(* 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 -> bool -> string -> unit
val generate_mash_feature_file_for_theory : theory -> bool -> string -> unit
val generate_mash_dependency_file_for_theory :
theory -> bool -> string -> unit
val generate_mash_problem_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
open ATP_Util
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 = #")" orelse c = #"?" orelse c = #"," then
String.str c
else if c = #"'" then
"~"
else
(* fixed width, in case more digits follow *)
"\\" ^ stringN_of_int 3 (Char.ord c)
val escape_meta = String.translate escape_meta_char
val thy_prefix = "y_"
val fact_name_of = escape_meta
val thy_name_of = prefix thy_prefix o escape_meta
val const_name_of = prefix const_prefix o escape_meta
val type_name_of = prefix type_const_prefix o escape_meta
val class_name_of = prefix class_prefix o escape_meta
val thy_name_of_thm = theory_of_thm #> Context.theory_name
fun has_thy thy th = (Context.theory_name thy = thy_name_of_thm th)
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_terms_types_and_classes thy term_max_depth type_max_depth t =
let
val ctxt = Proof_Context.init_global thy
val bad_types = [@{type_name prop}, @{type_name bool}, @{type_name fun}]
val bad_consts = atp_widely_irrelevant_consts
val add_classes =
subtract (op =) @{sort type} #> map class_name_of #> union (op =)
fun add_type (Type (s, Ts)) =
(not (member (op =) bad_types s) ? insert (op =) (type_name_of s))
#> fold add_type Ts
| add_type (TFree (_, S)) = add_classes S
| add_type (TVar (_, S)) = add_classes S
fun mk_app s args =
if member (op <>) args "?" then s ^ "(" ^ space_implode "," args ^ ")"
else s
fun patternify 0 t = "?"
| patternify depth t =
case strip_comb t of
(Const (s, _), args) =>
mk_app (const_name_of s) (map (patternify (depth - 1)) args)
| _ => "?"
fun add_term_patterns depth t =
if depth < 0 then
I
else
insert (op =) (patternify depth t)
#> add_term_patterns (depth - 1) t
val add_term = add_term_patterns term_max_depth
fun add_patterns t =
let val (head, args) = strip_comb t in
(case head of
Const (s, T) =>
not (member (op =) bad_consts s) ? (add_term t #> add_type T)
| Free (_, T) => add_type T
| Var (_, T) => add_type T
| Abs (_, T, body) => add_type T #> add_patterns body
| _ => I)
#> fold add_patterns args
end
in [] |> add_patterns t |> sort string_ord 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
val thm_ord = theory_ord o pairself theory_of_thm
fun parent_thms thy_ths thy =
Theory.parents_of thy
|> map Context.theory_name
|> map_filter (AList.lookup (op =) thy_ths)
|> map List.last
|> map (fact_name_of o Thm.get_name_hint)
val thms_by_thy =
map (snd #> `thy_name_of_thm)
#> AList.group (op =)
#> sort (int_ord
o pairself (length o Theory.ancestors_of o theory_of_thm o hd o snd))
#> map (apsnd (sort thm_ord))
fun generate_mash_accessibility_file_for_theory thy include_thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
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
|> not include_thy ? filter_out (has_thy thy o snd)
|> thms_by_thy
fun do_thy ths =
let
val thy = theory_of_thm (hd ths)
val parents = parent_thms thy_ths thy
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
fun has_bool @{typ bool} = true
| has_bool (Type (_, Ts)) = exists has_bool Ts
| has_bool _ = false
fun has_fun (Type (@{type_name fun}, _)) = true
| has_fun (Type (_, Ts)) = exists has_fun Ts
| has_fun _ = false
val is_conn = member (op =)
[@{const_name Trueprop}, @{const_name HOL.conj}, @{const_name HOL.disj},
@{const_name HOL.implies}, @{const_name Not},
@{const_name All}, @{const_name Ex}, @{const_name Ball}, @{const_name Bex},
@{const_name HOL.eq}]
val has_bool_arg_const =
exists_Const (fn (c, T) =>
not (is_conn c) andalso exists has_bool (binder_types T))
fun higher_inst_const thy (c, T) =
case binder_types T of
[] => false
| Ts => length (binder_types (Sign.the_const_type thy c)) <> length Ts
val binders = [@{const_name All}, @{const_name Ex}]
fun is_fo_term thy t =
let
val t =
t |> Envir.beta_eta_contract
|> transform_elim_prop
|> Object_Logic.atomize_term thy
in
Term.is_first_order binders t andalso
not (exists_subterm (fn Var (_, T) => has_bool T orelse has_fun T
| _ => false) t orelse
has_bool_arg_const t orelse exists_Const (higher_inst_const thy) t)
end
val is_abs = String.isSubstring Sledgehammer_Filter.pseudo_abs_name
val max_depth = 1
(* TODO: Add types, subterms *)
fun features_of thy (status, th) =
let val prop = Thm.prop_of th in
thy_name_of (thy_name_of_thm th) ::
interesting_terms_types_and_classes thy max_depth max_depth prop
(* ### skolem and "abs" *)
|> not (is_fo_term thy prop) ? cons "ho"
|> (case status of
General => I
| Induction => cons "induction"
| Intro => cons "intro"
| Inductive => cons "inductive"
| Elim => cons "elim"
| Simp => cons "simp"
| Def => cons "def")
end
fun generate_mash_feature_file_for_theory thy include_thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val facts = facts_of thy |> not include_thy ? filter_out (has_thy thy o snd)
fun do_fact ((_, (_, status)), th) =
let
val name = Thm.get_name_hint th
val feats = features_of thy (status, th)
val s = fact_name_of name ^ ": " ^ space_implode " " feats ^ "\n"
in File.append path s end
val _ = List.app do_fact facts
in () end
val dependencies_of = theorems_mentioned_in_proof_term o SOME
val known_tautologies =
[@{thm All_def}, @{thm Ex_def}, @{thm Ex1_def}, @{thm Ball_def},
@{thm Bex_def}, @{thm If_def}]
fun is_likely_tautology thy th =
(member Thm.eq_thm_prop known_tautologies th orelse
th |> prop_of |> interesting_terms_types_and_classes thy 0 ~1 |> null) andalso
not (Thm.eq_thm_prop (@{thm ext}, th))
fun generate_mash_dependency_file_for_theory thy include_thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val ths =
facts_of thy |> not include_thy ? filter_out (has_thy thy o snd)
|> map snd
val all_names =
ths |> filter_out (is_likely_tautology thy) |> map Thm.get_name_hint
fun do_thm th =
let
val name = Thm.get_name_hint th
val deps = dependencies_of all_names th
val s = fact_name_of name ^ ": " ^ space_implode " " deps ^ "\n"
in File.append path s end
val _ = List.app do_thm ths
in () end
fun generate_mash_problem_file_for_theory thy file_name =
let
val path = file_name |> Path.explode
val _ = File.write path ""
val facts = facts_of thy
val (new_facts, old_facts) =
facts |> List.partition (has_thy thy o snd)
|>> sort (thm_ord o pairself snd)
val ths = facts |> map snd
val all_names =
ths |> filter_out (is_likely_tautology thy) |> map Thm.get_name_hint
fun do_fact ((_, (_, status)), th) prevs =
let
val name = Thm.get_name_hint th
val feats = features_of thy (status, th)
val deps = dependencies_of all_names th
val th = fact_name_of name
val s =
th ^ ": " ^
space_implode " " prevs ^ "; " ^
space_implode " " feats ^ "; " ^
space_implode " " deps ^ "\n"
val _ = File.append path s
in [th] end
val thy_ths = old_facts |> thms_by_thy
val parents = parent_thms thy_ths thy
val _ = fold do_fact new_facts parents
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 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)
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 ths = facts |> map snd
val all_names =
ths |> filter_out (is_likely_tautology thy) |> map Thm.get_name_hint
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;