diff -r 80acc6ce26c3 -r 42fbb6abed5a src/Pure/Proof/proof_syntax.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/Proof/proof_syntax.ML Fri Aug 31 16:17:05 2001 +0200 @@ -0,0 +1,267 @@ +(* Title: Pure/Proof/proof_syntax.ML + ID: $Id$ + Author: Stefan Berghofer + Copyright 2000 TU Muenchen + +Function for parsing and printing proof terms. +*) + +signature PROOF_SYNTAX = +sig + val proofT : typ + val add_proof_syntax : Sign.sg -> Sign.sg + 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 : Sign.sg -> 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 lamT = Type ("lam_syn", []); +val idtT = Type ("idt", []); +val aT = TFree ("'a", ["logic"]); + +(** constants for theorems and axioms **) + +fun add_prefix a b = NameSpace.pack (a :: NameSpace.unpack b); + +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)), + ("Abst", (aT --> proofT) --> proofT, NoSyn), + ("AbsP", [propT, proofT --> proofT] ---> proofT, NoSyn)] + |> Sign.add_nonterminals ["lam_syn"] + |> 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))] + |> Sign.add_modesyntax_i (("xsymbols", true), + [("_Lam", [lamT, proofT] ---> proofT, Mixfix ("(3\\_./ _)", [0,0], 1)), + ("Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\/ _)", [4, 5], 4)), + ("AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\/ _)", [4, 5], 4))]) + |> Sign.add_trrules_i (map Syntax.ParsePrintRule + [(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 "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"]])]); + + +(**** 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)) (flat + (map PureThy.thms_of (thy :: Theory.ancestors_of thy))); + + val tab = Symtab.foldl (fn (tab, (key, ps)) => + let val prop = if_none (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) (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 (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 + 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 change_type T (PThm (name, prf, prop, _)) = PThm (name, prf, prop, T) + | change_type T (PAxm (name, prop, _)) = PAxm (name, prop, T) + | change_type _ _ = error "Not a proper theorem"; + +fun proof_of_term thy tab ty = + 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 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 (#2 (#der (rep_thm 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 (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, + 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 t) + | prf_of _ t = error ("Not a proof term:\n" ^ + Sign.string_of_term (sign_of thy) t) + + in prf_of [] end; + + +val AbsPt = Const ("AbsP", [propT, proofT --> proofT] ---> proofT); +val AppPt = Const ("AppP", [proofT, proofT] ---> proofT); +val Hypt = Free ("Hyp", propT --> proofT); +val Oraclet = Free ("Oracle", propT --> proofT); +val MinProoft = Free ("?", proofT); + +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) + | 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) + | term_of _ (PAxm (name, _, Some 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) = + AppPt $ term_of Ts prf1 $ term_of Ts prf2 + | 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 + | 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 thys = thy :: Theory.ancestors_of thy; + val thm_names = filter_out (equal "") (map fst (flat (map thms_of thys))) @ + 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) + in + (cterm_of sg (term_of_proof prf'), + proof_of_term thy tab true o Thm.term_of) + end; + +fun read_term thy = + let + val thys = thy :: Theory.ancestors_of thy; + 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) + in + (fn T => fn s => Thm.term_of (read_cterm sg (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 sg 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 sg' = sg |> + add_proof_syntax |> + add_proof_atom_consts + (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 = + let + val {sign, 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 sign + (if full then Reconstruct.reconstruct_prf sign prop prf' else prf') + end; + +val print_proof_of = Pretty.writeln oo pretty_proof_of; + +end;