wenzelm@17980: (*  Title:      Pure/goal.ML
wenzelm@17980:     ID:         $Id$
wenzelm@17980:     Author:     Makarius and Lawrence C Paulson
wenzelm@17980: 
wenzelm@18139: Goals in tactical theorem proving.
wenzelm@17980: *)
wenzelm@17980: 
wenzelm@17980: signature BASIC_GOAL =
wenzelm@17980: sig
wenzelm@17980:   val SELECT_GOAL: tactic -> int -> tactic
wenzelm@23414:   val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic
wenzelm@21687:   val CONJUNCTS: tactic -> int -> tactic
wenzelm@17980: end;
wenzelm@17980: 
wenzelm@17980: signature GOAL =
wenzelm@17980: sig
wenzelm@17980:   include BASIC_GOAL
wenzelm@17980:   val init: cterm -> thm
wenzelm@18027:   val protect: thm -> thm
wenzelm@17980:   val conclude: thm -> thm
wenzelm@17980:   val finish: thm -> thm
wenzelm@21604:   val norm_result: thm -> thm
wenzelm@21604:   val close_result: thm -> thm
wenzelm@23356:   val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm
wenzelm@20290:   val prove_multi: Proof.context -> string list -> term list -> term list ->
wenzelm@20290:     ({prems: thm list, context: Proof.context} -> tactic) -> thm list
wenzelm@20290:   val prove: Proof.context -> string list -> term list -> term ->
wenzelm@20290:     ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@20056:   val prove_global: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
wenzelm@19184:   val extract: int -> int -> thm -> thm Seq.seq
wenzelm@19184:   val retrofit: int -> int -> thm -> thm -> thm Seq.seq
wenzelm@23414:   val precise_conjunction_tac: int -> int -> tactic
wenzelm@21687:   val conjunction_tac: int -> tactic
wenzelm@21687:   val asm_rewrite_goal_tac: bool * bool * bool -> (simpset -> tactic) -> simpset -> int -> tactic
wenzelm@21687:   val rewrite_goal_tac: thm list -> int -> tactic
wenzelm@21687:   val norm_hhf_tac: int -> tactic
wenzelm@21687:   val compose_hhf: thm -> int -> thm -> thm Seq.seq
wenzelm@21687:   val compose_hhf_tac: thm -> int -> tactic
wenzelm@21687:   val comp_hhf: thm -> thm -> thm
wenzelm@23237:   val assume_rule_tac: Proof.context -> int -> tactic
wenzelm@17980: end;
wenzelm@17980: 
wenzelm@17980: structure Goal: GOAL =
wenzelm@17980: struct
wenzelm@17980: 
wenzelm@18027: (** goals **)
wenzelm@18027: 
wenzelm@18027: (*
wenzelm@18027:   -------- (init)
wenzelm@18027:   C ==> #C
wenzelm@18027: *)
wenzelm@20290: val init =
wenzelm@22902:   let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))
wenzelm@20290:   in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
wenzelm@17980: 
wenzelm@17980: (*
wenzelm@18119:    C
wenzelm@18119:   --- (protect)
wenzelm@18119:   #C
wenzelm@17980: *)
wenzelm@21579: fun protect th = th COMP_INCR Drule.protectI;
wenzelm@17980: 
wenzelm@17980: (*
wenzelm@18027:   A ==> ... ==> #C
wenzelm@18027:   ---------------- (conclude)
wenzelm@17980:   A ==> ... ==> C
wenzelm@17980: *)
wenzelm@17980: fun conclude th =
wenzelm@18497:   (case SINGLE (Thm.compose_no_flatten false (th, Thm.nprems_of th) 1)
wenzelm@18027:       (Drule.incr_indexes th Drule.protectD) of
wenzelm@17980:     SOME th' => th'
wenzelm@17980:   | NONE => raise THM ("Failed to conclude goal", 0, [th]));
wenzelm@17980: 
wenzelm@17980: (*
wenzelm@18027:   #C
wenzelm@18027:   --- (finish)
wenzelm@18027:    C
wenzelm@17983: *)
wenzelm@17980: fun finish th =
wenzelm@17980:   (case Thm.nprems_of th of
wenzelm@17980:     0 => conclude th
wenzelm@17980:   | n => raise THM ("Proof failed.\n" ^
wenzelm@17980:       Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^
wenzelm@17980:       ("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));
wenzelm@17980: 
wenzelm@17980: 
wenzelm@18027: 
wenzelm@18027: (** results **)
wenzelm@18027: 
wenzelm@21604: (* normal form *)
wenzelm@21604: 
wenzelm@21604: val norm_result =
wenzelm@21604:   Drule.flexflex_unique
wenzelm@21604:   #> MetaSimplifier.norm_hhf_protect
wenzelm@21604:   #> Thm.strip_shyps
wenzelm@21604:   #> Drule.zero_var_indexes;
wenzelm@21604: 
wenzelm@21604: val close_result =
wenzelm@21604:   Thm.compress
wenzelm@21604:   #> Drule.close_derivation;
wenzelm@21604: 
wenzelm@21604: 
wenzelm@18027: 
wenzelm@18027: (** tactical theorem proving **)
wenzelm@18027: 
wenzelm@23356: (* prove_internal -- minimal checks, no normalization of result! *)
wenzelm@20250: 
wenzelm@23356: fun prove_internal casms cprop tac =
wenzelm@20250:   (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
wenzelm@20250:     SOME th => Drule.implies_intr_list casms (finish th)
wenzelm@20250:   | NONE => error "Tactic failed.");
wenzelm@20250: 
wenzelm@20250: 
wenzelm@18119: (* prove_multi *)
wenzelm@17986: 
wenzelm@20056: fun prove_multi ctxt xs asms props tac =
wenzelm@17980:   let
wenzelm@21516:     val thy = ProofContext.theory_of ctxt;
wenzelm@20056:     val string_of_term = Sign.string_of_term thy;
wenzelm@20056: 
wenzelm@20250:     fun err msg = cat_error msg
wenzelm@20250:       ("The error(s) above occurred for the goal statement:\n" ^
wenzelm@20250:         string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)));
wenzelm@17980: 
wenzelm@20250:     fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))
wenzelm@17980:       handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
wenzelm@20250:     val casms = map cert_safe asms;
wenzelm@20250:     val cprops = map cert_safe props;
wenzelm@17980: 
wenzelm@20250:     val (prems, ctxt') = ctxt
wenzelm@20250:       |> Variable.add_fixes_direct xs
wenzelm@20250:       |> fold Variable.declare_internal (asms @ props)
wenzelm@20250:       |> Assumption.add_assumes casms;
wenzelm@17980: 
wenzelm@20250:     val goal = init (Conjunction.mk_conjunction_list cprops);
wenzelm@19774:     val res =
wenzelm@20250:       (case SINGLE (tac {prems = prems, context = ctxt'}) goal of
wenzelm@19774:         NONE => err "Tactic failed."
wenzelm@19774:       | SOME res => res);
wenzelm@20250:     val [results] = Conjunction.elim_precise [length props] (finish res)
wenzelm@20250:       handle THM (msg, _, _) => err msg;
wenzelm@20250:     val _ = Unify.matches_list thy (map Thm.term_of cprops) (map Thm.prop_of results)
wenzelm@20056:       orelse err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res));
wenzelm@17980:   in
wenzelm@20056:     results
wenzelm@20290:     |> map (Assumption.export false ctxt' ctxt)
wenzelm@20056:     |> Variable.export ctxt' ctxt
wenzelm@20250:     |> map Drule.zero_var_indexes
wenzelm@17980:   end;
wenzelm@17980: 
wenzelm@17980: 
wenzelm@18119: (* prove *)
wenzelm@17980: 
wenzelm@20056: fun prove ctxt xs asms prop tac = hd (prove_multi ctxt xs asms [prop] tac);
wenzelm@20056: 
wenzelm@20056: fun prove_global thy xs asms prop tac =
wenzelm@21516:   Drule.standard (prove (ProofContext.init thy) xs asms prop (fn {prems, ...} => tac prems));
wenzelm@18027: 
wenzelm@18027: 
wenzelm@17980: 
wenzelm@21687: (** goal structure **)
wenzelm@21687: 
wenzelm@21687: (* nested goals *)
wenzelm@18207: 
wenzelm@19184: fun extract i n st =
wenzelm@19184:   (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
wenzelm@19184:    else if n = 1 then Seq.single (Thm.cprem_of st i)
wenzelm@19423:    else Seq.single (foldr1 Conjunction.mk_conjunction (map (Thm.cprem_of st) (i upto i + n - 1))))
wenzelm@20260:   |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
wenzelm@17980: 
wenzelm@19221: fun retrofit i n st' st =
wenzelm@19221:   (if n = 1 then st
wenzelm@19423:    else st |> Drule.rotate_prems (i - 1) |> Conjunction.uncurry n |> Drule.rotate_prems (1 - i))
wenzelm@19221:   |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
wenzelm@18207: 
wenzelm@17980: fun SELECT_GOAL tac i st =
wenzelm@19191:   if Thm.nprems_of st = 1 andalso i = 1 then tac st
wenzelm@19184:   else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
wenzelm@17980: 
wenzelm@21687: 
wenzelm@21687: (* multiple goals *)
wenzelm@21687: 
wenzelm@23414: local
wenzelm@21687: 
wenzelm@23414: fun conj_intrs n =
wenzelm@23414:   let
wenzelm@23414:     val cert = Thm.cterm_of ProtoPure.thy;
wenzelm@23414:     val names = Name.invents Name.context "A" n;
wenzelm@23414:     val As = map (fn name => cert (Free (name, propT))) names;
wenzelm@23414:   in
wenzelm@23414:     Thm.generalize ([], names) 0
wenzelm@23414:       (Drule.implies_intr_list As (Conjunction.intr_list (map Thm.assume As)))
wenzelm@23414:   end;
wenzelm@23414: 
wenzelm@23414: fun count_conjs A =
wenzelm@23414:   (case try Logic.dest_conjunction A of
wenzelm@23414:     NONE => 1
wenzelm@23414:   | SOME (_, B) => count_conjs B + 1);
wenzelm@23414: 
wenzelm@23414: in
wenzelm@21687: 
wenzelm@21687: val precise_conjunction_tac =
wenzelm@21687:   let
wenzelm@21687:     fun tac 0 i = eq_assume_tac i
wenzelm@21687:       | tac 1 i = SUBGOAL (K all_tac) i
wenzelm@23414:       | tac 2 i = rtac Conjunction.conjunctionI i
wenzelm@23414:       | tac n i = rtac (conj_intrs n) i;
wenzelm@21687:   in TRY oo tac end;
wenzelm@21687: 
wenzelm@23414: val conjunction_tac = TRY o REPEAT_ALL_NEW (SUBGOAL (fn (goal, i) =>
wenzelm@23414:   let val n = count_conjs goal
wenzelm@23414:   in if n < 2 then no_tac else precise_conjunction_tac n i end));
wenzelm@23414: 
wenzelm@23414: fun PRECISE_CONJUNCTS n tac =
wenzelm@23414:   SELECT_GOAL (precise_conjunction_tac n 1
wenzelm@23414:     THEN tac
wenzelm@23414:     THEN PRIMITIVE (Conjunction.uncurry ~1));
wenzelm@23414: 
wenzelm@21687: fun CONJUNCTS tac =
wenzelm@21687:   SELECT_GOAL (conjunction_tac 1
wenzelm@21687:     THEN tac
wenzelm@21687:     THEN PRIMITIVE (Conjunction.uncurry ~1));
wenzelm@21687: 
wenzelm@23414: end;
wenzelm@21687: 
wenzelm@21687: 
wenzelm@21687: (* rewriting *)
wenzelm@21687: 
wenzelm@21687: (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
wenzelm@21687: fun asm_rewrite_goal_tac mode prover_tac ss =
wenzelm@21687:   SELECT_GOAL
wenzelm@21687:     (PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
wenzelm@21687: 
wenzelm@21687: fun rewrite_goal_tac rews =
wenzelm@21687:   let val ss = MetaSimplifier.empty_ss addsimps rews in
wenzelm@21687:     fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac)
wenzelm@21687:       (MetaSimplifier.theory_context (Thm.theory_of_thm st) ss) i st
wenzelm@21687:   end;
wenzelm@21687: 
wenzelm@21687: 
wenzelm@21687: (* hhf normal form *)
wenzelm@21687: 
wenzelm@21687: val norm_hhf_tac =
wenzelm@21687:   rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
wenzelm@21687:   THEN' SUBGOAL (fn (t, i) =>
wenzelm@21687:     if Drule.is_norm_hhf t then all_tac
wenzelm@21687:     else rewrite_goal_tac [Drule.norm_hhf_eq] i);
wenzelm@21687: 
wenzelm@21687: fun compose_hhf tha i thb =
wenzelm@21687:   Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of thb i) tha, 0) i thb;
wenzelm@21687: 
wenzelm@21687: fun compose_hhf_tac th i = PRIMSEQ (compose_hhf th i);
wenzelm@21687: 
wenzelm@21687: fun comp_hhf tha thb =
wenzelm@21687:   (case Seq.chop 2 (compose_hhf tha 1 thb) of
wenzelm@21687:     ([th], _) => th
wenzelm@21687:   | ([], _) => raise THM ("comp_hhf: no unifiers", 1, [tha, thb])
wenzelm@21687:   | _  => raise THM ("comp_hhf: multiple unifiers", 1, [tha, thb]));
wenzelm@21687: 
wenzelm@23237: 
wenzelm@23237: (* non-atomic goal assumptions *)
wenzelm@23237: 
wenzelm@23356: fun non_atomic (Const ("==>", _) $ _ $ _) = true
wenzelm@23356:   | non_atomic (Const ("all", _) $ _) = true
wenzelm@23356:   | non_atomic _ = false;
wenzelm@23356: 
wenzelm@23237: fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>
wenzelm@23237:   let
wenzelm@23237:     val ((_, goal'), ctxt') = Variable.focus goal ctxt;
wenzelm@23237:     val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';
wenzelm@23356:     val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');
wenzelm@23237:     val tacs = Rs |> map (fn R =>
wenzelm@23237:       Tactic.etac (MetaSimplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);
wenzelm@23237:   in fold_rev (curry op APPEND') tacs (K no_tac) i end);
wenzelm@23237: 
wenzelm@18207: end;
wenzelm@18207: 
wenzelm@17980: structure BasicGoal: BASIC_GOAL = Goal;
wenzelm@17980: open BasicGoal;