(*  Title:      Pure/goal.ML

     ID:         $Id$

     Author:     Makarius and Lawrence C Paulson

 Goals in tactical theorem proving.

 *)

 signature BASIC_GOAL =

 sig

   val SELECT_GOAL: tactic -> int -> tactic

   val CONJUNCTS: tactic -> int -> tactic

   val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic

 end;

 signature GOAL =

 sig

   include BASIC_GOAL

   val init: cterm -> thm

   val protect: thm -> thm

   val conclude: thm -> thm

   val finish: thm -> thm

   val norm_result: thm -> thm

   val close_result: thm -> thm

   val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm

   val prove_multi: Proof.context -> string list -> term list -> term list ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm list

   val prove: Proof.context -> string list -> term list -> term ->

     ({prems: thm list, context: Proof.context} -> tactic) -> thm

   val prove_global: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm

   val extract: int -> int -> thm -> thm Seq.seq

   val retrofit: int -> int -> thm -> thm -> thm Seq.seq

   val conjunction_tac: int -> tactic

   val precise_conjunction_tac: int -> int -> tactic

   val recover_conjunction_tac: tactic

   val asm_rewrite_goal_tac: bool * bool * bool -> (simpset -> tactic) -> simpset -> int -> tactic

   val rewrite_goal_tac: thm list -> int -> tactic

   val norm_hhf_tac: int -> tactic

   val compose_hhf: thm -> int -> thm -> thm Seq.seq

   val compose_hhf_tac: thm -> int -> tactic

   val comp_hhf: thm -> thm -> thm

   val assume_rule_tac: Proof.context -> int -> tactic

 end;

 structure Goal: GOAL =

 struct

 (** goals **)

 (*

   -------- (init)

   C ==> #C

 *)

 val init =

   let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))

   in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;

 (*

    C

   --- (protect)

   #C

 *)

 fun protect th = th COMP_INCR Drule.protectI;

 (*

   A ==> ... ==> #C

   ---------------- (conclude)

   A ==> ... ==> C

 *)

 fun conclude th =

   (case SINGLE (Thm.compose_no_flatten false (th, Thm.nprems_of th) 1)

       (Drule.incr_indexes th Drule.protectD) of

     SOME th' => th'

   | NONE => raise THM ("Failed to conclude goal", 0, [th]));

 (*

   #C

   --- (finish)

    C

 *)

 fun finish th =

   (case Thm.nprems_of th of

     0 => conclude th

   | n => raise THM ("Proof failed.\n" ^

       Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^

       ("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));

 (** results **)

 (* normal form *)

 val norm_result =

   Drule.flexflex_unique

   #> MetaSimplifier.norm_hhf_protect

   #> Thm.strip_shyps

   #> Drule.zero_var_indexes;

 val close_result =

   Thm.compress

   #> Drule.close_derivation;

 (** tactical theorem proving **)

 (* prove_internal -- minimal checks, no normalization of result! *)

 fun prove_internal casms cprop tac =

   (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of

     SOME th => Drule.implies_intr_list casms (finish th)

   | NONE => error "Tactic failed.");

 (* prove_multi *)

 fun prove_multi ctxt xs asms props tac =

   let

     val thy = ProofContext.theory_of ctxt;

     val string_of_term = Sign.string_of_term thy;

     fun err msg = cat_error msg

       ("The error(s) above occurred for the goal statement:\n" ^

         string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)));

     fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))

       handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;

     val casms = map cert_safe asms;

     val cprops = map cert_safe props;

     val (prems, ctxt') = ctxt

       |> Variable.add_fixes_direct xs

       |> fold Variable.declare_internal (asms @ props)

       |> Assumption.add_assumes casms;

     val goal = init (Conjunction.mk_conjunction_balanced cprops);

     val res =

       (case SINGLE (tac {prems = prems, context = ctxt'}) goal of

         NONE => err "Tactic failed."

       | SOME res => res);

     val results = Conjunction.elim_balanced (length props) (finish res)

       handle THM (msg, _, _) => err msg;

     val _ = Unify.matches_list thy (map Thm.term_of cprops) (map Thm.prop_of results)

       orelse err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res));

   in

     results

     |> map (Assumption.export false ctxt' ctxt)

     |> Variable.export ctxt' ctxt

     |> map Drule.zero_var_indexes

   end;

 (* prove *)

 fun prove ctxt xs asms prop tac = hd (prove_multi ctxt xs asms [prop] tac);

 fun prove_global thy xs asms prop tac =

   Drule.standard (prove (ProofContext.init thy) xs asms prop (fn {prems, ...} => tac prems));

 (** goal structure **)

 (* nested goals *)

 fun extract i n st =

   (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty

    else if n = 1 then Seq.single (Thm.cprem_of st i)

    else

      Seq.single (Conjunction.mk_conjunction_balanced (map (Thm.cprem_of st) (i upto i + n - 1))))

   |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);

 fun retrofit i n st' st =

   (if n = 1 then st

    else st |> Drule.with_subgoal i (Conjunction.uncurry_balanced n))

   |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;

 fun SELECT_GOAL tac i st =

   if Thm.nprems_of st = 1 andalso i = 1 then tac st

   else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;

 (* multiple goals *)

 fun precise_conjunction_tac 0 i = eq_assume_tac i

   | precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i

   | precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));

 val adhoc_conjunction_tac = REPEAT_ALL_NEW

   (SUBGOAL (fn (goal, i) =>

     if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i

     else no_tac));

 val conjunction_tac = SUBGOAL (fn (goal, i) =>

   precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE

   TRY (adhoc_conjunction_tac i));

 val recover_conjunction_tac = PRIMITIVE (fn th =>

   Conjunction.uncurry_balanced (Thm.nprems_of th) th);

 fun PRECISE_CONJUNCTS n tac =

   SELECT_GOAL (precise_conjunction_tac n 1

     THEN tac

     THEN recover_conjunction_tac);

 fun CONJUNCTS tac =

   SELECT_GOAL (conjunction_tac 1

     THEN tac

     THEN recover_conjunction_tac);

 (* rewriting *)

 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)

 fun asm_rewrite_goal_tac mode prover_tac ss =

   SELECT_GOAL

     (PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));

 fun rewrite_goal_tac rews =

   let val ss = MetaSimplifier.empty_ss addsimps rews in

     fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac)

       (MetaSimplifier.theory_context (Thm.theory_of_thm st) ss) i st

   end;

 (* hhf normal form *)

 val norm_hhf_tac =

   rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)

   THEN' SUBGOAL (fn (t, i) =>

     if Drule.is_norm_hhf t then all_tac

     else rewrite_goal_tac [Drule.norm_hhf_eq] i);

 fun compose_hhf tha i thb =

   Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of thb i) tha, 0) i thb;

 fun compose_hhf_tac th i = PRIMSEQ (compose_hhf th i);

 fun comp_hhf tha thb =

   (case Seq.chop 2 (compose_hhf tha 1 thb) of

     ([th], _) => th

   | ([], _) => raise THM ("comp_hhf: no unifiers", 1, [tha, thb])

   | _  => raise THM ("comp_hhf: multiple unifiers", 1, [tha, thb]));

 (* non-atomic goal assumptions *)

 fun non_atomic (Const ("==>", _) $ _ $ _) = true

   | non_atomic (Const ("all", _) $ _) = true

   | non_atomic _ = false;

 fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>

   let

     val ((_, goal'), ctxt') = Variable.focus goal ctxt;

     val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';

     val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');

     val tacs = Rs |> map (fn R =>

       Tactic.etac (MetaSimplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);

   in fold_rev (curry op APPEND') tacs (K no_tac) i end);

 end;

 structure BasicGoal: BASIC_GOAL = Goal;

 open BasicGoal;