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(* Title: Pure/Proof/proof_syntax.ML
Author: Stefan Berghofer, TU Muenchen
Function for parsing and printing proof terms.
*)
signature PROOF_SYNTAX =
sig
val add_proof_syntax: theory -> theory
val term_of_proof: proof -> term
val proof_of_term: theory -> bool -> term -> Proofterm.proof
val read_term: theory -> bool -> typ -> string -> term
val read_proof: theory -> bool -> 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_boxes_of: Proof.context ->
{full: bool, preproc: theory -> proof -> proof} -> thm -> Pretty.T
val standard_proof_of: {full: bool, expand_name: Proofterm.thm_header -> string option} ->
thm -> Proofterm.proof
val pretty_standard_proof_of: Proof.context -> bool -> thm -> Pretty.T
end;
structure Proof_Syntax : PROOF_SYNTAX =
struct
(**** add special syntax for embedding proof terms ****)
val proofT = Type ("Pure.proof", []);
local
val paramT = Type ("param", []);
val paramsT = Type ("params", []);
val idtT = Type ("idt", []);
val aT = Term.aT [];
fun mixfix (sy, ps, p) = Mixfix (Input.string sy, ps, p, Position.no_range);
in
fun add_proof_syntax thy =
thy
|> Sign.root_path
|> Sign.set_defsort []
|> Sign.add_nonterminals_global
[Binding.make ("param", \<^here>),
Binding.make ("params", \<^here>)]
|> Sign.add_syntax Syntax.mode_default
[("_Lam", [paramsT, proofT] ---> proofT, mixfix ("(1\<^bold>\_./ _)", [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, Mixfix.mixfix "'(_')"),
("", idtT --> paramsT, Mixfix.mixfix "_"),
("", paramT --> paramsT, Mixfix.mixfix "_"),
(Lexicon.mark_const "Pure.Appt", [proofT, aT] ---> proofT, mixfix ("(1_ \/ _)", [4, 5], 4)),
(Lexicon.mark_const "Pure.AppP", [proofT, proofT] ---> proofT, mixfix ("(1_ \/ _)", [4, 5], 4)),
(Lexicon.mark_const "Pure.MinProof", proofT, Mixfix.mixfix "\<^bold>?")]
|> Sign.add_trrules (map Syntax.Parse_Print_Rule
[(Ast.mk_appl (Ast.Constant "_Lam")
[Ast.mk_appl (Ast.Constant "_Lam0")
[Ast.Variable "l", Ast.Variable "m"], Ast.Variable "A"],
Ast.mk_appl (Ast.Constant "_Lam")
[Ast.Variable "l",
Ast.mk_appl (Ast.Constant "_Lam") [Ast.Variable "m", Ast.Variable "A"]]),
(Ast.mk_appl (Ast.Constant "_Lam")
[Ast.mk_appl (Ast.Constant "_Lam1")
[Ast.Variable "x", Ast.Variable "A"], Ast.Variable "B"],
Ast.mk_appl (Ast.Constant (Lexicon.mark_const "Pure.AbsP")) [Ast.Variable "A",
(Ast.mk_appl (Ast.Constant "_abs") [Ast.Variable "x", Ast.Variable "B"])]),
(Ast.mk_appl (Ast.Constant "_Lam") [Ast.Variable "x", Ast.Variable "A"],
Ast.mk_appl (Ast.Constant (Lexicon.mark_const "Pure.Abst"))
[(Ast.mk_appl (Ast.Constant "_abs") [Ast.Variable "x", Ast.Variable "A"])])]);
end;
(** constants for theorems and axioms **)
fun add_proof_atom_consts names thy =
thy
|> Sign.root_path
|> Sign.add_consts (map (fn name => (Binding.qualified_name name, proofT, NoSyn)) names);
(** proof terms as pure terms **)
(* term_of_proof *)
local
val AbsPt = Const ("Pure.AbsP", propT --> (proofT --> proofT) --> proofT);
val AppPt = Const ("Pure.AppP", proofT --> proofT --> proofT);
val Hypt = Const ("Pure.Hyp", propT --> proofT);
val Oraclet = Const ("Pure.Oracle", propT --> proofT);
val MinProoft = Const ("Pure.MinProof", proofT);
fun AppT T prf =
Const ("Pure.Appt", proofT --> Term.itselfT T --> proofT) $ prf $ Logic.mk_type T;
fun PClasst (T, c) =
let val U = Term.itselfT T --> propT
in Const ("Pure.PClass", U --> proofT) $ Const (Logic.const_of_class c, U) end;
fun term_of _ (PThm ({serial = i, name, types = Ts, ...}, _)) =
fold AppT (these Ts)
(Const (Long_Name.append "thm" (if name = "" then string_of_int i else name), proofT))
| term_of _ (PAxm (name, _, Ts)) =
fold AppT (these Ts) (Const (Long_Name.append "axm" name, proofT))
| term_of _ (PClass (T, c)) = AppT T (PClasst (T, c))
| term_of _ (PBound i) = Bound i
| term_of Ts (Abst (s, opT, prf)) =
let val T = the_default dummyT opT in
Const ("Pure.Abst", (T --> proofT) --> proofT) $
Abs (s, T, term_of (T::Ts) (Proofterm.incr_pboundvars 1 0 prf))
end
| term_of Ts (AbsP (s, t, prf)) =
AbsPt $ the_default Term.dummy_prop t $
Abs (s, proofT, term_of (proofT::Ts) (Proofterm.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 opt;
val T = fastype_of1 (Ts, t) handle TERM _ => dummyT;
in Const ("Pure.Appt", proofT --> T --> proofT) $ term_of Ts prf $ t end
| term_of _ (Hyp t) = Hypt $ t
| term_of _ (Oracle (_, t, _)) = Oraclet $ t
| term_of _ MinProof = MinProoft;
in
val term_of_proof = term_of [];
end;
(* proof_of_term *)
fun proof_of_term thy ty =
let
val thms = Global_Theory.all_thms_of thy true;
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 ("Pure.proof", _))) =
Proofterm.change_types (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 (Proofterm.strip_combt (fst (Proofterm.strip_combP (Thm.proof_of thm))))
| NONE => error ("Unknown theorem " ^ quote name))
end
| _ => error ("Illegal proof constant name: " ^ quote s))
| prf_of Ts (Const ("Pure.PClass", _) $ Const (c_class, _)) =
(case try Logic.class_of_const c_class of
SOME c =>
Proofterm.change_types (if ty then SOME Ts else NONE)
(PClass (TVar ((Name.aT, 0), []), c))
| NONE => error ("Bad class constant: " ^ quote c_class))
| prf_of Ts (Const ("Pure.Hyp", _) $ prop) = Hyp prop
| prf_of Ts (v as Var ((_, Type ("Pure.proof", _)))) = Hyp v
| prf_of [] (Const ("Pure.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,
Proofterm.incr_pboundvars (~1) 0 (prf_of [] prf))
| prf_of [] (Const ("Pure.AbsP", _) $ t $ Abs (s, _, prf)) =
AbsP (s, case t of
Const ("Pure.dummy_pattern", _) => NONE
| _ $ Const ("Pure.dummy_pattern", _) => NONE
| _ => SOME (mk_term t),
Proofterm.incr_pboundvars 0 (~1) (prf_of [] prf))
| prf_of [] (Const ("Pure.AppP", _) $ prf1 $ prf2) =
prf_of [] prf1 %% prf_of [] prf2
| prf_of Ts (Const ("Pure.Appt", _) $ prf $ Const ("Pure.type", Type ("itself", [T]))) =
prf_of (T::Ts) prf
| prf_of [] (Const ("Pure.Appt", _) $ prf $ t) = prf_of [] prf %
(case t of Const ("Pure.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;
fun read_term thy topsort =
let
val thm_names = filter_out (fn s => s = "") (map fst (Global_Theory.all_thms_of thy true));
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)
|> Proof_Context.init_global
|> Proof_Context.allow_dummies
|> Proof_Context.set_mode Proof_Context.mode_schematic
|> topsort ?
(Proof_Context.set_defsort [] #>
Config.put Type_Infer.object_logic false #>
Config.put Type_Infer_Context.const_sorts false);
in
fn ty => fn s =>
(if ty = propT then Syntax.parse_prop else Syntax.parse_term) ctxt s
|> Type.constraint ty |> Syntax.check_term ctxt
end;
fun read_proof thy topsort =
let val rd = read_term thy topsort proofT
in fn ty => fn s => proof_of_term thy ty (Logic.varify_global (rd s)) end;
fun proof_syntax prf =
let
val thm_names = Symtab.keys (Proofterm.fold_proof_atoms true
(fn PThm ({name, ...}, _) => if name <> "" then Symtab.update (name, ()) else I
| _ => I) [prf] Symtab.empty);
val axm_names = Symtab.keys (Proofterm.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;
in
(case fst (Proofterm.strip_combt (fst (Proofterm.strip_combP prf))) of
PThm ({prop = prop', ...}, thm_body) =>
if prop = prop' then Proofterm.thm_body_proof_raw thm_body else prf
| _ => prf)
|> full ? Proofterm.reconstruct_proof thy prop
end;
fun pretty_proof ctxt prf =
Proof_Context.pretty_term_abbrev
(Proof_Context.transfer (proof_syntax prf (Proof_Context.theory_of ctxt)) ctxt)
(term_of_proof prf);
fun pretty_proof_boxes_of ctxt {full, preproc} thm =
let
val thy = Proof_Context.theory_of ctxt;
val selection =
{included = Proofterm.this_id (Thm.derivation_id thm),
excluded = is_some o Global_Theory.lookup_thm_id thy}
in
Proofterm.proof_boxes selection [Thm.proof_of thm]
|> map (fn ({serial = i, pos, prop, ...}, proof) =>
let
val proof' = proof
|> Proofterm.reconstruct_proof thy prop
|> preproc thy
|> not full ? Proofterm.shrink_proof
|> Proofterm.forall_intr_variables prop;
val prop' = prop
|> Proofterm.forall_intr_variables_term;
val name = Long_Name.append "thm" (string_of_int i);
in
Pretty.item
[Pretty.str (name ^ Position.here_list pos ^ ":"), Pretty.brk 1,
Syntax.pretty_term ctxt prop', Pretty.fbrk, pretty_proof ctxt proof']
end)
|> Pretty.chunks
end;
(* standardized proofs *)
fun standard_proof_of {full, expand_name} thm =
let val thy = Thm.theory_of_thm thm in
Thm.reconstruct_proof_of thm
|> Proofterm.expand_proof thy expand_name
|> Proofterm.rewrite_proof thy ([], Proof_Rewrite_Rules.rprocs true)
|> Proofterm.no_thm_proofs
|> not full ? Proofterm.shrink_proof
end;
fun pretty_standard_proof_of ctxt full thm =
pretty_proof ctxt (standard_proof_of {full = full, expand_name = Thm.expand_name thm} thm);
end;
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