(* Title: HOL/TPTP/atp_theory_export.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2011
Export Isabelle theories as MaSh (Machine-learning for Sledgehammer) or as
first-order TPTP inferences.
*)
signature ATP_THEORY_EXPORT =
sig
type atp_format = ATP_Problem.atp_format
val theorems_mentioned_in_proof_term :
string list option -> thm -> string list
val generate_mash_accessibility_file_for_theory : theory -> string -> unit
val generate_mash_feature_file_for_theory :
Proof.context -> theory -> string -> unit
val generate_mash_dependency_file_for_theory : theory -> string -> unit
val generate_tptp_inference_file_for_theory :
Proof.context -> theory -> atp_format -> string -> string -> unit
end;
structure ATP_Theory_Export : ATP_THEORY_EXPORT =
struct
open ATP_Problem
open ATP_Proof
open ATP_Problem_Generate
open ATP_Systems
fun stringN_of_int 0 _ = ""
| stringN_of_int k n =
stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
fun escape_meta_char c =
if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse
c = #")" then
String.str c
else
(* fixed width, in case more digits follow *)
"~" ^ stringN_of_int 3 (Char.ord c)
val escape_meta = String.translate escape_meta_char
val fact_name_of = escape_meta
val thy_name_of = escape_meta
fun facts_of thy =
let val ctxt = Proof_Context.init_global thy in
Sledgehammer_Filter.all_facts ctxt false Symtab.empty true [] []
(Sledgehammer_Filter.clasimpset_rule_table_of ctxt)
|> filter (curry (op =) @{typ bool} o fastype_of
o Object_Logic.atomize_term thy o prop_of o snd)
|> rev
end
(* FIXME: Similar yet different code in "mirabelle.ML". The code here has a few
fixes that seem to be missing over there; or maybe the two code portions are
not doing the same? *)
fun fold_body_thms thm_name f =
let
fun app n (PBody {thms, ...}) =
thms |> fold (fn (_, (name, prop, body)) => fn x =>
let
val body' = Future.join body
val n' =
n + (if name = "" orelse
(* uncommon case where the proved theorem occurs twice
(e.g., "Transitive_Closure.trancl_into_trancl") *)
(n = 1 andalso name = thm_name) then
0
else
1)
val x' = x |> n' <= 1 ? app n' body'
in (x' |> n = 1 ? f (name, prop, body')) end)
in fold (app 0) end
fun theorems_mentioned_in_proof_term all_names th =
let
val is_name_ok =
case all_names of
SOME names => member (op =) names
| NONE => (fn s => s <> "" andalso not (String.isPrefix "Pure." s))
fun collect (s, _, _) = is_name_ok s ? insert (op =) s
val names =
[] |> fold_body_thms (Thm.get_name_hint th) collect [Thm.proof_body_of th]
|> map fact_name_of
in names end
fun interesting_const_names ctxt =
let val thy = Proof_Context.theory_of ctxt in
Sledgehammer_Filter.const_names_in_fact thy
(Sledgehammer_Provers.is_built_in_const_for_prover ctxt eN)
end
fun theory_ord p =
if Theory.eq_thy p then EQUAL
else if Theory.subthy p then LESS
else if Theory.subthy (swap p) then GREATER
else EQUAL
fun generate_mash_accessibility_file_for_theory thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val thy_name_of_thm = theory_of_thm #> Context.theory_name
fun do_thm th prevs =
let
val s = th ^ ": " ^ space_implode " " prevs ^ "\n"
val _ = File.append path s
in [th] end
val thy_ths =
facts_of thy
|> map (snd #> `thy_name_of_thm)
|> AList.group (op =)
|> sort (theory_ord o pairself (theory_of_thm o hd o snd))
|> map (apsnd (sort (theory_ord o pairself theory_of_thm)))
fun do_thy ths =
let
val thy = theory_of_thm (hd ths)
val parents =
Theory.parents_of thy
|> map (thy_name_of o Context.theory_name)
|> map_filter (AList.lookup (op =) thy_ths)
|> map List.last
|> map (fact_name_of o Thm.get_name_hint)
val ths = ths |> map (fact_name_of o Thm.get_name_hint)
val _ = fold do_thm ths parents
in () end
val _ = List.app (do_thy o snd) thy_ths
in () end
(* TODO: Add types, subterms *)
fun generate_mash_feature_file_for_theory ctxt thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val axioms = Theory.all_axioms_of thy |> map fst
val facts = facts_of thy
fun do_fact ((_, (_, status)), th) =
let
val is_boring =
String.isSubstring Sledgehammer_Filter.pseudo_skolem_prefix
val name = Thm.get_name_hint th
val features =
map (prefix const_prefix o escape_meta)
(interesting_const_names ctxt (Thm.prop_of th))
|> (fn features =>
features |> forall is_boring features
? cons "likely_tautology")
|> (member (op =) axioms name ? cons "axiom")
|> (case status of
General => I
| Induction => cons "induction"
| Intro => cons "intro"
| Inductive => cons "inductive"
| Elim => cons "elim"
| Simp => cons "simp"
| Def => cons "def")
val s = fact_name_of name ^ ": " ^ space_implode " " features ^ "\n"
in File.append path s end
val _ = List.app do_fact facts
in () end
fun generate_mash_dependency_file_for_theory thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val ths = facts_of thy |> map snd
val all_names = map Thm.get_name_hint ths
fun do_thm th =
let
val name = Thm.get_name_hint th
val ths = theorems_mentioned_in_proof_term (SOME all_names) th
val s = fact_name_of name ^ ": " ^ space_implode " " ths ^ "\n"
in File.append path s end
val _ = List.app do_thm ths
in () end
fun inference_term [] = NONE
| inference_term ss =
ATerm (("inference", []),
[ATerm (("isabelle", []), []),
ATerm ((tptp_empty_list, []), []),
ATerm ((tptp_empty_list, []),
map (fn s => ATerm ((s, []), [])) ss)])
|> SOME
fun inference infers ident =
these (AList.lookup (op =) infers ident) |> inference_term
fun add_inferences_to_problem_line infers
(Formula (ident, Axiom, phi, NONE, tms)) =
Formula (ident, Lemma, phi, inference infers ident, tms)
| add_inferences_to_problem_line _ line = line
fun add_inferences_to_problem infers =
map (apsnd (map (add_inferences_to_problem_line infers)))
fun ident_of_problem_line (Class_Decl (ident, _, _)) = ident
| ident_of_problem_line (Type_Decl (ident, _, _)) = ident
| ident_of_problem_line (Sym_Decl (ident, _, _)) = ident
| ident_of_problem_line (Class_Memb (ident, _, _, _)) = ident
| ident_of_problem_line (Formula (ident, _, _, _, _)) = ident
fun run_some_atp ctxt format problem =
let
val thy = Proof_Context.theory_of ctxt
val prob_file = File.tmp_path (Path.explode "prob")
val atp = case format of DFG _ => spassN | _ => eN
val {exec, arguments, proof_delims, known_failures, ...} =
get_atp thy atp ()
val ord = effective_term_order ctxt atp
val _ = problem |> lines_for_atp_problem format ord (K [])
|> File.write_list prob_file
val path = getenv (List.last (fst exec)) ^ "/" ^ snd exec
val command =
File.shell_path (Path.explode path) ^
" " ^ arguments ctxt false "" (seconds 1.0) (ord, K [], K []) ^ " " ^
File.shell_path prob_file
in
TimeLimit.timeLimit (seconds 0.3) Isabelle_System.bash_output command
|> fst
|> extract_tstplike_proof_and_outcome false true proof_delims known_failures
|> snd
end
handle TimeLimit.TimeOut => SOME TimedOut
val likely_tautology_prefixes =
[@{theory HOL}, @{theory Meson}, @{theory ATP}, @{theory Metis}]
|> map (fact_name_of o Context.theory_name)
fun is_problem_line_tautology ctxt format (Formula (ident, _, phi, _, _)) =
exists (fn prefix => String.isPrefix prefix ident)
likely_tautology_prefixes andalso
is_none (run_some_atp ctxt format
[(factsN, [Formula (ident, Conjecture, phi, NONE, [])])])
| is_problem_line_tautology _ _ _ = false
fun order_facts ord = sort (ord o pairself ident_of_problem_line)
fun order_problem_facts _ [] = []
| order_problem_facts ord ((heading, lines) :: problem) =
if heading = factsN then (heading, order_facts ord lines) :: problem
else (heading, lines) :: order_problem_facts ord problem
(* A fairly random selection of types used for monomorphizing. *)
val ground_types =
[@{typ nat}, HOLogic.intT, HOLogic.realT, @{typ "nat => bool"}, @{typ bool},
@{typ unit}]
fun ground_type_for_tvar _ [] tvar =
raise TYPE ("ground_type_for_sorts", [TVar tvar], [])
| ground_type_for_tvar thy (T :: Ts) tvar =
if can (Sign.typ_match thy (TVar tvar, T)) Vartab.empty then T
else ground_type_for_tvar thy Ts tvar
fun monomorphize_term ctxt t =
let val thy = Proof_Context.theory_of ctxt in
t |> map_types (map_type_tvar (ground_type_for_tvar thy ground_types))
handle TYPE _ => @{prop True}
end
fun generate_tptp_inference_file_for_theory ctxt thy format type_enc file_name =
let
val type_enc = type_enc |> type_enc_from_string Strict
|> adjust_type_enc format
val mono = not (is_type_enc_polymorphic type_enc)
val path = file_name |> Path.explode
val _ = File.write path ""
val facts = facts_of thy
val atp_problem =
facts
|> map (fn ((_, loc), th) =>
((Thm.get_name_hint th, loc),
th |> prop_of |> mono ? monomorphize_term ctxt))
|> prepare_atp_problem ctxt format Axiom type_enc Exporter combsN false
false true [] @{prop False}
|> #1
val atp_problem =
atp_problem
|> map (apsnd (filter_out (is_problem_line_tautology ctxt format)))
val all_names = facts |> map (Thm.get_name_hint o snd)
val infers =
facts |> map (fn (_, th) =>
(fact_name_of (Thm.get_name_hint th),
theorems_mentioned_in_proof_term (SOME all_names) th))
val all_atp_problem_names =
atp_problem |> maps (map ident_of_problem_line o snd)
val infers =
infers |> filter (member (op =) all_atp_problem_names o fst)
|> map (apsnd (filter (member (op =) all_atp_problem_names)))
val ordered_names =
String_Graph.empty
|> fold (String_Graph.new_node o rpair ()) all_atp_problem_names
|> fold (fn (to, froms) =>
fold (fn from => String_Graph.add_edge (from, to)) froms)
infers
|> String_Graph.topological_order
val order_tab =
Symtab.empty
|> fold (Symtab.insert (op =))
(ordered_names ~~ (1 upto length ordered_names))
val name_ord = int_ord o pairself (the o Symtab.lookup order_tab)
val atp_problem =
atp_problem
|> (case format of DFG _ => I | _ => add_inferences_to_problem infers)
|> order_problem_facts name_ord
val ord = effective_term_order ctxt eN (* dummy *)
val ss = lines_for_atp_problem format ord (K []) atp_problem
val _ = app (File.append path) ss
in () end
end;