Quelle proof_checker.ML Sprache: SML

(*  Title:      Pure/Proof/proof_checker.ML
    Author:     Stefan Berghofer, TU Muenchen

Simple proof checker based only on the core inference rules
of Isabelle/Pure.
*)

signature PROOF_CHECKER =
sig
  val thm_of_proof : theory -> Proofterm.proof -> thm
end;

structure Proof_Checker : PROOF_CHECKER =
struct

(***** construct a theorem out of a proof term *****)

fun lookup_thm thy =
  let
    val tab =
      Thm_Name.Table.build (Global_Theory.all_thms_of thy true |> fold_rev Thm_Name.Table.update);
  in
    fn name =>
      (case Thm_Name.Table.lookup tab name of
        NONE => error ("Unknown theorem " ^ quote (Thm_Name.print name))
      | SOME thm => thm)
  end;

val beta_eta_convert =
  Conv.fconv_rule Drule.beta_eta_conversion;

(* equality modulo renaming of type variables *)
fun is_equal t t' =
  let
    val atoms = fold_types (fold_atyps (insert (op =))) t [];
    val atoms' = fold_types (fold_atyps (insert (op =))) t' []
  in
    length atoms = length atoms' andalso
    map_types (map_atyps (the o AList.lookup (op =) (atoms ~~ atoms'))) t aconv t'
  end;

fun pretty_prf thy vs Hs prf =
  let val prf' = prf |> Proofterm.subst_bounds (map Free vs) |>
    Proofterm.subst_pbounds (map (Hyp o Thm.prop_of) Hs)
  in
    (Proof_Syntax.pretty_proof (Syntax.init_pretty_global thy) prf',
     Syntax.pretty_term_global thy (Proofterm.prop_of prf'))
  end;

fun pretty_term thy vs _ t =
  let val t' = subst_bounds (map Free vs, t)
  in
    (Syntax.pretty_term_global thy t',
     Syntax.pretty_typ_global thy (fastype_of t'))
  end;

fun appl_error thy prt vs Hs s f a =
  let
    val (pp_f, pp_fT) = pretty_prf thy vs Hs f;
    val (pp_a, pp_aT) = prt thy vs Hs a
  in
    error (cat_lines
      [s,
       "",
       Pretty.string_of (Pretty.block
         [Pretty.str "Operator:", Pretty.brk 2, pp_f,
           Pretty.str " ::", Pretty.brk 1, pp_fT]),
       Pretty.string_of (Pretty.block
         [Pretty.str "Operand:", Pretty.brk 3, pp_a,
           Pretty.str " ::", Pretty.brk 1, pp_aT]),
       ""])
  end;

fun thm_of_proof thy =
  let
    val global_ctxt = Syntax.init_pretty_global thy;
    val lookup = lookup_thm thy;
  in
    fn prf =>
      let
        val prf_names =
          Name.build_context (prf |> Proofterm.fold_proof_terms Term.declare_free_names);

        fun thm_of_atom thm Ts =
          let
            val tvars = build_rev (Term.add_tvars (Thm.full_prop_of thm));
            val (names, thm') = Thm.varifyT_global' TFrees.empty thm;
            val ctye = tvars @ map #2 names ~~ map (Thm.global_ctyp_of thy) Ts;
          in
            Thm.instantiate (TVars.make ctye, Vars.empty)
              (Thm.forall_intr_vars (Thm.forall_intr_frees thm'))
          end;

        fun thm_of _ _ (PThm ({thm_name = (thm_name, thm_pos), prop = prop', types = SOME Ts, ...}, _)) =
              let
                val thm = Thm.unconstrainT (Drule.implies_intr_hyps (lookup thm_name));
                val prop = Thm.prop_of thm;
                val _ =
                  if is_equal prop prop' then ()
                  else
                    error ("Duplicate use of theorem name " ^
                      quote (Global_Theory.print_thm_name global_ctxt thm_name) ^ Position.here thm_pos
                      ^ "\n" ^ Syntax.string_of_term global_ctxt prop
                      ^ "\n\n" ^ Syntax.string_of_term global_ctxt prop');
              in thm_of_atom thm Ts end

          | thm_of _ _ (PAxm (name, _, SOME Ts)) =
              thm_of_atom (Thm.axiom thy name) Ts

          | thm_of _ Hs (PBound i) = nth Hs i

          | thm_of (vs, names) Hs (Abst (s, SOME T, prf)) =
              let
                val (x, names') = Name.variant s names;
                val thm = thm_of ((x, T) :: vs, names') Hs prf
              in
                Thm.forall_intr (Thm.global_cterm_of thy (Free (x, T))) thm
              end

          | thm_of (vs, names) Hs (prf % SOME t) =
              let
                val thm = thm_of (vs, names) Hs prf;
                val ct = Thm.global_cterm_of thy (Term.subst_bounds (map Free vs, t));
              in
                Thm.forall_elim ct thm
                handle THM (s, _, _) => appl_error thy pretty_term vs Hs s prf t
              end

          | thm_of (vs, names) Hs (AbsP (_, SOME t, prf)) =
              let
                val ct = Thm.global_cterm_of thy (Term.subst_bounds (map Free vs, t));
                val thm = thm_of (vs, names) (Thm.assume ct :: Hs) prf;
              in
                Thm.implies_intr ct thm
              end

          | thm_of vars Hs (prf %% prf') =
              let
                val thm = beta_eta_convert (thm_of vars Hs prf);
                val thm' = beta_eta_convert (thm_of vars Hs prf');
              in
                Thm.implies_elim thm thm'
                handle THM (s, _, _) => appl_error thy pretty_prf (fst vars) Hs s prf prf'
              end

          | thm_of _ _ (Hyp t) = Thm.assume (Thm.global_cterm_of thy t)

          | thm_of _ _ (PClass (T, c)) =
              if Sign.of_sort thy (T, [c])
              then Thm.of_class (Thm.global_ctyp_of thy T, c)
              else
                error ("thm_of_proof: bad PClass proof " ^
                  Syntax.string_of_term_global thy (Logic.mk_of_class (T, c)))

          | thm_of _ _ _ = error "thm_of_proof: partial proof term";

      in beta_eta_convert (thm_of ([], prf_names) [] prf) end
  end;

end;

quality100%

¤ Dauer der Verarbeitung: 0.13 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.