src/Pure/Isar/obtain.ML
author wenzelm
Mon Jul 03 19:33:09 2006 +0200 (2006-07-03)
changeset 19978 df19a7876183
parent 19906 c23a0e65b285
child 20004 e6d3f2b031e6
permissions -rw-r--r--
obtain_export: Thm.generalize;
guess: fixed handling of mixfixes of vars;
tuned;
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(*  Title:      Pure/Isar/obtain.ML
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    ID:         $Id$
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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 obtain: string -> (string * string option * mixfix) list ->
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    ((string * Attrib.src list) * (string * string list) list) list
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    -> bool -> Proof.state -> Proof.state
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  val obtain_i: string -> (string * typ option * mixfix) list ->
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    ((string * attribute list) * (term * term list) list) list
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    -> bool -> Proof.state -> Proof.state
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  val guess: (string * string option * mixfix) list -> bool -> Proof.state -> Proof.state
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  val guess_i: (string * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
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  val statement: (string * ((string * 'typ option) list * 'term list)) list ->
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    (('typ, 'term, 'fact) Element.ctxt list *
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      ((string * Attrib.src list) * ('term * 'term list) list) list) *
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    (((string * Attrib.src list) * (term * term list) list) list -> Proof.context ->
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      (((string * Attrib.src list) * (term * term list) list) list * thm list) * Proof.context)
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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 obtain_export ctxt parms rule cprops thm =
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  let
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    val {thy, prop, ...} = Thm.rep_thm thm;
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    val concl = Logic.strip_assums_concl prop;
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    val bads = Term.fold_aterms (fn v as Free (x, _) =>
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      if member (op =) parms x then insert (op aconv) v else I | _ => I) concl [];
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    val thm' = thm |> Drule.implies_intr_protected cprops;
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    val thm'' = thm' |> Thm.generalize ([], parms) (Thm.maxidx_of thm' + 1);
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    val elim_tacs = replicate (length cprops) (Tactic.etac Drule.protectI);
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  in
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    if not (null bads) then
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      error ("Conclusion contains obtained parameters: " ^
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        space_implode " " (map (ProofContext.string_of_term ctxt) bads))
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    else if not (ObjectLogic.is_judgment thy concl) then
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      error "Conclusion in obtained context must be object-logic judgment"
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    else (Tactic.rtac thm'' THEN' RANGE elim_tacs) 1 rule
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  end;
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(** obtain **)
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fun bind_judgment ctxt name =
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  let
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    val (bind, _) = ProofContext.bind_fixes [name] ctxt;
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    val (t as _ $ Free v) = bind (ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name);
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  in (v, t) 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 ctxt = Proof.context_of state;
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    val thy = Proof.theory_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 (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
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    val xs = map #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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    val _ = Variable.warn_extra_tfrees fix_ctxt asms_ctxt;
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    (*obtain statements*)
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    val thesisN = Term.variant xs AutoBind.thesisN;
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    val (thesis_var, thesis) = bind_judgment fix_ctxt thesisN;
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    fun occs_var x = Library.get_first (fn t =>
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      Term.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;
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    val parms =
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      map_filter (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (map occs_var xs ~~ xs);
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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 (map #1 parms, Logic.list_implies (asm_props, thesis))
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      |> Library.curry Logic.list_rename_params (map #2 parms);
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    val obtain_prop =
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      Logic.list_rename_params ([AutoBind.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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      #> Seq.map (`Proof.the_fact #-> (fn rule =>
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        Proof.fix_i (map2 (fn x => fn (_, T, mx) => (x, T, mx)) xs vars)
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        #> Proof.assm_i (K (obtain_export ctxt (map (#1 o #1) parms) rule)) asms));
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  in
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    state
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    |> Proof.enter_forward
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    |> Proof.have_i NONE (K Seq.single) [(("", []), [(obtain_prop, [])])] int
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    |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
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    |> Proof.fix_i [(thesisN, NONE, NoSyn)]
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    |> Proof.assume_i [((that_name, [ContextRules.intro_query NONE]), [(that_prop, [])])]
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    |> `Proof.the_facts
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    ||> Proof.chain_facts chain_facts
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    ||> Proof.show_i NONE after_qed [(("", []), [(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 Attrib.attribute ProofContext.read_vars ProofContext.read_propp;
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val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;
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end;
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(** guess **)
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local
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fun unify_params vars thesis_name raw_rule ctxt =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val certT = Thm.ctyp_of thy;
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    val cert = Thm.cterm_of thy;
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    val string_of_typ = ProofContext.string_of_typ ctxt;
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    val string_of_term = setmp show_types true (ProofContext.string_of_term ctxt);
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    fun err msg th = error (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th);
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    val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
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    val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
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    val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
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    val m = length vars;
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    val n = length params;
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    val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
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    fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
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      handle Type.TUNIFY =>
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        err ("Failed to unify variable " ^
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          string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
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          string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;
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    val (tyenv, _) = fold unify (map #1 vars ~~ Library.take (m, params))
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      (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
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    val norm_type = Envir.norm_type tyenv;
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    val xs = map (apsnd norm_type o fst) vars;
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    val ys = map (apsnd norm_type) (Library.drop (m, params));
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    val ys' = map Term.internal (Term.variantlist (map fst ys, map fst xs)) ~~ map #2 ys;
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    val terms = map (Drule.mk_term o cert o Free) (xs @ ys');
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    val instT =
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      fold (Term.add_tvarsT o #2) params []
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      |> map (TVar #> (fn T => (certT T, certT (norm_type T))));
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    val (rule' :: terms', ctxt') =
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      Variable.import false (Thm.instantiate (instT, []) rule :: terms) ctxt;
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    val vars' =
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      map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
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      (map snd vars @ replicate (length ys) NoSyn);
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    val rule'' = Thm.generalize ([], [thesis_name]) (Thm.maxidx_of rule' + 1) rule';
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  in ((vars', rule''), ctxt') end;
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fun inferred_type (x, _, mx) ctxt =
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  let val ((_, T), ctxt') = ProofContext.inferred_param x ctxt
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  in ((x, T, mx), ctxt') end;
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fun polymorphic (vars, ctxt) =
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  let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
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  in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
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fun gen_guess prep_vars raw_vars 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 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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    val ((thesis_name, _), thesis) = bind_judgment ctxt AutoBind.thesisN;
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    val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> polymorphic;
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    fun check_result 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 ()
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          else error ("Guessed a different clause:\n" ^ ProofContext.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" ^ ProofContext.string_of_thm ctxt th));
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    fun guess_context raw_rule state' =
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      let
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        val ((parms, rule), ctxt') =
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          unify_params vars thesis_name raw_rule (Proof.context_of state');
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        val (bind, _) = ProofContext.bind_fixes (map (#1 o #1) parms) ctxt';
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        val ts = map (bind o Free o #1) parms;
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        val ps = map dest_Free ts;
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        val asms =
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          Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
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          |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));
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        val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
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      in
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        state'
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        |> Proof.map_context (K ctxt')
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        |> Proof.fix_i (map (fn ((x, T), mx) => (x, SOME T, mx)) parms)
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        |> Proof.assm_i (K (obtain_export ctxt' (map #1 ps) rule)) [(("", []), asms)]
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        |> Proof.add_binds_i AutoBind.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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      ProofDisplay.print_results int ctxt' (k, [(s, [th])]);
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    val before_qed = SOME (Method.primitive_text (Goal.conclude #> (fn th =>
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      Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));
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    fun after_qed [[_, res]] =
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      (check_result res; Proof.end_block #> Seq.map (guess_context 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_i [(AutoBind.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 [(("", []), [Logic.mk_term goal, goal])]
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    |> Proof.refine (Method.primitive_text (K (Goal.init (Thm.cterm_of thy thesis)))) |> Seq.hd
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  end;
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in
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val guess = gen_guess ProofContext.read_vars;
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val guess_i = gen_guess ProofContext.cert_vars;
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end;
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(** statements with several cases **)
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fun statement cases =
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  let
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    val names =
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      cases |> map_index (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);
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    val elems = cases |> map (fn (_, (vars, _)) =>
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      Element.Constrains (vars |> map_filter (fn (x, SOME T) => SOME (x, T) | _ => NONE)));
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    val concl = cases |> map (fn (_, (_, props)) => (("", []), map (rpair []) props));
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    fun mk_stmt stmt ctxt =
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      let
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        val thesis =
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          ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
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        val atts = map Attrib.internal
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          [RuleCases.consumes (~ (length cases)), RuleCases.case_names names];
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        fun assume_case ((name, (vars, _)), (_, propp)) ctxt' =
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          let
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            val xs = map fst vars;
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            val props = map fst propp;
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            val (parms, ctxt'') =
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              ctxt'
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              |> fold Variable.declare_term props
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              |> fold_map ProofContext.inferred_param xs;
wenzelm@18897
   313
            val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));
wenzelm@18897
   314
          in
wenzelm@18897
   315
            ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));
wenzelm@18897
   316
            ctxt' |> ProofContext.add_assms_i ProofContext.assume_export
wenzelm@19585
   317
              [((name, [ContextRules.intro_query NONE]), [(asm, [])])]
wenzelm@18897
   318
            |>> (fn [(_, [th])] => th)
wenzelm@18897
   319
          end;
wenzelm@18897
   320
        val (ths, ctxt') = ctxt
wenzelm@18897
   321
          |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])
wenzelm@18897
   322
          |> fold_map assume_case (cases ~~ stmt)
wenzelm@18897
   323
          |-> (fn ths => ProofContext.note_thmss_i [((thatN, []), [(ths, [])])] #> #2 #> pair ths);
wenzelm@19585
   324
      in (([(("", atts), [(thesis, [])])], ths), ctxt') end;
wenzelm@18897
   325
  in ((elems, concl), mk_stmt) end;
wenzelm@18897
   326
wenzelm@17858
   327
end;