(*  Title:      Pure/tactical.ML

    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

Tacticals.

*)

infix 1 THEN THEN' THEN_ALL_NEW;

infix 0 ORELSE APPEND INTLEAVE ORELSE' APPEND' INTLEAVE';

infix 0 THEN_ELSE;

signature TACTICAL =

sig

  type tactic = thm -> thm Seq.seq

  val THEN: tactic * tactic -> tactic

  val ORELSE: tactic * tactic -> tactic

  val APPEND: tactic * tactic -> tactic

  val INTLEAVE: tactic * tactic -> tactic

  val THEN_ELSE: tactic * (tactic*tactic) -> tactic

  val THEN': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic

  val ORELSE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic

  val APPEND': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic

  val INTLEAVE': ('a -> tactic) * ('a -> tactic) -> 'a -> tactic

  val all_tac: tactic

  val no_tac: tactic

  val DETERM: tactic -> tactic

  val COND: (thm -> bool) -> tactic -> tactic -> tactic

  val TRY: tactic -> tactic

  val EVERY: tactic list -> tactic

  val EVERY': ('a -> tactic) list -> 'a -> tactic

  val EVERY1: (int -> tactic) list -> tactic

  val FIRST: tactic list -> tactic

  val FIRST': ('a -> tactic) list -> 'a -> tactic

  val FIRST1: (int -> tactic) list -> tactic

  val RANGE: (int -> tactic) list -> int -> tactic

  val print_tac: string -> tactic

  val pause_tac: tactic

  val trace_REPEAT: bool Unsynchronized.ref

  val suppress_tracing: bool Unsynchronized.ref

  val tracify: bool Unsynchronized.ref -> tactic -> tactic

  val traced_tac: (thm -> (thm * thm Seq.seq) option) -> tactic

  val DETERM_UNTIL: (thm -> bool) -> tactic -> tactic

  val REPEAT_DETERM_N: int -> tactic -> tactic

  val REPEAT_DETERM: tactic -> tactic

  val REPEAT: tactic -> tactic

  val REPEAT_DETERM1: tactic -> tactic

  val REPEAT1: tactic -> tactic

  val FILTER: (thm -> bool) -> tactic -> tactic

  val CHANGED: tactic -> tactic

  val CHANGED_PROP: tactic -> tactic

  val ALLGOALS: (int -> tactic) -> tactic

  val SOMEGOAL: (int -> tactic) -> tactic

  val FIRSTGOAL: (int -> tactic) -> tactic

  val REPEAT_SOME: (int -> tactic) -> tactic

  val REPEAT_DETERM_SOME: (int -> tactic) -> tactic

  val REPEAT_FIRST: (int -> tactic) -> tactic

  val REPEAT_DETERM_FIRST: (int -> tactic) -> tactic

  val TRYALL: (int -> tactic) -> tactic

  val CSUBGOAL: ((cterm * int) -> tactic) -> int -> tactic

  val SUBGOAL: ((term * int) -> tactic) -> int -> tactic

  val CHANGED_GOAL: (int -> tactic) -> int -> tactic

  val SOLVED': (int -> tactic) -> int -> tactic

  val THEN_ALL_NEW: (int -> tactic) * (int -> tactic) -> int -> tactic

  val REPEAT_ALL_NEW: (int -> tactic) -> int -> tactic

  val PRIMSEQ: (thm -> thm Seq.seq) -> tactic

  val PRIMITIVE: (thm -> thm) -> tactic

  val SINGLE: tactic -> thm -> thm option

  val CONVERSION: conv -> int -> tactic

end;

structure Tactical : TACTICAL =

struct

(**** 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.*)

type tactic = thm -> thm Seq.seq;

(*** LCF-style tacticals ***)

(*the tactical THEN performs one tactic followed by another*)

fun (tac1 THEN tac2) st = Seq.maps tac2 (tac1 st);

(*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 (tac1 ORELSE tac2) st =

    case Seq.pull(tac1 st) of

        NONE       => tac2 st

      | sequencecell => Seq.make(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 (tac1 APPEND tac2) st =

  Seq.append (tac1 st) (Seq.make(fn()=> Seq.pull (tac2 st)));

(*Like APPEND, but interleaves results of tac1 and tac2.*)

fun (tac1 INTLEAVE tac2) st =

    Seq.interleave(tac1 st,

                        Seq.make(fn()=> Seq.pull (tac2 st)));

(*Conditional tactic.

        tac1 ORELSE tac2 = tac1 THEN_ELSE (all_tac, tac2)

        tac1 THEN tac2   = tac1 THEN_ELSE (tac2, no_tac)

*)

fun (tac THEN_ELSE (tac1, tac2)) st =

    case Seq.pull(tac st) of

        NONE    => tac2 st                                   (*failed; try tactic 2*)

      | seqcell => Seq.maps tac1 (Seq.make(fn()=> seqcell)); (*succeeded; use tactic 1*)

(*Versions for combining tactic-valued functions, as in

     SOMEGOAL (resolve_tac rls THEN' assume_tac) *)

fun (tac1 THEN' tac2) x = tac1 x THEN tac2 x;

fun (tac1 ORELSE' tac2) x = tac1 x ORELSE tac2 x;

fun (tac1 APPEND' tac2) x = tac1 x APPEND tac2 x;

fun (tac1 INTLEAVE' tac2) x = tac1 x INTLEAVE tac2 x;

(*passes all proofs through unchanged;  identity of THEN*)

fun all_tac st = Seq.single st;

(*passes no proofs through;  identity of ORELSE and APPEND*)

fun no_tac st  = Seq.empty;

(*Make a tactic deterministic by chopping the tail of the proof sequence*)

fun DETERM tac = Seq.DETERM tac;

(*Conditional tactical: testfun controls which tactic to use next.

  Beware: due to eager evaluation, both thentac and elsetac are evaluated.*)

fun COND testfun thenf elsef = (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 ***)

local

  (*This version of EVERY avoids backtracking over repeated states*)

  fun EVY (trail, []) st =

        Seq.make (fn()=> SOME(st,

                        Seq.make (fn()=> Seq.pull (evyBack trail))))

    | EVY (trail, tac::tacs) st =

          case Seq.pull(tac st) of

              NONE    => evyBack trail              (*failed: backtrack*)

            | SOME(st',q) => EVY ((st',q,tacs)::trail, tacs) st'

  and evyBack [] = Seq.empty (*no alternatives*)

    | evyBack ((st',q,tacs)::trail) =

          case Seq.pull q of

              NONE        => evyBack trail

            | SOME(st,q') => if Thm.eq_thm (st',st)

                             then evyBack ((st',q',tacs)::trail)

                             else EVY ((st,q',tacs)::trail, tacs) st

in

(* EVERY [tac1,...,tacn]   equals    tac1 THEN ... THEN tacn   *)

fun EVERY tacs = EVY ([], tacs);

end;

(* EVERY' [tac1,...,tacn] i  equals    tac1 i THEN ... THEN tacn i   *)

fun EVERY' tacs i = EVERY (map (fn f => f i) tacs);

(*Apply every tactic to 1*)

fun EVERY1 tacs = EVERY' tacs 1;

(* FIRST [tac1,...,tacn]   equals    tac1 ORELSE ... ORELSE tacn   *)

fun FIRST tacs = fold_rev (curry op ORELSE) tacs no_tac;

(* FIRST' [tac1,...,tacn] i  equals    tac1 i ORELSE ... ORELSE tacn i   *)

fun FIRST' tacs = fold_rev (curry op ORELSE') tacs (K no_tac);

(*Apply first tactic to 1*)

fun FIRST1 tacs = FIRST' tacs 1;

(*Apply tactics on consecutive subgoals*)

fun RANGE [] _ = all_tac

  | RANGE (tac :: tacs) i = RANGE tacs (i + 1) THEN tac i;

(*** Tracing tactics ***)

(*Print the current proof state and pass it on.*)

fun print_tac msg st =

 (tracing (msg ^ "\n" ^

    Pretty.string_of (Pretty.chunks (Goal_Display.pretty_goals_without_context st)));

  Seq.single st);

(*Pause until a line is typed -- if non-empty then fail. *)

fun pause_tac st =

  (tracing "** Press RETURN to continue:";

   if TextIO.inputLine TextIO.stdIn = SOME "\n" then Seq.single st

   else (tracing "Goodbye";  Seq.empty));

exception TRACE_EXIT of thm

and TRACE_QUIT;

(*Tracing flags*)

val trace_REPEAT= Unsynchronized.ref false

and suppress_tracing = Unsynchronized.ref false;

(*Handle all tracing commands for current state and tactic *)

fun exec_trace_command flag (tac, st) =

   case TextIO.inputLine TextIO.stdIn of

       SOME "\n" => tac st

     | SOME "f\n" => Seq.empty

     | SOME "o\n" => (flag := false;  tac st)

     | SOME "s\n" => (suppress_tracing := true;  tac st)

     | SOME "x\n" => (tracing "Exiting now";  raise (TRACE_EXIT st))

     | SOME "quit\n" => raise TRACE_QUIT

     | _     => (tracing

"Type RETURN to continue or...\n\

\     f    - to fail here\n\

\     o    - to switch tracing off\n\

\     s    - to suppress tracing until next entry to a tactical\n\

\     x    - to exit at this point\n\

\     quit - to abort this tracing run\n\

\** Well? "     ;  exec_trace_command flag (tac, st));

(*Extract from a tactic, a thm->thm seq function that handles tracing*)

fun tracify flag tac st =

  if !flag andalso not (!suppress_tracing) then

    (tracing (Pretty.string_of (Pretty.chunks

        (Goal_Display.pretty_goals_without_context st @

          [Pretty.str "** Press RETURN to continue:"])));

     exec_trace_command flag (tac, st))

  else tac st;

(*Create a tactic whose outcome is given by seqf, handling TRACE_EXIT*)

fun traced_tac seqf st =

    (suppress_tracing := false;

     Seq.make (fn()=> seqf st

                         handle TRACE_EXIT st' => SOME(st', Seq.empty)));

(*Deterministic DO..UNTIL: only retains the first outcome; tail recursive.

  Forces repitition until predicate on state is fulfilled.*)

fun DETERM_UNTIL p tac =

let val tac = tracify trace_REPEAT tac

    fun drep st = if p st then SOME (st, Seq.empty)

                          else (case Seq.pull(tac st) of

                                  NONE        => NONE

                                | SOME(st',_) => drep st')

in  traced_tac drep  end;

(*Deterministic REPEAT: only retains the first outcome;

  uses less space than REPEAT; tail recursive.

  If non-negative, n bounds the number of repetitions.*)

fun REPEAT_DETERM_N n tac =

  let val tac = tracify trace_REPEAT tac

      fun drep 0 st = SOME(st, Seq.empty)

        | drep n st =

           (case Seq.pull(tac st) of

                NONE       => SOME(st, Seq.empty)

              | SOME(st',_) => drep (n-1) st')

  in  traced_tac (drep n)  end;

(*Allows any number of repetitions*)

val REPEAT_DETERM = REPEAT_DETERM_N ~1;

(*General REPEAT: maintains a stack of alternatives; tail recursive*)

fun REPEAT tac =

  let val tac = tracify trace_REPEAT tac

      fun rep qs st =

        case Seq.pull(tac st) of

            NONE       => SOME(st, Seq.make(fn()=> repq qs))

          | SOME(st',q) => rep (q::qs) st'

      and repq [] = NONE

        | repq(q::qs) = case Seq.pull q of

            NONE       => repq qs

          | SOME(st,q) => rep (q::qs) st

  in  traced_tac (rep [])  end;

(*Repeat 1 or more times*)

fun REPEAT_DETERM1 tac = DETERM tac THEN REPEAT_DETERM tac;

fun REPEAT1 tac = tac THEN REPEAT tac;

(** Filtering tacticals **)

fun FILTER pred tac st = Seq.filter pred (tac st);

(*Accept only next states that change the theorem somehow*)

fun CHANGED tac st =

  let fun diff st' = not (Thm.eq_thm (st, st'));

  in Seq.filter diff (tac st) end;

(*Accept only next states that change the theorem's prop field

  (changes to signature, hyps, etc. don't count)*)

fun CHANGED_PROP tac st =

  let fun diff st' = not (Thm.eq_thm_prop (st, st'));

  in Seq.filter diff (tac st) end;

(*** Tacticals based on subgoal numbering ***)

(*For n subgoals, performs tac(n) THEN ... THEN tac(1)

  Essential to work backwards since tac(i) may add/delete subgoals at i. *)

fun ALLGOALS tac st =

  let fun doall 0 = all_tac

        | doall n = tac(n) THEN doall(n-1)

  in  doall(nprems_of st)st  end;

(*For n subgoals, performs tac(n) ORELSE ... ORELSE tac(1)  *)

fun SOMEGOAL tac st =

  let fun find 0 = no_tac

        | find n = tac(n) ORELSE find(n-1)

  in  find(nprems_of st)st  end;

(*For n subgoals, performs tac(1) ORELSE ... ORELSE tac(n).

  More appropriate than SOMEGOAL in some cases.*)

fun FIRSTGOAL tac st =

  let fun find (i,n) = if i>n then no_tac else  tac(i) ORELSE find (i+1,n)

  in  find(1, nprems_of st)st  end;

(*Repeatedly solve some using tac. *)

fun REPEAT_SOME tac = REPEAT1 (SOMEGOAL (REPEAT1 o tac));

fun REPEAT_DETERM_SOME tac = REPEAT_DETERM1 (SOMEGOAL (REPEAT_DETERM1 o tac));

(*Repeatedly solve the first possible subgoal using tac. *)

fun REPEAT_FIRST tac = REPEAT1 (FIRSTGOAL (REPEAT1 o tac));

fun REPEAT_DETERM_FIRST tac = REPEAT_DETERM1 (FIRSTGOAL (REPEAT_DETERM1 o tac));

(*For n subgoals, tries to apply tac to n,...1  *)

fun TRYALL tac = ALLGOALS (TRY o tac);

(*Make a tactic for subgoal i, if there is one.  *)

fun CSUBGOAL goalfun i st =

  (case SOME (Thm.cprem_of st i) handle THM _ => NONE of

    SOME goal => goalfun (goal, i) st

  | NONE => Seq.empty);

fun SUBGOAL goalfun =

  CSUBGOAL (fn (goal, i) => goalfun (Thm.term_of goal, i));

(*Returns all states that have changed in subgoal i, counted from the LAST

  subgoal.  For stac, for example.*)

fun CHANGED_GOAL tac i st =

    let val np = Thm.nprems_of st

        val d = np-i                 (*distance from END*)

        val t = Thm.term_of (Thm.cprem_of st i)

        fun diff st' =

            Thm.nprems_of st' - d <= 0   (*the subgoal no longer exists*)

            orelse

             not (Pattern.aeconv (t, Thm.term_of (Thm.cprem_of st' (Thm.nprems_of st' - d))))

    in  Seq.filter diff (tac i st)  end

    handle General.Subscript => Seq.empty  (*no subgoal i*);

(*Returns all states where some subgoals have been solved.  For

  subgoal-based tactics this means subgoal i has been solved

  altogether -- no new subgoals have emerged.*)

fun SOLVED' tac i st =

  tac i st |> Seq.filter (fn st' => nprems_of st' < nprems_of st);

(*Apply second tactic to all subgoals emerging from the first --

  following usual convention for subgoal-based tactics.*)

fun (tac1 THEN_ALL_NEW tac2) i st =

  st |> (tac1 i THEN (fn st' => Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st) st'));

(*Repeatedly dig into any emerging subgoals.*)

fun REPEAT_ALL_NEW tac =

  tac THEN_ALL_NEW (TRY o (fn i => REPEAT_ALL_NEW tac i));

(*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)

fun PRIMSEQ thmfun st =  thmfun st handle THM _ => Seq.empty;

(*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)

fun PRIMITIVE thmfun = PRIMSEQ (Seq.single o thmfun);

(*Inverse (more or less) of PRIMITIVE*)

fun SINGLE tacf = Option.map fst o Seq.pull o tacf

(*Conversions as tactics*)

fun CONVERSION cv i st = Seq.single (Conv.gconv_rule cv i st)

  handle THM _ => Seq.empty

    | CTERM _ => Seq.empty

    | TERM _ => Seq.empty

    | TYPE _ => Seq.empty;

end;

open Tactical;