src/Pure/Isar/obtain.ML
author wenzelm
Mon Nov 13 22:01:07 2000 +0100 (2000-11-13)
changeset 10464 b7b916a82dca
parent 10379 93630e0c5ae9
child 10582 49ebade930ea
permissions -rw-r--r--
tuned statement args;
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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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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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The 'obtain' language element -- generalized existence at the level of
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proof texts.
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  <chain_facts>
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  obtain x where "P x" <proof> ==
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  {
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    fix thesis
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    assume that: "!!x. P x ==> thesis"
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    <chain_facts> have thesis <proof (insert that)>
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  }
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  fix x assm (obtained) "P x"
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*)
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signature OBTAIN =
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sig
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  val obtain: ((string list * string option) * Comment.text) list
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    * (((string * Args.src list) * (string * (string list * string list)) list)
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      * Comment.text) list -> ProofHistory.T -> ProofHistory.T
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  val obtain_i: ((string list * typ option) * Comment.text) list
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    * (((string * Proof.context attribute list) * (term * (term list * term list)) list)
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      * Comment.text) list -> ProofHistory.T -> ProofHistory.T
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end;
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structure Obtain: OBTAIN =
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struct
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(** disch_obtained **)
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fun disch_obtained state parms rule cprops thm =
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  let
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    val {sign, prop, maxidx, ...} = Thm.rep_thm thm;
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    val cparms = map (Thm.cterm_of sign) parms;
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    val thm' = thm
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      |> Drule.implies_intr_list cprops
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      |> Drule.forall_intr_list cparms
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      |> Drule.forall_elim_vars (maxidx + 1);
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    val elim_tacs = replicate (length cprops) Proof.hard_asm_tac;
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    val concl = Logic.strip_assums_concl prop;
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    val bads = parms inter (Term.term_frees concl);
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  in
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    if not (null bads) then
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      raise Proof.STATE ("Conclusion contains obtained parameters: " ^
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        space_implode " " (map (Sign.string_of_term sign) bads), state)
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    else if not (AutoBind.is_judgment (Logic.strip_assums_concl prop)) then
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      raise Proof.STATE ("Conclusions of 'obtain' context must be object-logic judgments", state)
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    else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule
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  end;
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(** obtain(_i) **)
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val thatN = "that";
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fun gen_obtain prep_vars prep_propp prep_att (raw_vars, raw_asms) state =
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  let
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    val _ = Proof.assert_forward_or_chain state;
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    val chain_facts = if Proof.is_chain state then Proof.the_facts state else [];
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    val thy = Proof.theory_of state;
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    (*obtain vars*)
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    val (vars_ctxt, vars) =
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      foldl_map prep_vars (Proof.context_of state, map Comment.ignore raw_vars);
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    val xs = flat (map fst vars);
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    val thesisN = Term.variant xs AutoBind.thesisN;
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    val bind_skolem = ProofContext.bind_skolem vars_ctxt (xs @ [thesisN]);
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    fun bind_propp (prop, (pats1, pats2)) =
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      (bind_skolem prop, (map bind_skolem pats1, map bind_skolem pats2));
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    (*obtain asms*)
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    val (asms_ctxt, proppss) = prep_propp (vars_ctxt, map (snd o Comment.ignore) raw_asms);
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    val asm_props = flat (map (map fst) proppss);
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    fun prep_asm ((name, src), propps) = ((name, map (prep_att thy) src), map bind_propp propps);
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    val asms = map2 prep_asm (map (fst o Comment.ignore) raw_asms, proppss);
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    val _ = ProofContext.warn_extra_tfrees vars_ctxt asms_ctxt;
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    (*that_prop*)
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    fun find_free x t =
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      (case ProofContext.find_free t x of Some (Free a) => Some a | _ => None);
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    fun occs_var x = Library.get_first (find_free x) asm_props;
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    val xs' = mapfilter occs_var xs;
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    val parms = map (bind_skolem o Free) xs';
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    val bound_thesis = bind_skolem (AutoBind.atomic_judgment thy thesisN);
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    val that_prop = Term.list_all_free (xs', Logic.list_implies (asm_props, bound_thesis));
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    fun export_obtained rule =
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      (disch_obtained state parms rule, fn _ => fn _ => []);
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    fun after_qed st = st
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      |> Proof.end_block
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      |> Seq.map (fn st' => st'
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        |> Proof.fix_i vars
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        |> Proof.assm_i (export_obtained (Proof.the_fact st')) asms);
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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 [([thesisN], None)]
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    |> Proof.assume_i [((thatN, [Method.intro_local]), [(that_prop, ([], []))])]
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    |> (fn state' =>
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      state'
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      |> Proof.from_facts chain_facts
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      |> Proof.have_i after_qed "" [] (bound_thesis, ([], []))
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      |> Method.refine (Method.Basic (K (Method.insert (Proof.the_facts state')))))
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  end;
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val obtain = ProofHistory.applys o
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  (gen_obtain ProofContext.read_vars ProofContext.read_propp Attrib.local_attribute);
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val obtain_i = ProofHistory.applys o
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  (gen_obtain ProofContext.cert_vars ProofContext.cert_propp (K I));
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(** outer syntax **)
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local structure P = OuterParse and K = OuterSyntax.Keyword in
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val obtainP =
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  OuterSyntax.command "obtain" "generalized existence"
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    K.prf_asm_goal
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    (Scan.optional
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      (P.and_list1 (Scan.repeat1 P.name -- Scan.option (P.$$$ "::" |-- P.typ) -- P.marg_comment)
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        --| P.$$$ "where") [] --
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      P.and_list1 (P.opt_thm_name ":" -- Scan.repeat1 P.propp -- P.marg_comment)
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    >> (Toplevel.print oo (Toplevel.proof o obtain)));
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val _ = OuterSyntax.add_keywords ["where"];
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val _ = OuterSyntax.add_parsers [obtainP];
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end;
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end;