berghofe@11522: (*  Title:      Pure/Proof/proof_syntax.ML
berghofe@11522:     ID:         $Id$
wenzelm@11539:     Author:     Stefan Berghofer, TU Muenchen
berghofe@11522: 
berghofe@11522: Function for parsing and printing proof terms.
berghofe@11522: *)
berghofe@11522: 
berghofe@11522: signature PROOF_SYNTAX =
berghofe@11522: sig
wenzelm@17078:   val proofT: typ
wenzelm@17078:   val add_proof_syntax: theory -> theory
wenzelm@17078:   val disambiguate_names: theory -> Proofterm.proof ->
berghofe@11522:     Proofterm.proof * Proofterm.proof Symtab.table
wenzelm@17078:   val proof_of_term: theory -> Proofterm.proof Symtab.table ->
berghofe@11522:     bool -> term -> Proofterm.proof
wenzelm@17078:   val term_of_proof: Proofterm.proof -> term
wenzelm@17078:   val cterm_of_proof: theory -> Proofterm.proof -> cterm * (cterm -> Proofterm.proof)
wenzelm@17078:   val read_term: theory -> typ -> string -> term
wenzelm@17078:   val read_proof: theory -> bool -> string -> Proofterm.proof
wenzelm@17078:   val proof_syntax: Proofterm.proof -> theory -> theory
wenzelm@17078:   val proof_of: bool -> thm -> Proofterm.proof
wenzelm@17078:   val pretty_proof: theory -> Proofterm.proof -> Pretty.T
wenzelm@17078:   val pretty_proof_of: bool -> thm -> Pretty.T
wenzelm@17078:   val print_proof_of: bool -> thm -> unit
berghofe@11522: end;
berghofe@11522: 
berghofe@11522: structure ProofSyntax : PROOF_SYNTAX =
berghofe@11522: struct
berghofe@11522: 
berghofe@11522: open Proofterm;
berghofe@11522: 
berghofe@11522: (**** add special syntax for embedding proof terms ****)
berghofe@11522: 
berghofe@11522: val proofT = Type ("proof", []);
berghofe@11614: val paramT = Type ("param", []);
berghofe@11614: val paramsT = Type ("params", []);
berghofe@11522: val idtT = Type ("idt", []);
wenzelm@14854: val aT = TFree ("'a", []);
berghofe@11522: 
berghofe@11522: (** constants for theorems and axioms **)
berghofe@11522: 
wenzelm@16425: fun add_proof_atom_consts names thy =
wenzelm@16425:   thy
wenzelm@22796:   |> Sign.absolute_path
wenzelm@22796:   |> Sign.add_consts_i (map (fn name => (name, proofT, NoSyn)) names);
berghofe@11522: 
berghofe@11522: (** constants for application and abstraction **)
berghofe@11614: 
wenzelm@16425: fun add_proof_syntax thy =
wenzelm@16425:   thy
wenzelm@16425:   |> Theory.copy
wenzelm@22796:   |> Sign.root_path
wenzelm@22796:   |> Sign.add_defsort_i []
wenzelm@22796:   |> Sign.add_types [("proof", 0, NoSyn)]
wenzelm@22796:   |> Sign.add_consts_i
berghofe@11614:       [("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ %/ _)", [4, 5], 4)),
berghofe@11614:        ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ %%/ _)", [4, 5], 4)),
berghofe@11522:        ("Abst", (aT --> proofT) --> proofT, NoSyn),
berghofe@13199:        ("AbsP", [propT, proofT --> proofT] ---> proofT, NoSyn),
berghofe@13199:        ("Hyp", propT --> proofT, NoSyn),
berghofe@13199:        ("Oracle", propT --> proofT, NoSyn),
berghofe@13199:        ("MinProof", proofT, Delimfix "?")]
wenzelm@22796:   |> Sign.add_nonterminals ["param", "params"]
wenzelm@22796:   |> Sign.add_syntax_i
berghofe@11640:       [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1Lam _./ _)", [0, 3], 3)),
berghofe@11614:        ("_Lam0", [paramT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
berghofe@11614:        ("_Lam0", [idtT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
berghofe@11614:        ("_Lam1", [idtT, propT] ---> paramT, Mixfix ("_: _", [0, 0], 0)),
berghofe@11614:        ("", paramT --> paramT, Delimfix "'(_')"),
berghofe@11614:        ("", idtT --> paramsT, Delimfix "_"),
berghofe@11614:        ("", paramT --> paramsT, Delimfix "_")]
wenzelm@22796:   |> Sign.add_modesyntax_i ("xsymbols", true)
berghofe@11640:       [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<Lambda>_./ _)", [0, 3], 3)),
berghofe@11522:        ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
wenzelm@16425:        ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
wenzelm@22796:   |> Sign.add_modesyntax_i ("latex", false)
wenzelm@16425:       [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<^bold>\\<lambda>_./ _)", [0, 3], 3))]
wenzelm@22796:   |> Sign.add_trrules_i (map Syntax.ParsePrintRule
berghofe@11522:       [(Syntax.mk_appl (Constant "_Lam")
berghofe@11614:           [Syntax.mk_appl (Constant "_Lam0") [Variable "l", Variable "m"], Variable "A"],
berghofe@11614:         Syntax.mk_appl (Constant "_Lam")
berghofe@11614:           [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]]),
berghofe@11614:        (Syntax.mk_appl (Constant "_Lam")
berghofe@11522:           [Syntax.mk_appl (Constant "_Lam1") [Variable "x", Variable "A"], Variable "B"],
berghofe@11522:         Syntax.mk_appl (Constant "AbsP") [Variable "A",
berghofe@11522:           (Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "B"])]),
berghofe@11614:        (Syntax.mk_appl (Constant "_Lam") [Variable "x", Variable "A"],
berghofe@11522:         Syntax.mk_appl (Constant "Abst")
berghofe@11614:           [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);
berghofe@11522: 
berghofe@11522: 
berghofe@11522: (**** create unambiguous theorem names ****)
berghofe@11522: 
berghofe@11522: fun disambiguate_names thy prf =
berghofe@11522:   let
berghofe@17019:     val thms = thms_of_proof prf Symtab.empty;
wenzelm@16866:     val thms' = map (apsnd Thm.full_prop_of) (PureThy.all_thms_of thy);
berghofe@11522: 
haftmann@21056:     val tab = Symtab.fold (fn (key, ps) => fn tab =>
wenzelm@19473:       let val prop = the_default (Bound 0) (AList.lookup (op =) thms' key)
haftmann@21056:       in fst (fold_rev (fn (prop', prf) => fn x as (tab, i) => 
berghofe@11522:         if prop <> prop' then
wenzelm@17412:           (Symtab.update (key ^ "_" ^ string_of_int i, prf) tab, i+1)
haftmann@21056:         else x) ps (tab, 1))
haftmann@21056:       end) thms Symtab.empty;
berghofe@11522: 
berghofe@11522:     fun rename (Abst (s, T, prf)) = Abst (s, T, rename prf)
berghofe@11522:       | rename (AbsP (s, t, prf)) = AbsP (s, t, rename prf)
berghofe@11614:       | rename (prf1 %% prf2) = rename prf1 %% rename prf2
berghofe@11614:       | rename (prf % t) = rename prf % t
wenzelm@21646:       | rename (prf' as PThm (s, prf, prop, Ts)) =
berghofe@11522:           let
wenzelm@19473:             val prop' = the_default (Bound 0) (AList.lookup (op =) thms' s);
wenzelm@19305:             val ps = remove (op =) prop' (map fst (the (Symtab.lookup thms s)))
berghofe@11522:           in if prop = prop' then prf' else
wenzelm@21646:             PThm (s ^ "_" ^ string_of_int (length ps - find_index (fn p => p = prop) ps),
berghofe@11522:               prf, prop, Ts)
berghofe@11522:           end
berghofe@11522:       | rename prf = prf
berghofe@11522: 
berghofe@11522:   in (rename prf, tab) end;
berghofe@11522: 
berghofe@11522: 
berghofe@11522: (**** translation between proof terms and pure terms ****)
berghofe@11522: 
berghofe@11522: fun proof_of_term thy tab ty =
berghofe@11522:   let
wenzelm@16350:     val thms = PureThy.all_thms_of thy;
wenzelm@16350:     val axms = Theory.all_axioms_of thy;
berghofe@11522: 
wenzelm@20548:     fun mk_term t = (if ty then I else map_types (K dummyT))
berghofe@11614:       (Term.no_dummy_patterns t);
berghofe@11614: 
berghofe@11522:     fun prf_of [] (Bound i) = PBound i
berghofe@11522:       | prf_of Ts (Const (s, Type ("proof", _))) =
skalberg@15531:           change_type (if ty then SOME Ts else NONE)
wenzelm@21858:             (case NameSpace.explode s of
berghofe@11614:                "axm" :: xs =>
berghofe@11522:                  let
wenzelm@21858:                    val name = NameSpace.implode xs;
wenzelm@17223:                    val prop = (case AList.lookup (op =) axms name of
skalberg@15531:                        SOME prop => prop
skalberg@15531:                      | NONE => error ("Unknown axiom " ^ quote name))
skalberg@15531:                  in PAxm (name, prop, NONE) end
berghofe@11614:              | "thm" :: xs =>
wenzelm@21858:                  let val name = NameSpace.implode xs;
wenzelm@17223:                  in (case AList.lookup (op =) thms name of
skalberg@15531:                      SOME thm => fst (strip_combt (Thm.proof_of thm))
wenzelm@17412:                    | NONE => (case Symtab.lookup tab name of
skalberg@15531:                          SOME prf => prf
skalberg@15531:                        | NONE => error ("Unknown theorem " ^ quote name)))
berghofe@11522:                  end
berghofe@11522:              | _ => error ("Illegal proof constant name: " ^ quote s))
berghofe@13199:       | prf_of Ts (Const ("Hyp", _) $ prop) = Hyp prop
berghofe@11522:       | prf_of Ts (v as Var ((_, Type ("proof", _)))) = Hyp v
berghofe@11522:       | prf_of [] (Const ("Abst", _) $ Abs (s, T, prf)) =
skalberg@15531:           Abst (s, if ty then SOME T else NONE,
berghofe@11522:             incr_pboundvars (~1) 0 (prf_of [] prf))
berghofe@11522:       | prf_of [] (Const ("AbsP", _) $ t $ Abs (s, _, prf)) =
berghofe@11614:           AbsP (s, case t of
skalberg@15531:                 Const ("dummy_pattern", _) => NONE
skalberg@15531:               | _ $ Const ("dummy_pattern", _) => NONE
skalberg@15531:               | _ => SOME (mk_term t),
berghofe@11522:             incr_pboundvars 0 (~1) (prf_of [] prf))
berghofe@11522:       | prf_of [] (Const ("AppP", _) $ prf1 $ prf2) =
berghofe@11614:           prf_of [] prf1 %% prf_of [] prf2
berghofe@11522:       | prf_of Ts (Const ("Appt", _) $ prf $ Const ("TYPE", Type (_, [T]))) =
berghofe@11522:           prf_of (T::Ts) prf
berghofe@11614:       | prf_of [] (Const ("Appt", _) $ prf $ t) = prf_of [] prf %
skalberg@15531:           (case t of Const ("dummy_pattern", _) => NONE | _ => SOME (mk_term t))
berghofe@11522:       | prf_of _ t = error ("Not a proof term:\n" ^
wenzelm@16425:           Sign.string_of_term thy t)
berghofe@11522: 
berghofe@11522:   in prf_of [] end;
berghofe@11522: 
berghofe@11522: 
berghofe@11522: val AbsPt = Const ("AbsP", [propT, proofT --> proofT] ---> proofT);
berghofe@11522: val AppPt = Const ("AppP", [proofT, proofT] ---> proofT);
berghofe@13199: val Hypt = Const ("Hyp", propT --> proofT);
berghofe@13199: val Oraclet = Const ("Oracle", propT --> proofT);
berghofe@13199: val MinProoft = Const ("MinProof", proofT);
berghofe@11522: 
wenzelm@19473: val mk_tyapp = fold (fn T => fn prf => Const ("Appt",
wenzelm@19391:   [proofT, Term.itselfT T] ---> proofT) $ prf $ Logic.mk_type T);
berghofe@11522: 
wenzelm@21646: fun term_of _ (PThm (name, _, _, NONE)) =
wenzelm@16195:       Const (NameSpace.append "thm" name, proofT)
wenzelm@21646:   | term_of _ (PThm (name, _, _, SOME Ts)) =
wenzelm@19473:       mk_tyapp Ts (Const (NameSpace.append "thm" name, proofT))
wenzelm@16195:   | term_of _ (PAxm (name, _, NONE)) = Const (NameSpace.append "axm" name, proofT)
skalberg@15531:   | term_of _ (PAxm (name, _, SOME Ts)) =
wenzelm@19473:       mk_tyapp Ts (Const (NameSpace.append "axm" name, proofT))
berghofe@11522:   | term_of _ (PBound i) = Bound i
berghofe@11522:   | term_of Ts (Abst (s, opT, prf)) = 
wenzelm@18939:       let val T = the_default dummyT opT
berghofe@11522:       in Const ("Abst", (T --> proofT) --> proofT) $
berghofe@11522:         Abs (s, T, term_of (T::Ts) (incr_pboundvars 1 0 prf))
berghofe@11522:       end
berghofe@11522:   | term_of Ts (AbsP (s, t, prf)) =
wenzelm@18939:       AbsPt $ the_default (Term.dummy_pattern propT) t $
berghofe@11522:         Abs (s, proofT, term_of (proofT::Ts) (incr_pboundvars 0 1 prf))
berghofe@11614:   | term_of Ts (prf1 %% prf2) =
berghofe@11522:       AppPt $ term_of Ts prf1 $ term_of Ts prf2
berghofe@11614:   | term_of Ts (prf % opt) = 
wenzelm@18939:       let val t = the_default (Term.dummy_pattern dummyT) opt
berghofe@11522:       in Const ("Appt",
berghofe@11522:         [proofT, fastype_of1 (Ts, t) handle TERM _ => dummyT] ---> proofT) $
berghofe@11522:           term_of Ts prf $ t
berghofe@11522:       end
berghofe@11522:   | term_of Ts (Hyp t) = Hypt $ t
berghofe@11522:   | term_of Ts (Oracle (_, t, _)) = Oraclet $ t
berghofe@11522:   | term_of Ts (MinProof _) = MinProoft;
berghofe@11522: 
berghofe@11522: val term_of_proof = term_of [];
berghofe@11522: 
berghofe@11522: fun cterm_of_proof thy prf =
berghofe@11522:   let
berghofe@11522:     val (prf', tab) = disambiguate_names thy prf;
wenzelm@16350:     val thm_names = filter_out (equal "")
wenzelm@16350:       (map fst (PureThy.all_thms_of thy) @ map fst (Symtab.dest tab));
wenzelm@16350:     val axm_names = map fst (Theory.all_axioms_of thy);
wenzelm@16425:     val thy' = thy
wenzelm@16425:       |> add_proof_syntax
wenzelm@16425:       |> add_proof_atom_consts
wenzelm@16195:         (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names)
berghofe@11522:   in
wenzelm@16425:     (cterm_of thy' (term_of_proof prf'),
berghofe@11522:      proof_of_term thy tab true o Thm.term_of)
berghofe@11522:   end;
berghofe@11522: 
berghofe@11522: fun read_term thy =
berghofe@11522:   let
wenzelm@16350:     val thm_names = filter_out (equal "") (map fst (PureThy.all_thms_of thy));
wenzelm@16350:     val axm_names = map fst (Theory.all_axioms_of thy);
wenzelm@16425:     val thy' = thy
wenzelm@16425:       |> add_proof_syntax
wenzelm@16425:       |> add_proof_atom_consts
wenzelm@16195:         (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names)
wenzelm@22675:   in Sign.simple_read_term thy' end;
berghofe@11522: 
berghofe@11522: fun read_proof thy =
berghofe@11522:   let val rd = read_term thy proofT
berghofe@11522:   in
berghofe@11522:     (fn ty => fn s => proof_of_term thy Symtab.empty ty (Logic.varify (rd s)))
berghofe@11522:   end;
berghofe@11522: 
wenzelm@17078: fun proof_syntax prf =
berghofe@11522:   let
wenzelm@19305:     val thm_names = filter_out (equal "")
wenzelm@19305:       (map fst (Symtab.dest (thms_of_proof prf Symtab.empty)));
berghofe@17019:     val axm_names = map fst (Symtab.dest (axms_of_proof prf Symtab.empty));
berghofe@11522:   in
wenzelm@17078:     add_proof_syntax #>
wenzelm@17078:     add_proof_atom_consts
wenzelm@17078:       (map (NameSpace.append "thm") thm_names @ map (NameSpace.append "axm") axm_names)
berghofe@11522:   end;
berghofe@11522: 
wenzelm@17078: fun proof_of full thm =
wenzelm@17078:   let
wenzelm@17078:     val {thy, der = (_, prf), ...} = Thm.rep_thm thm;
wenzelm@17078:     val prop = Thm.full_prop_of thm;
wenzelm@17078:     val prf' = (case strip_combt (fst (strip_combP prf)) of
wenzelm@17078:         (PThm (_, prf', prop', _), _) => if prop = prop' then prf' else prf
wenzelm@17078:       | _ => prf)
wenzelm@17078:   in if full then Reconstruct.reconstruct_proof thy prop prf' else prf' end;
wenzelm@17078: 
wenzelm@17078: fun pretty_proof thy prf =
wenzelm@17078:   Sign.pretty_term (proof_syntax prf thy) (term_of_proof prf);
wenzelm@17078: 
berghofe@11522: fun pretty_proof_of full thm =
wenzelm@17078:   pretty_proof (Thm.theory_of_thm thm) (proof_of full thm);
berghofe@11522: 
berghofe@11522: val print_proof_of = Pretty.writeln oo pretty_proof_of;
berghofe@11522: 
berghofe@11522: end;