(* Title: Pure/Proof/proof_syntax.ML
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 proof_of_term: theory -> 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 proof_syntax: Proofterm.proof -> theory -> theory
val proof_of: bool -> thm -> Proofterm.proof
val pretty_proof: Proof.context -> Proofterm.proof -> Pretty.T
val pretty_proof_of: Proof.context -> bool -> thm -> Pretty.T
end;
structure Proof_Syntax : 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 (Name.aT, []);
(** constants for theorems and axioms **)
fun add_proof_atom_consts names thy =
thy
|> Sign.root_path
|> Sign.add_consts_i (map (fn name => (Binding.qualified_name name, proofT, NoSyn)) names);
(** constants for application and abstraction **)
fun add_proof_syntax thy =
thy
|> Theory.copy
|> Sign.root_path
|> Sign.add_defsort_i []
|> Sign.add_types [(Binding.name "proof", 0, NoSyn)]
|> fold (snd oo Sign.declare_const)
[((Binding.name "Appt", [proofT, aT] ---> proofT), Mixfix ("(1_ %/ _)", [4, 5], 4)),
((Binding.name "AppP", [proofT, proofT] ---> proofT), Mixfix ("(1_ %%/ _)", [4, 5], 4)),
((Binding.name "Abst", (aT --> proofT) --> proofT), NoSyn),
((Binding.name "AbsP", [propT, proofT --> proofT] ---> proofT), NoSyn),
((Binding.name "Hyp", propT --> proofT), NoSyn),
((Binding.name "Oracle", propT --> proofT), NoSyn),
((Binding.name "OfClass", (Term.a_itselfT --> propT) --> proofT), NoSyn),
((Binding.name "MinProof", proofT), Delimfix "?")]
|> Sign.add_nonterminals [Binding.name "param", Binding.name "params"]
|> Sign.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 "_")]
|> Sign.add_modesyntax_i (Symbol.xsymbolsN, true)
[("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<Lambda>_./ _)", [0, 3], 3)),
(Syntax.constN ^ "Appt", [proofT, aT] ---> proofT, Mixfix ("(1_ \\<cdot>/ _)", [4, 5], 4)),
(Syntax.constN ^ "AppP", [proofT, proofT] ---> proofT, Mixfix ("(1_ \\<bullet>/ _)", [4, 5], 4))]
|> Sign.add_modesyntax_i ("latex", false)
[("_Lam", [paramsT, proofT] ---> proofT, Mixfix ("(1\\<^bold>\\<lambda>_./ _)", [0, 3], 3))]
|> 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 (Syntax.constN ^ "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 (Syntax.constN ^ "Abst"))
[(Syntax.mk_appl (Constant "_abs") [Variable "x", Variable "A"])])]);
(**** translation between proof terms and pure terms ****)
fun proof_of_term thy 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_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 Long_Name.explode s of
"axm" :: xs =>
let
val name = Long_Name.implode xs;
val prop = (case AList.lookup (op =) axms name of
SOME prop => prop
| NONE => error ("Unknown axiom " ^ quote name))
in PAxm (name, prop, NONE) end
| "thm" :: xs =>
let val name = Long_Name.implode xs;
in (case AList.lookup (op =) thms name of
SOME thm => fst (strip_combt (Thm.proof_of thm))
| NONE => error ("Unknown theorem " ^ quote name))
end
| _ => error ("Illegal proof constant name: " ^ quote s))
| prf_of Ts (Const ("OfClass", _) $ Const (c_class, _)) =
(case try Logic.class_of_const c_class of
SOME c =>
change_type (if ty then SOME Ts else NONE)
(OfClass (TVar ((Name.aT, 0), []), c))
| NONE => error ("Bad class constant: " ^ quote c_class))
| 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)) =
if T = proofT then
error ("Term variable abstraction may not bind proof variable " ^ quote s)
else 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" ^
Syntax.string_of_term_global 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 OfClasst = Const ("OfClass", (Term.itselfT dummyT --> propT) --> proofT);
val MinProoft = Const ("MinProof", proofT);
val mk_tyapp = fold (fn T => fn prf => Const ("Appt",
[proofT, Term.itselfT T] ---> proofT) $ prf $ Logic.mk_type T);
fun term_of _ (PThm (_, ((name, _, NONE), _))) =
Const (Long_Name.append "thm" name, proofT)
| term_of _ (PThm (_, ((name, _, SOME Ts), _))) =
mk_tyapp Ts (Const (Long_Name.append "thm" name, proofT))
| term_of _ (PAxm (name, _, NONE)) = Const (Long_Name.append "axm" name, proofT)
| term_of _ (PAxm (name, _, SOME Ts)) =
mk_tyapp Ts (Const (Long_Name.append "axm" name, proofT))
| term_of _ (OfClass (T, c)) =
mk_tyapp [T] (OfClasst $ Const (Logic.const_of_class c, Term.itselfT dummyT --> propT))
| term_of _ (PBound i) = Bound i
| term_of Ts (Abst (s, opT, prf)) =
let val T = the_default dummyT opT
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 $ the_default (Term.dummy_pattern propT) t $
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 = the_default (Term.dummy_pattern dummyT) opt
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 thm_names = 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 (Long_Name.append "axm") axm_names @ map (Long_Name.append "thm") thm_names);
in
(cterm_of thy' (term_of_proof prf), proof_of_term thy true o Thm.term_of)
end;
fun read_term thy =
let
val thm_names = filter_out (fn s => s = "") (map fst (PureThy.all_thms_of thy));
val axm_names = map fst (Theory.all_axioms_of thy);
val ctxt = thy
|> add_proof_syntax
|> add_proof_atom_consts
(map (Long_Name.append "axm") axm_names @ map (Long_Name.append "thm") thm_names)
|> ProofContext.init
|> ProofContext.allow_dummies
|> ProofContext.set_mode ProofContext.mode_schematic;
in
fn ty => fn s =>
(if ty = propT then Syntax.parse_prop else Syntax.parse_term) ctxt s
|> TypeInfer.constrain ty |> Syntax.check_term ctxt
end;
fun read_proof thy =
let val rd = read_term thy proofT
in fn ty => fn s => proof_of_term thy ty (Logic.varify (rd s)) end;
fun proof_syntax prf =
let
val thm_names = Symtab.keys (fold_proof_atoms true
(fn PThm (_, ((name, _, _), _)) => if name <> "" then Symtab.update (name, ()) else I
| _ => I) [prf] Symtab.empty);
val axm_names = Symtab.keys (fold_proof_atoms true
(fn PAxm (name, _, _) => Symtab.update (name, ()) | _ => I) [prf] Symtab.empty);
in
add_proof_syntax #>
add_proof_atom_consts
(map (Long_Name.append "thm") thm_names @ map (Long_Name.append "axm") axm_names)
end;
fun proof_of full thm =
let
val thy = Thm.theory_of_thm thm;
val prop = Thm.full_prop_of thm;
val prf = Thm.proof_of thm;
val prf' = (case strip_combt (fst (strip_combP prf)) of
(PThm (_, ((_, prop', _), body)), _) => if prop = prop' then join_proof body else prf
| _ => prf)
in if full then Reconstruct.reconstruct_proof thy prop prf' else prf' end;
fun pretty_proof ctxt prf =
ProofContext.pretty_term_abbrev
(ProofContext.transfer_syntax (proof_syntax prf (ProofContext.theory_of ctxt)) ctxt)
(term_of_proof prf);
fun pretty_proof_of ctxt full th =
pretty_proof ctxt (proof_of full th);
end;