src/Pure/Proof/proof_syntax.ML

tuned;

(*  Title:      Pure/Proof/proof_syntax.ML
    ID:         $Id$
    Author:     Stefan Berghofer, TU Muenchen

Function for parsing and printing proof terms.
*)

signature PROOF_SYNTAX =
sig
  val proofT : typ
  val add_proof_syntax : theory -> theory
  val disambiguate_names : theory -> Proofterm.proof ->
    Proofterm.proof * Proofterm.proof Symtab.table
  val proof_of_term : theory -> Proofterm.proof Symtab.table ->
    bool -> term -> Proofterm.proof
  val term_of_proof : Proofterm.proof -> term
  val cterm_of_proof : theory -> Proofterm.proof -> cterm * (cterm -> Proofterm.proof)
  val read_term : theory -> typ -> string -> term
  val read_proof : theory -> bool -> string -> Proofterm.proof
  val pretty_proof : theory -> Proofterm.proof -> Pretty.T
  val pretty_proof_of : bool -> thm -> Pretty.T
  val print_proof_of : bool -> thm -> unit
end;

structure ProofSyntax : PROOF_SYNTAX =
struct

open Proofterm;

(**** add special syntax for embedding proof terms ****)

val proofT = Type ("proof", []);
val paramT = Type ("param", []);
val paramsT = Type ("params", []);
val idtT = Type ("idt", []);
val aT = TFree ("'a", []);

(** constants for theorems and axioms **)

fun add_proof_atom_consts names thy =
  thy
  |> Theory.absolute_path
  |> Theory.add_consts_i (map (fn name => (name, proofT, NoSyn)) names);

(** constants for application and abstraction **)

fun add_proof_syntax thy =
  thy
  |> Theory.copy
  |> Theory.root_path
  |> Theory.add_defsort_i []
  |> Theory.add_types [("proof", 0, NoSyn)]
  |> Theory.add_consts_i
      [("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),
       ("Hyp", propT --> proofT, NoSyn),
       ("Oracle", propT --> proofT, NoSyn),
       ("MinProof", proofT, Delimfix "?")]
  |> Theory.add_nonterminals ["param", "params"]
  |> Theory.add_syntax_i
      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1Lam _./ _)", [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 "_")]
  |> Theory.add_modesyntax_i ("xsymbols", true)
      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<Lambda>_./ _)", [0, 3], 3)),
       ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
       ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
  |> Theory.add_modesyntax_i ("latex", false)
      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<^bold>\\<lambda>_./ _)", [0, 3], 3))]
  |> Theory.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") [Variable "x", Variable "A"],
        Syntax.mk_appl (Constant "Abst")
          [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);


(**** create unambiguous theorem names ****)

fun disambiguate_names thy prf =
  let
    val thms = thms_of_proof Symtab.empty prf;
    val thms' = map (apsnd (#prop o rep_thm)) (PureThy.all_thms_of thy);

    val tab = Symtab.foldl (fn (tab, (key, ps)) =>
      let val prop = getOpt (assoc (thms', key), Bound 0)
      in fst (foldr (fn ((prop', prf), x as (tab, i)) =>
        if prop <> prop' then
          (Symtab.update ((key ^ "_" ^ string_of_int i, prf), tab), i+1)
        else x) (tab, 1) ps)
      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 (prf' as PThm ((s, tags), prf, prop, Ts)) =
          let
            val prop' = getOpt (assoc (thms', s), Bound 0);
            val ps = map fst (valOf (Symtab.lookup (thms, s))) \ prop'
          in if prop = prop' then prf' else
            PThm ((s ^ "_" ^ string_of_int (length ps - find_index_eq prop ps), tags),
              prf, prop, Ts)
          end
      | rename prf = prf

  in (rename prf, tab) end;


(**** translation between proof terms and pure terms ****)

fun proof_of_term thy tab ty =
  let
    val thms = PureThy.all_thms_of thy;
    val axms = Theory.all_axioms_of thy;

    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 =>
                 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 =>
                 let val name = NameSpace.pack xs;
                 in (case assoc (thms, name) of
                     SOME thm => fst (strip_combt (Thm.proof_of thm))
                   | NONE => (case Symtab.lookup (tab, name) of
                         SOME prf => prf
                       | NONE => error ("Unknown theorem " ^ quote name)))
                 end
             | _ => error ("Illegal proof constant name: " ^ quote s))
      | prf_of Ts (Const ("Hyp", _) $ prop) = Hyp prop
      | 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
              | _ $ 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 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 (mk_term t))
      | prf_of _ t = error ("Not a proof term:\n" ^
          Sign.string_of_term thy t)

  in prf_of [] end;


val AbsPt = Const ("AbsP", [propT, proofT --> proofT] ---> proofT);
val AppPt = Const ("AppP", [proofT, proofT] ---> proofT);
val Hypt = Const ("Hyp", propT --> proofT);
val Oraclet = Const ("Oracle", propT --> proofT);
val MinProoft = Const ("MinProof", proofT);

val mk_tyapp = Library.foldl (fn (prf, T) => Const ("Appt",
  [proofT, itselfT T] ---> proofT) $ prf $ Logic.mk_type T);

fun term_of _ (PThm ((name, _), _, _, NONE)) =
      Const (NameSpace.append "thm" name, proofT)
  | term_of _ (PThm ((name, _), _, _, SOME Ts)) =
      mk_tyapp (Const (NameSpace.append "thm" name, proofT), Ts)
  | term_of _ (PAxm (name, _, NONE)) = Const (NameSpace.append "axm" name, proofT)
  | term_of _ (PAxm (name, _, SOME Ts)) =
      mk_tyapp (Const (NameSpace.append "axm" name, proofT), Ts)
  | term_of _ (PBound i) = Bound i
  | term_of Ts (Abst (s, opT, prf)) = 
      let val T = getOpt (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 $ getOpt (t, Const ("dummy_pattern", propT)) $
        Abs (s, proofT, term_of (proofT::Ts) (incr_pboundvars 0 1 prf))
  | term_of Ts (prf1 %% prf2) =
      AppPt $ term_of Ts prf1 $ term_of Ts prf2
  | term_of Ts (prf % opt) = 
      let val t = getOpt (opt, Const ("dummy_pattern", dummyT))
      in Const ("Appt",
        [proofT, fastype_of1 (Ts, t) handle TERM _ => dummyT] ---> proofT) $
          term_of Ts prf $ t
      end
  | term_of Ts (Hyp t) = Hypt $ t
  | term_of Ts (Oracle (_, t, _)) = Oraclet $ t
  | term_of Ts (MinProof _) = MinProoft;

val term_of_proof = term_of [];

fun cterm_of_proof thy prf =
  let
    val (prf', tab) = disambiguate_names thy prf;
    val thm_names = filter_out (equal "")
      (map fst (PureThy.all_thms_of thy) @ map fst (Symtab.dest tab));
    val axm_names = map fst (Theory.all_axioms_of thy);
    val thy' = thy
      |> add_proof_syntax
      |> add_proof_atom_consts
        (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names)
  in
    (cterm_of thy' (term_of_proof prf'),
     proof_of_term thy tab true o Thm.term_of)
  end;

fun read_term thy =
  let
    val thm_names = filter_out (equal "") (map fst (PureThy.all_thms_of thy));
    val axm_names = map fst (Theory.all_axioms_of thy);
    val thy' = thy
      |> add_proof_syntax
      |> add_proof_atom_consts
        (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names)
  in
    fn T => fn s => Thm.term_of (read_cterm thy' (s, T))
  end;

fun read_proof thy =
  let val rd = read_term thy proofT
  in
    (fn ty => fn s => proof_of_term thy Symtab.empty ty (Logic.varify (rd s)))
  end;

fun pretty_proof thy prf =
  let
    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 thy' = thy |>
      add_proof_syntax |>
      add_proof_atom_consts
        (map (NameSpace.append "thm") thm_names @ map (NameSpace.append "axm") axm_names)
  in
    Sign.pretty_term thy' (term_of_proof prf)
  end;

fun pretty_proof_of full thm =
  let
    val {thy, der = (_, prf), prop, ...} = rep_thm 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 thy
      (if full then Reconstruct.reconstruct_proof thy prop prf' else prf')
  end;

val print_proof_of = Pretty.writeln oo pretty_proof_of;

end;