems_of st
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        val d = np-i                 (*distance from END*)
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        val t = Thm.term_of (Thm.cprem_of st i)
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        fun diff st' =
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            Thm.nprems_of st' - d <= 0   (*the subgoal no longer exists*)
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            orelse
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             not (Pattern.aeconv (t, Thm.term_of (Thm.cprem_of st' (Thm.nprems_of st' - d))))
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    in  Seq.filter diff (tac i st)  end
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    handle Subscript => Seq.empty  (*no subgoal i*);
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fun (tac1 THEN_ALL_NEW tac2) i st =
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  st |> (tac1 i THEN (fn st' => Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st) st'));
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(*repeatedly dig into any emerging subgoals*)
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fun REPEAT_ALL_NEW tac =
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  tac THEN_ALL_NEW (TRY o (fn i => REPEAT_ALL_NEW tac i));
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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 st =  thmfun st handle THM _ => Seq.empty;
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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 (Seq.single o thmfun);
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(*Inverse (more or less) of PRIMITIVE*)
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fun SINGLE tacf = Option.map fst o Seq.pull o tacf
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(*Conversions as tactics*)
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fun CONVERSION cv i st = Seq.single (Conv.gconv_rule cv i st)
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  handle THM _ => Seq.empty
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    | CTERM _ => Seq.empty
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    | TERM _ => Seq.empty
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    | TYPE _ => Seq.empty;
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end;
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open Tactical;