src/Pure/goal.ML
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(*  Title:      Pure/goal.ML
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    ID:         $Id$
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    Author:     Makarius and Lawrence C Paulson
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Goals in tactical theorem proving.
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*)
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signature BASIC_GOAL =
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sig
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  val SELECT_GOAL: tactic -> int -> tactic
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end;
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signature GOAL =
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sig
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  include BASIC_GOAL
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  val init: cterm -> thm
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  val protect: thm -> thm
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  val conclude: thm -> thm
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  val finish: thm -> thm
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  val norm_hhf: thm -> thm
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  val norm_hhf_protect: thm -> thm
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  val compose_hhf: thm -> int -> thm -> thm Seq.seq
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  val compose_hhf_tac: thm -> int -> tactic
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  val comp_hhf: thm -> thm -> thm
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  val prove_multi: theory -> string list -> term list -> term list ->
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    (thm list -> tactic) -> thm list
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  val prove: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
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  val prove_raw: cterm list -> cterm -> (thm list -> tactic) -> thm
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end;
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structure Goal: GOAL =
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struct
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(** goals **)
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(*
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  -------- (init)
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  C ==> #C
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*)
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fun init ct = Drule.instantiate' [] [SOME ct] Drule.protectI;
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(*
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   C
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  --- (protect)
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  #C
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*)
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fun protect th = th COMP Drule.incr_indexes th Drule.protectI;
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(*
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  A ==> ... ==> #C
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  ---------------- (conclude)
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  A ==> ... ==> C
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*)
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fun conclude th =
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  (case SINGLE (Thm.bicompose false (false, th, Thm.nprems_of th) 1)
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      (Drule.incr_indexes th Drule.protectD) of
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    SOME th' => th'
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  | NONE => raise THM ("Failed to conclude goal", 0, [th]));
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(*
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  #C
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  --- (finish)
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   C
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*)
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fun finish th =
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  (case Thm.nprems_of th of
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    0 => conclude th
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  | n => raise THM ("Proof failed.\n" ^
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      Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^
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      ("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));
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(** results **)
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(* HHF normal form: !! before ==>, outermost !! generalized *)
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local
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fun gen_norm_hhf ss =
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  (not o Drule.is_norm_hhf o Thm.prop_of) ?
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    Drule.fconv_rule (MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE)) ss)
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  #> Thm.adjust_maxidx_thm
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  #> Drule.gen_all;
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val ss =
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  MetaSimplifier.theory_context ProtoPure.thy MetaSimplifier.empty_ss
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    addsimps [Drule.norm_hhf_eq];
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in
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val norm_hhf = gen_norm_hhf ss;
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val norm_hhf_protect = gen_norm_hhf (ss addeqcongs [Drule.protect_cong]);
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end;
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(* composition of normal results *)
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fun compose_hhf tha i thb =
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  Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of thb i) tha, 0) i thb;
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fun compose_hhf_tac th i = PRIMSEQ (compose_hhf th i);
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fun comp_hhf tha thb =
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  (case Seq.chop (2, compose_hhf tha 1 thb) of
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    ([th], _) => th
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  | ([], _) => raise THM ("comp_hhf: no unifiers", 1, [tha, thb])
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  | _  => raise THM ("comp_hhf: multiple unifiers", 1, [tha, thb]));
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0450847646c3 prove_raw: cterms, explicit asms;
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(** tactical theorem proving **)
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(* prove_multi *)
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fun prove_multi thy xs asms props tac =
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  let
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    val prop = Logic.mk_conjunction_list props;
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    val statement = Logic.list_implies (asms, prop);
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    val frees = Term.add_frees statement [];
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    val fixed_frees = filter_out (member (op =) xs o #1) frees;
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    val fixed_tfrees = fold (Term.add_tfreesT o #2) fixed_frees [];
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    val params = List.mapPartial (fn x => Option.map (pair x) (AList.lookup (op =) frees x)) xs;
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    fun err msg = raise ERROR_MESSAGE
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      (msg ^ "\nThe error(s) above occurred for the goal statement:\n" ^
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        Sign.string_of_term thy (Term.list_all_free (params, statement)));
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    fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm t)
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      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
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    val _ = cert_safe statement;
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    val _ = Term.no_dummy_patterns statement handle TERM (msg, _) => err msg;
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    val cparams = map (cert_safe o Free) params;
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    val casms = map cert_safe asms;
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    val prems = map (norm_hhf o Thm.assume) casms;
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    val goal = init (cert_safe prop);
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    val goal' = case SINGLE (tac prems) goal of SOME goal' => goal' | _ => err "Tactic failed.";
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    val raw_result = finish goal' handle THM (msg, _, _) => err msg;
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    val prop' = Thm.prop_of raw_result;
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    val _ = conditional (not (Pattern.matches thy (Envir.beta_norm prop, prop'))) (fn () =>
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      err ("Proved a different theorem: " ^ Sign.string_of_term thy prop'));
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  in
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    Drule.conj_elim_precise (length props) raw_result
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    |> map
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      (Drule.implies_intr_list casms
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        #> Drule.forall_intr_list cparams
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        #> norm_hhf
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        #> Thm.varifyT' fixed_tfrees
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        #-> K Drule.zero_var_indexes)
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  end;
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(* prove *)
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fun prove thy xs asms prop tac = hd (prove_multi thy xs asms [prop] tac);
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(* prove_raw -- no checks, no normalization of result! *)
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fun prove_raw casms cprop tac =
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  (case SINGLE (tac (map (norm_hhf o Thm.assume) casms)) (init cprop) of
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    SOME th => Drule.implies_intr_list casms (finish th)
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  | NONE => raise ERROR_MESSAGE "Tactic failed.");
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(* SELECT_GOAL *)
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(*Tactical for restricting the effect of a tactic to subgoal i.  Works
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  by making a new state from subgoal i, applying tac to it, and
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  composing the resulting thm with the original state.*)
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local
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fun SELECT tac i st =
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  init (Thm.adjust_maxidx (Thm.cprem_of st i))
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  |> tac
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  |> Seq.maps (fn st' => Thm.bicompose false (false, conclude st', Thm.nprems_of st') i st);
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in
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fun SELECT_GOAL tac i st =
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  let val n = Thm.nprems_of st in
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    if 1 <= i andalso i <= n then
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      if n = 1 then tac st else SELECT tac i st
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    else Seq.empty
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  end;
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end;
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end;
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structure BasicGoal: BASIC_GOAL = Goal;
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open BasicGoal;