src/Pure/Proof/proof_syntax.ML
author wenzelm
Tue Jan 27 00:29:37 2009 +0100 (2009-01-27)
changeset 29635 31d14e9fa0da
parent 29606 fedb8be05f24
child 30344 10a67c5ddddb
permissions -rw-r--r--
proof_body: turned lazy into future -- ensures that body is fulfilled eventually, without explicit force;
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(*  Title:      Pure/Proof/proof_syntax.ML
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    Author:     Stefan Berghofer, TU Muenchen
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Function for parsing and printing proof terms.
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*)
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signature PROOF_SYNTAX =
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sig
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  val proofT: typ
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  val add_proof_syntax: theory -> theory
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  val proof_of_term: theory -> bool -> term -> Proofterm.proof
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  val term_of_proof: Proofterm.proof -> term
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  val cterm_of_proof: theory -> Proofterm.proof -> cterm * (cterm -> Proofterm.proof)
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  val read_term: theory -> typ -> string -> term
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  val read_proof: theory -> bool -> string -> Proofterm.proof
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  val proof_syntax: Proofterm.proof -> theory -> theory
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  val proof_of: bool -> thm -> Proofterm.proof
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  val pretty_proof: Proof.context -> Proofterm.proof -> Pretty.T
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  val pretty_proof_of: Proof.context -> bool -> thm -> Pretty.T
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end;
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structure ProofSyntax : PROOF_SYNTAX =
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struct
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open Proofterm;
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(**** add special syntax for embedding proof terms ****)
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val proofT = Type ("proof", []);
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val paramT = Type ("param", []);
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val paramsT = Type ("params", []);
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val idtT = Type ("idt", []);
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val aT = TFree (Name.aT, []);
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(** constants for theorems and axioms **)
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fun add_proof_atom_consts names thy =
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  thy
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  |> Sign.absolute_path
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  |> Sign.add_consts_i (map (fn name => (name, proofT, NoSyn)) names);
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(** constants for application and abstraction **)
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fun add_proof_syntax thy =
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  thy
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  |> Theory.copy
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  |> Sign.root_path
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  |> Sign.add_defsort_i []
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  |> Sign.add_types [("proof", 0, NoSyn)]
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  |> Sign.add_consts_i
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      [("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ %/ _)", [4, 5], 4)),
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       ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ %%/ _)", [4, 5], 4)),
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       ("Abst", (aT --> proofT) --> proofT, NoSyn),
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       ("AbsP", [propT, proofT --> proofT] ---> proofT, NoSyn),
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       ("Hyp", propT --> proofT, NoSyn),
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       ("Oracle", propT --> proofT, NoSyn),
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       ("MinProof", proofT, Delimfix "?")]
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  |> Sign.add_nonterminals ["param", "params"]
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  |> Sign.add_syntax_i
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      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1Lam _./ _)", [0, 3], 3)),
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       ("_Lam0", [paramT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
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       ("_Lam0", [idtT, paramsT] ---> paramsT, Mixfix ("_/ _", [1, 0], 0)),
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       ("_Lam1", [idtT, propT] ---> paramT, Mixfix ("_: _", [0, 0], 0)),
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       ("", paramT --> paramT, Delimfix "'(_')"),
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       ("", idtT --> paramsT, Delimfix "_"),
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       ("", paramT --> paramsT, Delimfix "_")]
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  |> Sign.add_modesyntax_i ("xsymbols", true)
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      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<Lambda>_./ _)", [0, 3], 3)),
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       ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
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       ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
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  |> Sign.add_modesyntax_i ("latex", false)
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      [("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<^bold>\\<lambda>_./ _)", [0, 3], 3))]
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  |> Sign.add_trrules_i (map Syntax.ParsePrintRule
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      [(Syntax.mk_appl (Constant "_Lam")
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          [Syntax.mk_appl (Constant "_Lam0") [Variable "l", Variable "m"], Variable "A"],
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        Syntax.mk_appl (Constant "_Lam")
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          [Variable "l", Syntax.mk_appl (Constant "_Lam") [Variable "m", Variable "A"]]),
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       (Syntax.mk_appl (Constant "_Lam")
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          [Syntax.mk_appl (Constant "_Lam1") [Variable "x", Variable "A"], Variable "B"],
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        Syntax.mk_appl (Constant "AbsP") [Variable "A",
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          (Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "B"])]),
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       (Syntax.mk_appl (Constant "_Lam") [Variable "x", Variable "A"],
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        Syntax.mk_appl (Constant "Abst")
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          [(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);
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(**** translation between proof terms and pure terms ****)
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fun proof_of_term thy ty =
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  let
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    val thms = PureThy.all_thms_of thy;
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    val axms = Theory.all_axioms_of thy;
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    fun mk_term t = (if ty then I else map_types (K dummyT))
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      (Term.no_dummy_patterns t);
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    fun prf_of [] (Bound i) = PBound i
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      | prf_of Ts (Const (s, Type ("proof", _))) =
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          change_type (if ty then SOME Ts else NONE)
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            (case NameSpace.explode s of
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               "axm" :: xs =>
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                 let
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                   val name = NameSpace.implode xs;
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                   val prop = (case AList.lookup (op =) axms name of
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                       SOME prop => prop
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                     | NONE => error ("Unknown axiom " ^ quote name))
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                 in PAxm (name, prop, NONE) end
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             | "thm" :: xs =>
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                 let val name = NameSpace.implode xs;
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                 in (case AList.lookup (op =) thms name of
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                     SOME thm => fst (strip_combt (Thm.proof_of thm))
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                   | NONE => error ("Unknown theorem " ^ quote name))
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                 end
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             | _ => error ("Illegal proof constant name: " ^ quote s))
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      | prf_of Ts (Const ("Hyp", _) $ prop) = Hyp prop
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      | prf_of Ts (v as Var ((_, Type ("proof", _)))) = Hyp v
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      | prf_of [] (Const ("Abst", _) $ Abs (s, T, prf)) =
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          if T = proofT then
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            error ("Term variable abstraction may not bind proof variable " ^ quote s)
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          else Abst (s, if ty then SOME T else NONE,
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            incr_pboundvars (~1) 0 (prf_of [] prf))
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      | prf_of [] (Const ("AbsP", _) $ t $ Abs (s, _, prf)) =
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          AbsP (s, case t of
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                Const ("dummy_pattern", _) => NONE
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              | _ $ Const ("dummy_pattern", _) => NONE
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              | _ => SOME (mk_term t),
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            incr_pboundvars 0 (~1) (prf_of [] prf))
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      | prf_of [] (Const ("AppP", _) $ prf1 $ prf2) =
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          prf_of [] prf1 %% prf_of [] prf2
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      | prf_of Ts (Const ("Appt", _) $ prf $ Const ("TYPE", Type (_, [T]))) =
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          prf_of (T::Ts) prf
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      | prf_of [] (Const ("Appt", _) $ prf $ t) = prf_of [] prf %
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          (case t of Const ("dummy_pattern", _) => NONE | _ => SOME (mk_term t))
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      | prf_of _ t = error ("Not a proof term:\n" ^
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          Syntax.string_of_term_global thy t)
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  in prf_of [] end;
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val AbsPt = Const ("AbsP", [propT, proofT --> proofT] ---> proofT);
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val AppPt = Const ("AppP", [proofT, proofT] ---> proofT);
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val Hypt = Const ("Hyp", propT --> proofT);
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val Oraclet = Const ("Oracle", propT --> proofT);
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val MinProoft = Const ("MinProof", proofT);
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val mk_tyapp = fold (fn T => fn prf => Const ("Appt",
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  [proofT, Term.itselfT T] ---> proofT) $ prf $ Logic.mk_type T);
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fun term_of _ (PThm (_, ((name, _, NONE), _))) =
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      Const (NameSpace.append "thm" name, proofT)
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  | term_of _ (PThm (_, ((name, _, SOME Ts), _))) =
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      mk_tyapp Ts (Const (NameSpace.append "thm" name, proofT))
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  | term_of _ (PAxm (name, _, NONE)) = Const (NameSpace.append "axm" name, proofT)
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  | term_of _ (PAxm (name, _, SOME Ts)) =
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      mk_tyapp Ts (Const (NameSpace.append "axm" name, proofT))
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  | term_of _ (PBound i) = Bound i
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  | term_of Ts (Abst (s, opT, prf)) =
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      let val T = the_default dummyT opT
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      in Const ("Abst", (T --> proofT) --> proofT) $
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        Abs (s, T, term_of (T::Ts) (incr_pboundvars 1 0 prf))
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      end
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  | term_of Ts (AbsP (s, t, prf)) =
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      AbsPt $ the_default (Term.dummy_pattern propT) t $
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        Abs (s, proofT, term_of (proofT::Ts) (incr_pboundvars 0 1 prf))
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  | term_of Ts (prf1 %% prf2) =
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      AppPt $ term_of Ts prf1 $ term_of Ts prf2
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  | term_of Ts (prf % opt) =
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      let val t = the_default (Term.dummy_pattern dummyT) opt
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      in Const ("Appt",
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        [proofT, fastype_of1 (Ts, t) handle TERM _ => dummyT] ---> proofT) $
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          term_of Ts prf $ t
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      end
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  | term_of Ts (Hyp t) = Hypt $ t
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  | term_of Ts (Oracle (_, t, _)) = Oraclet $ t
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  | term_of Ts MinProof = MinProoft;
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val term_of_proof = term_of [];
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fun cterm_of_proof thy prf =
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  let
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    val thm_names = map fst (PureThy.all_thms_of thy);
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    val axm_names = map fst (Theory.all_axioms_of thy);
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    val thy' = thy
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      |> add_proof_syntax
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      |> add_proof_atom_consts
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        (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names);
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  in
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    (cterm_of thy' (term_of_proof prf), proof_of_term thy true o Thm.term_of)
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  end;
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fun read_term thy =
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  let
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    val thm_names = filter_out (fn s => s = "") (map fst (PureThy.all_thms_of thy));
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    val axm_names = map fst (Theory.all_axioms_of thy);
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    val ctxt = thy
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      |> add_proof_syntax
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      |> add_proof_atom_consts
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        (map (NameSpace.append "axm") axm_names @ map (NameSpace.append "thm") thm_names)
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      |> ProofContext.init
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      |> ProofContext.allow_dummies
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      |> ProofContext.set_mode ProofContext.mode_schematic;
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  in
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    fn ty => fn s =>
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      (if ty = propT then Syntax.parse_prop else Syntax.parse_term) ctxt s
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      |> TypeInfer.constrain ty |> Syntax.check_term ctxt
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  end;
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fun read_proof thy =
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  let val rd = read_term thy proofT
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  in fn ty => fn s => proof_of_term thy ty (Logic.varify (rd s)) end;
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fun proof_syntax prf =
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  let
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    val thm_names = Symtab.keys (fold_proof_atoms true
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      (fn PThm (_, ((name, _, _), _)) => if name <> "" then Symtab.update (name, ()) else I
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        | _ => I) [prf] Symtab.empty);
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    val axm_names = Symtab.keys (fold_proof_atoms true
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      (fn PAxm (name, _, _) => Symtab.update (name, ()) | _ => I) [prf] Symtab.empty);
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  in
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    add_proof_syntax #>
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    add_proof_atom_consts
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      (map (NameSpace.append "thm") thm_names @ map (NameSpace.append "axm") axm_names)
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  end;
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fun proof_of full thm =
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  let
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    val thy = Thm.theory_of_thm thm;
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    val prop = Thm.full_prop_of thm;
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    val prf = Thm.proof_of thm;
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    val prf' = (case strip_combt (fst (strip_combP prf)) of
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        (PThm (_, ((_, prop', _), body)), _) => if prop = prop' then join_proof body else prf
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      | _ => prf)
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  in if full then Reconstruct.reconstruct_proof thy prop prf' else prf' end;
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fun pretty_proof ctxt prf =
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  ProofContext.pretty_term_abbrev
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    (ProofContext.transfer_syntax (proof_syntax prf (ProofContext.theory_of ctxt)) ctxt)
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    (term_of_proof prf);
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fun pretty_proof_of ctxt full th =
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  pretty_proof ctxt (proof_of full th);
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end;