src/Pure/Isar/obtain.ML
author haftmann
Sat, 20 Aug 2011 01:21:22 +0200
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merged
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(*  Title:      Pure/Isar/obtain.ML
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    Author:     Markus Wenzel, TU Muenchen
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The 'obtain' and 'guess' language elements -- generalized existence at
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the level of proof texts: 'obtain' involves a proof that certain
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fixes/assumes may be introduced into the present context; 'guess' is
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similar, but derives these elements from the course of reasoning!
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  <chain_facts>
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  obtain x where "A x" <proof> ==
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  have "!!thesis. (!!x. A x ==> thesis) ==> thesis"
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  proof succeed
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    fix thesis
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    assume that [intro?]: "!!x. A x ==> thesis"
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    <chain_facts>
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    show thesis
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      apply (insert that)
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      <proof>
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  qed
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  fix x assm <<obtain_export>> "A x"
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  <chain_facts>
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  guess x <proof body> <proof end> ==
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  {
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    fix thesis
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    <chain_facts> have "PROP ?guess"
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      apply magic      -- {* turns goal into "thesis ==> #thesis" *}
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      <proof body>
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      apply_end magic  -- {* turns final "(!!x. P x ==> thesis) ==> #thesis" into
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        "#((!!x. A x ==> thesis) ==> thesis)" which is a finished goal state *}
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      <proof end>
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  }
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  fix x assm <<obtain_export>> "A x"
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*)
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signature OBTAIN =
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sig
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  val thatN: string
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  val obtain: string -> (binding * typ option * mixfix) list ->
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    (Thm.binding * (term * term list) list) list -> bool -> Proof.state -> Proof.state
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  val obtain_cmd: string -> (binding * string option * mixfix) list ->
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    (Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state
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  val result: (Proof.context -> tactic) -> thm list -> Proof.context ->
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    ((string * cterm) list * thm list) * Proof.context
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  val guess: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
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  val guess_cmd: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state
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end;
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structure Obtain: OBTAIN =
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struct
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(** obtain_export **)
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(*
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  [x, A x]
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     :
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     B
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  --------
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     B
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*)
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fun eliminate_term ctxt xs tm =
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  let
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    val vs = map (dest_Free o Thm.term_of) xs;
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    val bads = Term.fold_aterms (fn t as Free v =>
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      if member (op =) vs v then insert (op aconv) t else I | _ => I) tm [];
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    val _ = null bads orelse
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      error ("Result contains obtained parameters: " ^
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        space_implode " " (map (Syntax.string_of_term ctxt) bads));
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  in tm end;
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fun eliminate fix_ctxt rule xs As thm =
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  let
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    val thy = Proof_Context.theory_of fix_ctxt;
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    val _ = eliminate_term fix_ctxt xs (Thm.full_prop_of thm);
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    val _ = Object_Logic.is_judgment thy (Thm.concl_of thm) orelse
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      error "Conclusion in obtained context must be object-logic judgment";
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    val ((_, [thm']), ctxt') = Variable.import true [thm] fix_ctxt;
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    val prems = Drule.strip_imp_prems (#prop (Thm.crep_thm thm'));
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  in
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    ((Drule.implies_elim_list thm' (map Thm.assume prems)
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        |> Drule.implies_intr_list (map Drule.norm_hhf_cterm As)
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        |> Drule.forall_intr_list xs)
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      COMP rule)
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    |> Drule.implies_intr_list prems
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    |> singleton (Variable.export ctxt' fix_ctxt)
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  end;
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fun obtain_export ctxt rule xs _ As =
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  (eliminate ctxt rule xs As, eliminate_term ctxt xs);
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(** obtain **)
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fun bind_judgment ctxt name =
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  let
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    val thy = Proof_Context.theory_of ctxt;
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    val ([x], ctxt') = Proof_Context.add_fixes [(Binding.name name, NONE, NoSyn)] ctxt;
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    val (t as _ $ Free v) = Object_Logic.fixed_judgment thy x;
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  in ((v, t), ctxt') end;
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val thatN = "that";
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local
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fun gen_obtain prep_att prep_vars prep_propp
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    name raw_vars raw_asms int state =
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  let
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    val _ = Proof.assert_forward_or_chain state;
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    val thy = Proof.theory_of state;
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    val cert = Thm.cterm_of thy;
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    val ctxt = Proof.context_of state;
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    val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
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    (*obtain vars*)
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    val (vars, vars_ctxt) = prep_vars raw_vars ctxt;
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    val (xs', fix_ctxt) = vars_ctxt |> Proof_Context.add_fixes vars;
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    val xs = map (Variable.check_name o #1) vars;
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    (*obtain asms*)
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    val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
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    val asm_props = maps (map fst) proppss;
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    val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
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    (*obtain parms*)
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    val (Ts, parms_ctxt) = fold_map Proof_Context.inferred_param xs' asms_ctxt;
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    val parms = xs' ~~ Ts;
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    val _ = Variable.warn_extra_tfrees fix_ctxt parms_ctxt;
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    (*obtain statements*)
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    val thesisN = singleton (Name.variant_list xs) Auto_Bind.thesisN;
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    val (thesis_var, thesis) = #1 (bind_judgment fix_ctxt thesisN);
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    val that_name = if name = "" then thatN else name;
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    val that_prop =
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      Term.list_all_free (parms, Logic.list_implies (asm_props, thesis))
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      |> Library.curry Logic.list_rename_params xs;
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    val obtain_prop =
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      Logic.list_rename_params ([Auto_Bind.thesisN],
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        Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));
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    fun after_qed _ =
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      Proof.local_qed (NONE, false)
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      #> `Proof.the_fact #-> (fn rule =>
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        Proof.fix vars
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        #> Proof.assm (obtain_export fix_ctxt rule (map (cert o Free) parms)) asms);
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  in
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    state
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    |> Proof.enter_forward
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    |> Proof.have NONE (K I) [(Thm.empty_binding, [(obtain_prop, [])])] int
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    |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
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    |> Proof.fix [(Binding.name thesisN, NONE, NoSyn)]
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    |> Proof.assume
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      [((Binding.name that_name, [Context_Rules.intro_query NONE]), [(that_prop, [])])]
16842
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    |> `Proof.the_facts
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    ||> Proof.chain_facts chain_facts
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    ||> Proof.show NONE after_qed [(Thm.empty_binding, [(thesis, [])])] false
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    |-> Proof.refine_insert
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  end;
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in
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val obtain = gen_obtain (K I) Proof_Context.cert_vars Proof_Context.cert_propp;
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val obtain_cmd = gen_obtain Attrib.attribute Proof_Context.read_vars Proof_Context.read_propp;
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62b45a2e6ecb ObtainFun;
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end;
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bc4db8cfd92f added 'guess', which derives the obtained context from the course of reasoning;
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bc4db8cfd92f added 'guess', which derives the obtained context from the course of reasoning;
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(** tactical result **)
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fun check_result ctxt thesis th =
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  (case Thm.prems_of th of
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    [prem] =>
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      if Thm.concl_of th aconv thesis andalso
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        Logic.strip_assums_concl prem aconv thesis then th
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      else error ("Guessed a different clause:\n" ^ Display.string_of_thm ctxt th)
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  | [] => error "Goal solved -- nothing guessed"
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  | _ => error ("Guess split into several cases:\n" ^ Display.string_of_thm ctxt th));
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fun result tac facts ctxt =
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  let
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    val thy = Proof_Context.theory_of ctxt;
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    val cert = Thm.cterm_of thy;
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    val ((thesis_var, thesis), thesis_ctxt) = bind_judgment ctxt Auto_Bind.thesisN;
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    val rule =
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      (case SINGLE (Method.insert_tac facts 1 THEN tac thesis_ctxt) (Goal.init (cert thesis)) of
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        NONE => raise THM ("Obtain.result: tactic failed", 0, facts)
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      | SOME th => check_result ctxt thesis (Raw_Simplifier.norm_hhf (Goal.conclude th)));
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   196
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    val closed_rule = Thm.forall_intr (cert (Free thesis_var)) rule;
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    val ((_, [rule']), ctxt') = Variable.import false [closed_rule] ctxt;
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   199
    val obtain_rule = Thm.forall_elim (cert (Logic.varify_global (Free thesis_var))) rule';
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1af81b70cf09 clarified Variable.focus vs. Variable.focus_cterm -- eliminated clone;
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    val ((params, stmt), fix_ctxt) = Variable.focus_cterm (Thm.cprem_of obtain_rule 1) ctxt';
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    val (prems, ctxt'') =
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      Assumption.add_assms (obtain_export fix_ctxt obtain_rule (map #2 params))
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        (Drule.strip_imp_prems stmt) fix_ctxt;
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  in ((params, prems), ctxt'') end;
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(** guess **)
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local
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fun unify_params vars thesis_var raw_rule ctxt =
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  let
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    val thy = Proof_Context.theory_of ctxt;
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   215
    val certT = Thm.ctyp_of thy;
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   216
    val cert = Thm.cterm_of thy;
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   217
    val string_of_term = Syntax.string_of_term (Config.put show_types true ctxt);
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   218
32091
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   219
    fun err msg th = error (msg ^ ":\n" ^ Display.string_of_thm ctxt th);
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   221
    val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
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   222
    val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
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   223
33368
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   224
    val params = Rule_Cases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
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    val m = length vars;
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   226
    val n = length params;
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   227
    val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
17858
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   228
19779
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   229
    fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
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   230
      handle Type.TUNIFY =>
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   231
        err ("Failed to unify variable " ^
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   232
          string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
42284
326f57825e1a explicit structure Syntax_Trans;
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   233
          string_of_term (Syntax_Trans.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;
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   234
    val (tyenv, _) = fold unify (map #1 vars ~~ take m params)
19779
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   235
      (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
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   236
    val norm_type = Envir.norm_type tyenv;
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   237
19978
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   238
    val xs = map (apsnd norm_type o fst) vars;
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   239
    val ys = map (apsnd norm_type) (drop m params);
20085
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   240
    val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
19978
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   241
    val terms = map (Drule.mk_term o cert o Free) (xs @ ys');
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   242
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   243
    val instT =
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   244
      fold (Term.add_tvarsT o #2) params []
19978
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   245
      |> map (TVar #> (fn T => (certT T, certT (norm_type T))));
20308
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   246
    val closed_rule = rule
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   247
      |> Thm.forall_intr (cert (Free thesis_var))
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   248
      |> Thm.instantiate (instT, []);
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   249
31794
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   250
    val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;
19978
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   251
    val vars' =
df19a7876183 obtain_export: Thm.generalize;
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   252
      map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
df19a7876183 obtain_export: Thm.generalize;
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   253
      (map snd vars @ replicate (length ys) NoSyn);
35845
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   254
    val rule'' = Thm.forall_elim (cert (Logic.varify_global (Free thesis_var))) rule';
19978
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   255
  in ((vars', rule''), ctxt') end;
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   256
28080
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   257
fun inferred_type (binding, _, mx) ctxt =
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   258
  let
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   259
    val x = Variable.check_name binding;
42360
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   260
    val (T, ctxt') = Proof_Context.inferred_param x ctxt
19779
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   261
  in ((x, T, mx), ctxt') end;
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   262
20004
e6d3f2b031e6 guess: proper context for polymorphic parameters;
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diff changeset
   263
fun polymorphic ctxt vars =
19897
fe661eb3b0e7 ProofContext: moved variable operations to struct Variable;
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parents: 19844
diff changeset
   264
  let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
19779
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diff changeset
   265
  in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
18693
8ae076ee5e19 guess: used fixed inferred_type of vars;
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diff changeset
   266
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   267
fun gen_guess prep_vars raw_vars int state =
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   268
  let
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   269
    val _ = Proof.assert_forward_or_chain state;
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   270
    val thy = Proof.theory_of state;
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   271
    val cert = Thm.cterm_of thy;
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   272
    val ctxt = Proof.context_of state;
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   273
    val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
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   274
33386
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   275
    val (thesis_var, thesis) = #1 (bind_judgment ctxt Auto_Bind.thesisN);
20004
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   276
    val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> fst |> polymorphic ctxt;
17858
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   277
19978
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   278
    fun guess_context raw_rule state' =
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   279
      let
19978
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   280
        val ((parms, rule), ctxt') =
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   281
          unify_params vars thesis_var raw_rule (Proof.context_of state');
42501
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wenzelm
parents: 42496
diff changeset
   282
        val (xs, _) = Variable.add_fixes (map (#1 o #1) parms) ctxt';
2b8c34f53388 eliminated slightly odd Proof_Context.bind_fixes;
wenzelm
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   283
        val ps = xs ~~ map (#2 o #1) parms;
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diff changeset
   284
        val ts = map Free ps;
17858
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   285
        val asms =
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diff changeset
   286
          Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
19585
70a1ce3b23ae removed 'concl is' patterns;
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parents: 19482
diff changeset
   287
          |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));
19779
5c77dfb74c7b guess: more careful about local polymorphism;
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diff changeset
   288
        val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
17858
bc4db8cfd92f added 'guess', which derives the obtained context from the course of reasoning;
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diff changeset
   289
      in
19978
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diff changeset
   290
        state'
df19a7876183 obtain_export: Thm.generalize;
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diff changeset
   291
        |> Proof.map_context (K ctxt')
36323
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parents: 35845
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        |> Proof.fix (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)
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        |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm
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          (obtain_export fix_ctxt rule (map cert ts)) [(Thm.empty_binding, asms)])
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        |> Proof.bind_terms Auto_Bind.no_facts
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      end;
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    val goal = Var (("guess", 0), propT);
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    fun print_result ctxt' (k, [(s, [_, th])]) =
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      Proof_Display.print_results int ctxt' (k, [(s, [th])]);
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    val before_qed = SOME (Method.primitive_text (Goal.conclude #> Raw_Simplifier.norm_hhf #>
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        (fn th => Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));
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    fun after_qed [[_, res]] =
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      Proof.end_block #> guess_context (check_result ctxt thesis res);
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  in
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    state
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    |> Proof.enter_forward
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    |> Proof.begin_block
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    |> Proof.fix [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)]
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    |> Proof.chain_facts chain_facts
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    |> Proof.local_goal print_result (K I) (apsnd (rpair I))
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      "guess" before_qed after_qed [(Thm.empty_binding, [Logic.mk_term goal, goal])]
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    |> Proof.refine (Method.primitive_text (K (Goal.init (cert thesis)))) |> Seq.hd
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  end;
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in
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val guess = gen_guess Proof_Context.cert_vars;
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val guess_cmd = gen_guess Proof_Context.read_vars;
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end;
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end;