src/Pure/Proof/proof_syntax.ML

 open Proofterm;
 
 (**** add special syntax for embedding proof terms ****)
 
 val proofT = Type ("proof", []);
-val lamT = Type ("lam_syn", []);
+val paramT = Type ("param", []);
+val paramsT = Type ("params", []);
 val idtT = Type ("idt", []);
 val aT = TFree ("'a", ["logic"]);
 
 (** constants for theorems and axioms **)
 

 
 fun add_proof_atom_consts names sg = Sign.add_consts_i
   (map (fn name => (name, proofT, NoSyn)) names) (Sign.add_path "//" sg);
 
 (** constants for application and abstraction **)
-  
+
 fun add_proof_syntax sg =
   sg
   |> Sign.copy
   |> Sign.add_path "/"
   |> Sign.add_defsort_i ["logic"]
   |> Sign.add_types [("proof", 0, NoSyn)]
   |> Sign.add_arities [("proof", [], "logic")]
   |> Sign.add_consts_i
-      [("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ %%/ _)", [4, 5], 4)),
-       ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ %/ _)", [4, 5], 4)),
+      [("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ %/ _)", [4, 5], 4)),
+       ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ %%/ _)", [4, 5], 4)),
        ("Abst", (aT --> proofT) --> proofT, NoSyn),
        ("AbsP", [propT, proofT --> proofT] ---> proofT, NoSyn)]
-  |> Sign.add_nonterminals ["lam_syn"]
+  |> Sign.add_nonterminals ["param", "params"]
   |> Sign.add_syntax_i
-      [("_Lam", [lamT, proofT] ---> proofT, Mixfix ("(3Lam _./ _)", [0,0], 1)),
-       ("_Lam0", [lamT, lamT] ---> lamT, Mixfix ("_,/ _", [1, 0], 0)),
-       ("_Lam1", [idtT, propT] ---> lamT, Mixfix ("_ : _", [0, 0], 1)),
-       ("_Lam2", idtT --> lamT, Mixfix ("_", [0], 1))]
+      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(3Lam _./ _)", [0, 3], 3)),
+       ("_Lam0", [paramT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
+       ("_Lam0", [idtT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
+       ("_Lam1", [idtT, propT] ---> paramT, Mixfix ("_: _", [0, 0], 0)),
+       ("", paramT --> paramT, Delimfix "'(_')"),
+       ("", idtT --> paramsT, Delimfix "_"),
+       ("", paramT --> paramsT, Delimfix "_")]
   |> Sign.add_modesyntax_i (("xsymbols", true),
-      [("_Lam", [lamT, proofT] ---> proofT, Mixfix ("(3\\<Lambda>_./ _)", [0,0], 1)),
+      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(3\\<Lambda>_./ _)", [0, 3], 3)),
        ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
        ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))])
   |> Sign.add_trrules_i (map Syntax.ParsePrintRule
       [(Syntax.mk_appl (Constant "_Lam")
+          [Syntax.mk_appl (Constant "_Lam0") [Variable "l", Variable "m"], Variable "A"],
+        Syntax.mk_appl (Constant "_Lam")
+          [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]]),
+       (Syntax.mk_appl (Constant "_Lam")
           [Syntax.mk_appl (Constant "_Lam1") [Variable "x", Variable "A"], Variable "B"],
         Syntax.mk_appl (Constant "AbsP") [Variable "A",
           (Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "B"])]),
-       (Syntax.mk_appl (Constant "_Lam")
-          [Syntax.mk_appl (Constant "_Lam2") [Variable "x"], Variable "A"],
+       (Syntax.mk_appl (Constant "_Lam") [Variable "x", Variable "A"],
         Syntax.mk_appl (Constant "Abst")
-          [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])]),
-       (Syntax.mk_appl (Constant "_Lam")
-          [Syntax.mk_appl (Constant "_Lam0") [Variable "l", Variable "m"], Variable "A"],
-        Syntax.mk_appl (Constant "_Lam")
-          [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]])]);
+          [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);
 
 
 (**** create unambiguous theorem names ****)
 
 fun disambiguate_names thy prf =

         else x) (ps, (tab, 1)))
       end) (Symtab.empty, thms);
 
     fun rename (Abst (s, T, prf)) = Abst (s, T, rename prf)
       | rename (AbsP (s, t, prf)) = AbsP (s, t, rename prf)
-      | rename (prf1 % prf2) = rename prf1 % rename prf2
-      | rename (prf %% t) = rename prf %% t
+      | rename (prf1 %% prf2) = rename prf1 %% rename prf2
+      | rename (prf % t) = rename prf % t
       | rename (prf' as PThm ((s, tags), prf, prop, Ts)) =
           let
             val prop' = if_none (assoc (thms', s)) (Bound 0);
             val ps = map fst (the (Symtab.lookup (thms, s))) \ prop'
           in if prop = prop' then prf' else

   let
     val thys = thy :: Theory.ancestors_of thy;
     val thms = flat (map thms_of thys);
     val axms = flat (map (Symtab.dest o #axioms o rep_theory) thys);
 
+    fun mk_term t = (if ty then I else map_term_types (K dummyT))
+      (Term.no_dummy_patterns t);
+
     fun prf_of [] (Bound i) = PBound i
       | prf_of Ts (Const (s, Type ("proof", _))) =
           change_type (if ty then Some Ts else None)
             (case NameSpace.unpack s of
-               "Axm" :: xs =>
+               "axm" :: xs =>
                  let
                    val name = NameSpace.pack xs;
                    val prop = (case assoc (axms, name) of
                        Some prop => prop
                      | None => error ("Unknown axiom " ^ quote name))
                  in PAxm (name, prop, None) end
-             | "Thm" :: xs =>
+             | "thm" :: xs =>
                  let val name = NameSpace.pack xs;
                  in (case assoc (thms, name) of
                      Some thm => fst (strip_combt (#2 (#der (rep_thm thm))))
                    | None => (case Symtab.lookup (tab, name) of
                          Some prf => prf

       | prf_of Ts (v as Var ((_, Type ("proof", _)))) = Hyp v
       | prf_of [] (Const ("Abst", _) $ Abs (s, T, prf)) =
           Abst (s, if ty then Some T else None,
             incr_pboundvars (~1) 0 (prf_of [] prf))
       | prf_of [] (Const ("AbsP", _) $ t $ Abs (s, _, prf)) =
-          AbsP (s, case t of Const ("dummy_pattern", _) => None | _ => Some t,
+          AbsP (s, case t of
+                Const ("dummy_pattern", _) => None
+              | _ $ Const ("dummy_pattern", _) => None
+              | _ => Some (mk_term t),
             incr_pboundvars 0 (~1) (prf_of [] prf))
       | prf_of [] (Const ("AppP", _) $ prf1 $ prf2) =
-          prf_of [] prf1 % prf_of [] prf2
+          prf_of [] prf1 %% prf_of [] prf2
       | prf_of Ts (Const ("Appt", _) $ prf $ Const ("TYPE", Type (_, [T]))) =
           prf_of (T::Ts) prf
-      | prf_of [] (Const ("Appt", _) $ prf $ t) = prf_of [] prf %%
-          (case t of Const ("dummy_pattern", _) => None | _ => Some t)
+      | prf_of [] (Const ("Appt", _) $ prf $ t) = prf_of [] prf %
+          (case t of Const ("dummy_pattern", _) => None | _ => Some (mk_term t))
       | prf_of _ t = error ("Not a proof term:\n" ^
           Sign.string_of_term (sign_of thy) t)
 
   in prf_of [] end;
 

 
 val mk_tyapp = foldl (fn (prf, T) => Const ("Appt",
   [proofT, itselfT T] ---> proofT) $ prf $ Logic.mk_type T);
 
 fun term_of _ (PThm ((name, _), _, _, None)) =
-      Const (add_prefix "Thm" name, proofT)
+      Const (add_prefix "thm" name, proofT)
   | term_of _ (PThm ((name, _), _, _, Some Ts)) =
-      mk_tyapp (Const (add_prefix "Thm" name, proofT), Ts)
-  | term_of _ (PAxm (name, _, None)) = Const (add_prefix "Axm" name, proofT)
+      mk_tyapp (Const (add_prefix "thm" name, proofT), Ts)
+  | term_of _ (PAxm (name, _, None)) = Const (add_prefix "axm" name, proofT)
   | term_of _ (PAxm (name, _, Some Ts)) =
-      mk_tyapp (Const (add_prefix "Axm" name, proofT), Ts)
+      mk_tyapp (Const (add_prefix "axm" name, proofT), Ts)
   | term_of _ (PBound i) = Bound i
   | term_of Ts (Abst (s, opT, prf)) = 
       let val T = if_none opT dummyT
       in Const ("Abst", (T --> proofT) --> proofT) $
         Abs (s, T, term_of (T::Ts) (incr_pboundvars 1 0 prf))
       end
   | term_of Ts (AbsP (s, t, prf)) =
       AbsPt $ if_none t (Const ("dummy_pattern", propT)) $
         Abs (s, proofT, term_of (proofT::Ts) (incr_pboundvars 0 1 prf))
-  | term_of Ts (prf1 % prf2) =
+  | term_of Ts (prf1 %% prf2) =
       AppPt $ term_of Ts prf1 $ term_of Ts prf2
-  | term_of Ts (prf %% opt) = 
+  | term_of Ts (prf % opt) = 
       let val t = if_none opt (Const ("dummy_pattern", dummyT))
       in Const ("Appt",
         [proofT, fastype_of1 (Ts, t) handle TERM _ => dummyT] ---> proofT) $
           term_of Ts prf $ t
       end

       map fst (Symtab.dest tab);
     val axm_names = map fst (flat (map (Symtab.dest o #axioms o rep_theory) thys));
     val sg = sign_of thy |>
       add_proof_syntax |>
       add_proof_atom_consts
-        (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names)
+        (map (add_prefix "thm") thm_names @ map (add_prefix "axm") axm_names)
   in
     (cterm_of sg (term_of_proof prf'),
      proof_of_term thy tab true o Thm.term_of)
   end;
 

     val thm_names = filter_out (equal "") (map fst (flat (map thms_of thys)));
     val axm_names = map fst (flat (map (Symtab.dest o #axioms o rep_theory) thys));
     val sg = sign_of thy |>
       add_proof_syntax |>
       add_proof_atom_consts
-        (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names)
+        (map (add_prefix "thm") thm_names @ map (add_prefix "axm") axm_names)
   in
     (fn T => fn s => Thm.term_of (read_cterm sg (s, T)))
   end;
 
 fun read_proof thy =

     val thm_names = map fst (Symtab.dest (thms_of_proof Symtab.empty prf)) \ "";
     val axm_names = map fst (Symtab.dest (axms_of_proof Symtab.empty prf));
     val sg' = sg |>
       add_proof_syntax |>
       add_proof_atom_consts
-        (map (add_prefix "Thm") thm_names @ map (add_prefix "Axm") axm_names)
+        (map (add_prefix "thm") thm_names @ map (add_prefix "axm") axm_names)
   in
     Sign.pretty_term sg' (term_of_proof prf)
   end;
 
 fun pretty_proof_of full thm =

     val prf' = (case strip_combt (fst (strip_combP prf)) of
         (PThm (_, prf', prop', _), _) => if prop=prop' then prf' else prf
       | _ => prf)
   in
     pretty_proof sign
-      (if full then Reconstruct.reconstruct_prf sign prop prf' else prf')
+      (if full then Reconstruct.reconstruct_proof sign prop prf' else prf')
   end;
 
 val print_proof_of = Pretty.writeln oo pretty_proof_of;
 
 end;