(* Author: Jia Meng, Cambridge University Computer Laboratory, NICTA
ID: $Id$
Copyright 2004 University of Cambridge
ATPs with TPTP format input.
*)
(*Currently unused, during debugging*)
signature RES_ATP =
sig
val prover: string ref
val custom_spass: string list ref
val destdir: string ref
val helper_path: string -> string -> string
val problem_name: string ref
val time_limit: int ref
val set_prover: string -> unit
datatype mode = Auto | Fol | Hol
val linkup_logic_mode : mode ref
val write_subgoal_file: bool -> mode -> Proof.context -> thm list -> thm list -> int -> string
val vampire_time: int ref
val eprover_time: int ref
val spass_time: int ref
val run_vampire: int -> unit
val run_eprover: int -> unit
val run_spass: int -> unit
val vampireLimit: unit -> int
val eproverLimit: unit -> int
val spassLimit: unit -> int
val atp_method: (Proof.context -> thm list -> int -> tactic) ->
Method.src -> Proof.context -> Proof.method
val cond_rm_tmp: string -> unit
val hol_full_types: unit -> unit
val hol_partial_types: unit -> unit
val hol_const_types_only: unit -> unit
val hol_no_types: unit -> unit
val hol_typ_level: unit -> ResHolClause.type_level
val include_all: bool ref
val run_relevance_filter: bool ref
val run_blacklist_filter: bool ref
val blacklist: string list ref
val add_all : unit -> unit
val add_claset : unit -> unit
val add_simpset : unit -> unit
val add_clasimp : unit -> unit
val add_atpset : unit -> unit
val rm_all : unit -> unit
val rm_claset : unit -> unit
val rm_simpset : unit -> unit
val rm_atpset : unit -> unit
val rm_clasimp : unit -> unit
val is_fol_thms : thm list -> bool
end;
structure ResAtp =
struct
fun timestamp s = Output.debug ("At " ^ Time.toString (Time.now()) ^ ": " ^ s);
(********************************************************************)
(* some settings for both background automatic ATP calling procedure*)
(* and also explicit ATP invocation methods *)
(********************************************************************)
(*** background linkup ***)
val call_atp = ref false;
val hook_count = ref 0;
val time_limit = ref 60;
val prover = ref "";
fun set_prover atp =
case String.map Char.toLower atp of
"e" =>
(ReduceAxiomsN.max_new := 100;
ReduceAxiomsN.theory_const := false;
prover := "E")
| "spass" =>
(ReduceAxiomsN.max_new := 40;
ReduceAxiomsN.theory_const := true;
prover := "spass")
| "vampire" =>
(ReduceAxiomsN.max_new := 60;
ReduceAxiomsN.theory_const := false;
prover := "vampire")
| _ => error ("No such prover: " ^ atp);
val _ = set_prover "E"; (* use E as the default prover *)
val custom_spass = (*specialized options for SPASS*)
ref ["-Auto=0","-FullRed=0","-IORe","-IOFc","-RTaut","-RFSub","-RBSub"];
val destdir = ref ""; (*Empty means write files to /tmp*)
val problem_name = ref "prob";
(*Return the path to a "helper" like SPASS or tptp2X, first checking that
it exists. FIXME: modify to use Path primitives and move to some central place.*)
fun helper_path evar base =
case getenv evar of
"" => error ("Isabelle environment variable " ^ evar ^ " not defined")
| home =>
let val path = home ^ "/" ^ base
in if File.exists (File.unpack_platform_path path) then path
else error ("Could not find the file " ^ path)
end;
fun probfile_nosuffix _ =
if !destdir = "" then File.platform_path (File.tmp_path (Path.basic (!problem_name)))
else if File.exists (File.unpack_platform_path (!destdir))
then !destdir ^ "/" ^ !problem_name
else error ("No such directory: " ^ !destdir);
fun prob_pathname n = probfile_nosuffix n ^ "_" ^ Int.toString n;
(*** ATP methods ***)
val vampire_time = ref 60;
val eprover_time = ref 60;
val spass_time = ref 60;
fun run_vampire time =
if (time >0) then vampire_time:= time
else vampire_time:=60;
fun run_eprover time =
if (time > 0) then eprover_time:= time
else eprover_time:=60;
fun run_spass time =
if (time > 0) then spass_time:=time
else spass_time:=60;
fun vampireLimit () = !vampire_time;
fun eproverLimit () = !eprover_time;
fun spassLimit () = !spass_time;
val hol_full_types = ResHolClause.full_types;
val hol_partial_types = ResHolClause.partial_types;
val hol_const_types_only = ResHolClause.const_types_only;
val hol_no_types = ResHolClause.no_types;
fun hol_typ_level () = ResHolClause.find_typ_level ();
fun is_typed_hol () =
let val tp_level = hol_typ_level()
in
not (tp_level = ResHolClause.T_NONE)
end;
fun atp_input_file () =
let val file = !problem_name
in
if !destdir = "" then File.platform_path (File.tmp_path (Path.basic file))
else if File.exists (File.unpack_platform_path (!destdir))
then !destdir ^ "/" ^ file
else error ("No such directory: " ^ !destdir)
end;
val include_all = ref true;
val include_simpset = ref false;
val include_claset = ref false;
val include_atpset = ref true;
(*Tests show that follow_defs gives VERY poor results with "include_all"*)
fun add_all() = (include_all:=true; ReduceAxiomsN.follow_defs := false);
fun rm_all() = include_all:=false;
fun add_simpset() = include_simpset:=true;
fun rm_simpset() = include_simpset:=false;
fun add_claset() = include_claset:=true;
fun rm_claset() = include_claset:=false;
fun add_clasimp() = (include_simpset:=true;include_claset:=true);
fun rm_clasimp() = (include_simpset:=false;include_claset:=false);
fun add_atpset() = include_atpset:=true;
fun rm_atpset() = include_atpset:=false;
(**** relevance filter ****)
val run_relevance_filter = ReduceAxiomsN.run_relevance_filter;
val run_blacklist_filter = ref true;
(******************************************************************)
(* detect whether a given problem (clauses) is FOL/HOL/HOLC/HOLCS *)
(******************************************************************)
datatype logic = FOL | HOL | HOLC | HOLCS;
fun string_of_logic FOL = "FOL"
| string_of_logic HOL = "HOL"
| string_of_logic HOLC = "HOLC"
| string_of_logic HOLCS = "HOLCS";
fun is_fol_logic FOL = true
| is_fol_logic _ = false
(*HOLCS will not occur here*)
fun upgrade_lg HOLC _ = HOLC
| upgrade_lg HOL HOLC = HOLC
| upgrade_lg HOL _ = HOL
| upgrade_lg FOL lg = lg;
(* check types *)
fun has_bool_hfn (Type("bool",_)) = true
| has_bool_hfn (Type("fun",_)) = true
| has_bool_hfn (Type(_, Ts)) = exists has_bool_hfn Ts
| has_bool_hfn _ = false;
fun is_hol_fn tp =
let val (targs,tr) = strip_type tp
in
exists (has_bool_hfn) (tr::targs)
end;
fun is_hol_pred tp =
let val (targs,tr) = strip_type tp
in
exists (has_bool_hfn) targs
end;
exception FN_LG of term;
fun fn_lg (t as Const(f,tp)) (lg,seen) =
if is_hol_fn tp then (upgrade_lg HOL lg, insert (op =) t seen) else (lg, insert (op =) t seen)
| fn_lg (t as Free(f,tp)) (lg,seen) =
if is_hol_fn tp then (upgrade_lg HOL lg, insert (op =) t seen) else (lg, insert (op =) t seen)
| fn_lg (t as Var(f,tp)) (lg,seen) =
if is_hol_fn tp then (upgrade_lg HOL lg,insert (op =) t seen) else (lg,insert (op =) t seen)
| fn_lg (t as Abs(_,_,_)) (lg,seen) = (upgrade_lg HOLC lg,insert (op =) t seen)
| fn_lg f _ = raise FN_LG(f);
fun term_lg [] (lg,seen) = (lg,seen)
| term_lg (tm::tms) (FOL,seen) =
let val (f,args) = strip_comb tm
val (lg',seen') = if f mem seen then (FOL,seen)
else fn_lg f (FOL,seen)
in
if is_fol_logic lg' then ()
else Output.debug ("Found a HOL term: " ^ Display.raw_string_of_term f);
term_lg (args@tms) (lg',seen')
end
| term_lg _ (lg,seen) = (lg,seen)
exception PRED_LG of term;
fun pred_lg (t as Const(P,tp)) (lg,seen)=
if is_hol_pred tp then (upgrade_lg HOL lg, insert (op =) t seen)
else (lg,insert (op =) t seen)
| pred_lg (t as Free(P,tp)) (lg,seen) =
if is_hol_pred tp then (upgrade_lg HOL lg, insert (op =) t seen)
else (lg,insert (op =) t seen)
| pred_lg (t as Var(_,_)) (lg,seen) = (upgrade_lg HOL lg, insert (op =) t seen)
| pred_lg P _ = raise PRED_LG(P);
fun lit_lg (Const("Not",_) $ P) (lg,seen) = lit_lg P (lg,seen)
| lit_lg P (lg,seen) =
let val (pred,args) = strip_comb P
val (lg',seen') = if pred mem seen then (lg,seen)
else pred_lg pred (lg,seen)
in
if is_fol_logic lg' then ()
else Output.debug ("Found a HOL predicate: " ^ Display.raw_string_of_term pred);
term_lg args (lg',seen')
end;
fun lits_lg [] (lg,seen) = (lg,seen)
| lits_lg (lit::lits) (FOL,seen) =
let val (lg,seen') = lit_lg lit (FOL,seen)
in
if is_fol_logic lg then ()
else Output.debug ("Found a HOL literal: " ^ Display.raw_string_of_term lit);
lits_lg lits (lg,seen')
end
| lits_lg lits (lg,seen) = (lg,seen);
fun dest_disj_aux (Const("Trueprop",_) $ t) disjs = dest_disj_aux t disjs
| dest_disj_aux (Const ("op |", _) $ t $ t') disjs = dest_disj_aux t (dest_disj_aux t' disjs)
| dest_disj_aux t disjs = t::disjs;
fun dest_disj t = dest_disj_aux t [];
fun logic_of_clause tm = lits_lg (dest_disj tm);
fun logic_of_clauses [] (lg,seen) = (lg,seen)
| logic_of_clauses (cls::clss) (FOL,seen) =
let val (lg,seen') = logic_of_clause cls (FOL,seen)
val _ =
if is_fol_logic lg then ()
else Output.debug ("Found a HOL clause: " ^ Display.raw_string_of_term cls)
in
logic_of_clauses clss (lg,seen')
end
| logic_of_clauses (cls::clss) (lg,seen) = (lg,seen);
fun problem_logic_goals_aux [] (lg,seen) = lg
| problem_logic_goals_aux (subgoal::subgoals) (lg,seen) =
problem_logic_goals_aux subgoals (logic_of_clauses subgoal (lg,seen));
fun problem_logic_goals subgoals = problem_logic_goals_aux subgoals (FOL,[]);
fun is_fol_thms ths = ((fst(logic_of_clauses (map prop_of ths) (FOL,[]))) = FOL);
(***************************************************************)
(* Retrieving and filtering lemmas *)
(***************************************************************)
(*** white list and black list of lemmas ***)
(*The rule subsetI is frequently omitted by the relevance filter.*)
val whitelist = ref [subsetI];
(*Names of theorems (not theorem lists! See multi_blacklist below) to be banned.
These theorems typically produce clauses that are prolific (match too many equality or
membership literals) and relate to seldom-used facts. Some duplicate other rules.
FIXME: this blacklist needs to be maintained using theory data and added to using
an attribute.*)
val blacklist = ref
["Datatype.prod.size",
"Divides.dvd_0_left_iff",
"Finite_Set.card_0_eq",
"Finite_Set.card_infinite",
"Finite_Set.Max_ge",
"Finite_Set.Max_in",
"Finite_Set.Max_le_iff",
"Finite_Set.Max_less_iff",
"Finite_Set.max.f_below_strict_below.below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.max.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.Min_ge_iff",
"Finite_Set.Min_gr_iff",
"Finite_Set.Min_in",
"Finite_Set.Min_le",
"Finite_Set.min.f_below_strict_below.below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.min.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
"Fun.vimage_image_eq", (*involves an existential quantifier*)
"HOL.split_if_asm", (*splitting theorem*)
"HOL.split_if", (*splitting theorem*)
"IntDef.abs_split",
"IntDef.Integ.Abs_Integ_inject",
"IntDef.Integ.Abs_Integ_inverse",
"IntDiv.zdvd_0_left",
"List.append_eq_append_conv",
"List.hd_Cons_tl", (*Says everything is [] or Cons. Probably prolific.*)
"List.in_listsD",
"List.in_listsI",
"List.lists.Cons",
"List.listsE",
"Nat.less_one", (*not directional? obscure*)
"Nat.not_gr0",
"Nat.one_eq_mult_iff", (*duplicate by symmetry*)
"Nat.of_nat_0_eq_iff",
"Nat.of_nat_eq_0_iff",
"Nat.of_nat_le_0_iff",
"NatSimprocs.divide_le_0_iff_number_of", (*too many clauses*)
"NatSimprocs.divide_less_0_iff_number_of",
"NatSimprocs.equation_minus_iff_1", (*not directional*)
"NatSimprocs.equation_minus_iff_number_of", (*not directional*)
"NatSimprocs.le_minus_iff_1", (*not directional*)
"NatSimprocs.le_minus_iff_number_of", (*not directional*)
"NatSimprocs.less_minus_iff_1", (*not directional*)
"NatSimprocs.less_minus_iff_number_of", (*not directional*)
"NatSimprocs.minus_equation_iff_number_of", (*not directional*)
"NatSimprocs.minus_le_iff_1", (*not directional*)
"NatSimprocs.minus_le_iff_number_of", (*not directional*)
"NatSimprocs.minus_less_iff_1", (*not directional*)
"NatSimprocs.mult_le_cancel_left_number_of", (*excessive case analysis*)
"NatSimprocs.mult_le_cancel_right_number_of", (*excessive case analysis*)
"NatSimprocs.mult_less_cancel_left_number_of", (*excessive case analysis*)
"NatSimprocs.mult_less_cancel_right_number_of", (*excessive case analysis*)
"NatSimprocs.zero_le_divide_iff_number_of", (*excessive case analysis*)
"NatSimprocs.zero_less_divide_iff_number_of",
"OrderedGroup.abs_0_eq", (*duplicate by symmetry*)
"OrderedGroup.diff_eq_0_iff_eq", (*prolific?*)
"OrderedGroup.join_0_eq_0",
"OrderedGroup.meet_0_eq_0",
"OrderedGroup.pprt_eq_0", (*obscure*)
"OrderedGroup.pprt_eq_id", (*obscure*)
"OrderedGroup.pprt_mono", (*obscure*)
"Orderings.split_max", (*splitting theorem*)
"Orderings.split_min", (*splitting theorem*)
"Power.zero_less_power_abs_iff",
"Product_Type.split_eta_SetCompr", (*involves an existential quantifier*)
"Product_Type.split_paired_Ball_Sigma", (*splitting theorem*)
"Product_Type.split_paired_Bex_Sigma", (*splitting theorem*)
"Product_Type.split_split_asm", (*splitting theorem*)
"Product_Type.split_split", (*splitting theorem*)
"Product_Type.unit_abs_eta_conv",
"Product_Type.unit_induct",
"Relation.diagI",
"Relation.Domain_def", (*involves an existential quantifier*)
"Relation.Image_def", (*involves an existential quantifier*)
"Relation.ImageI",
"Ring_and_Field.divide_cancel_left", (*fields are seldom used & often prolific*)
"Ring_and_Field.divide_cancel_right",
"Ring_and_Field.divide_divide_eq_left",
"Ring_and_Field.divide_divide_eq_right",
"Ring_and_Field.divide_eq_0_iff",
"Ring_and_Field.divide_eq_1_iff",
"Ring_and_Field.divide_eq_eq_1",
"Ring_and_Field.divide_le_0_1_iff",
"Ring_and_Field.divide_le_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.divide_le_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.divide_less_0_1_iff",
"Ring_and_Field.divide_less_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.divide_less_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.eq_divide_eq_1", (*duplicate by symmetry*)
"Ring_and_Field.field_mult_cancel_left",
"Ring_and_Field.field_mult_cancel_right",
"Ring_and_Field.inverse_le_iff_le_neg",
"Ring_and_Field.inverse_le_iff_le",
"Ring_and_Field.inverse_less_iff_less_neg",
"Ring_and_Field.inverse_less_iff_less",
"Ring_and_Field.le_divide_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.le_divide_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.less_divide_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.less_divide_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.one_eq_divide_iff", (*duplicate by symmetry*)
"Set.Collect_bex_eq", (*involves an existential quantifier*)
"Set.Collect_ex_eq", (*involves an existential quantifier*)
"Set.Diff_eq_empty_iff", (*redundant with paramodulation*)
"Set.Diff_insert0",
"Set.empty_Union_conv", (*redundant with paramodulation*)
"Set.full_SetCompr_eq", (*involves an existential quantifier*)
"Set.image_Collect", (*involves an existential quantifier*)
"Set.image_def", (*involves an existential quantifier*)
"Set.Int_UNIV", (*redundant with paramodulation*)
"Set.Inter_iff", (*We already have InterI, InterE*)
"Set.psubsetE", (*too prolific and obscure*)
"Set.psubsetI",
"Set.singleton_insert_inj_eq'",
"Set.singleton_insert_inj_eq",
"Set.singletonD", (*these two duplicate some "insert" lemmas*)
"Set.singletonI",
"Set.Un_empty", (*redundant with paramodulation*)
"Set.UNION_def", (*involves an existential quantifier*)
"Set.Union_empty_conv", (*redundant with paramodulation*)
"Set.Union_iff", (*We already have UnionI, UnionE*)
"SetInterval.atLeastAtMost_iff", (*obscure and prolific*)
"SetInterval.atLeastLessThan_iff", (*obscure and prolific*)
"SetInterval.greaterThanAtMost_iff", (*obscure and prolific*)
"SetInterval.greaterThanLessThan_iff", (*obscure and prolific*)
"SetInterval.ivl_subset"]; (*excessive case analysis*)
(*These might be prolific but are probably OK, and min and max are basic.
"Orderings.max_less_iff_conj",
"Orderings.min_less_iff_conj",
"Orderings.min_max.below_inf.below_inf_conv",
"Orderings.min_max.below_sup.above_sup_conv",
Very prolific and somewhat obscure:
"Set.InterD",
"Set.UnionI",
*)
(*** retrieve lemmas from clasimpset and atpset, may filter them ***)
(*Hashing to detect duplicate and variant clauses, e.g. from the [iff] attribute*)
exception HASH_CLAUSE and HASH_STRING;
(*Reject theorems with names like "List.filter.filter_list_def" or
"Accessible_Part.acc.defs", as these are definitions arising from packages.*)
fun is_package_def a =
let val names = NameSpace.unpack a
in
length names > 2 andalso
not (hd names = "local") andalso
String.isSuffix "_def" a orelse String.isSuffix "_defs" a
end;
fun make_banned_test xs =
let val ht = Polyhash.mkTable (Polyhash.hash_string, op =)
(6000, HASH_STRING)
fun banned s =
isSome (Polyhash.peek ht s) orelse is_package_def s
in app (fn x => Polyhash.insert ht (x,())) (!blacklist);
banned
end;
(** a hash function from Term.term to int, and also a hash table **)
val xor_words = List.foldl Word.xorb 0w0;
fun hashw_term ((Const(c,_)), w) = Polyhash.hashw_string (c,w)
| hashw_term ((Free(a,_)), w) = Polyhash.hashw_string (a,w)
| hashw_term ((Var(_,_)), w) = w
| hashw_term ((Bound i), w) = Polyhash.hashw_int(i,w)
| hashw_term ((Abs(_,_,t)), w) = hashw_term (t, w)
| hashw_term ((P$Q), w) = hashw_term (Q, (hashw_term (P, w)));
fun hash_literal (Const("Not",_)$P) = Word.notb(hashw_term(P,0w0))
| hash_literal P = hashw_term(P,0w0);
fun hash_term t = Word.toIntX (xor_words (map hash_literal (dest_disj t)));
fun equal_thm (thm1,thm2) = Term.aconv(prop_of thm1, prop_of thm2);
(*Create a hash table for clauses, of the given size*)
fun mk_clause_table n =
Polyhash.mkTable (hash_term o prop_of, equal_thm)
(n, HASH_CLAUSE);
(*Use a hash table to eliminate duplicates from xs. Argument is a list of
(thm * (string * int)) tuples. The theorems are hashed into the table. *)
fun make_unique xs =
let val ht = mk_clause_table 7000
in
Output.debug("make_unique gets " ^ Int.toString (length xs) ^ " clauses");
app (ignore o Polyhash.peekInsert ht) xs;
Polyhash.listItems ht
end;
(*Remove existing axiom clauses from the conjecture clauses, as this can dramatically
boost an ATP's performance (for some reason)*)
fun subtract_cls c_clauses ax_clauses =
let val ht = mk_clause_table 2200
fun known x = isSome (Polyhash.peek ht x)
in
app (ignore o Polyhash.peekInsert ht) ax_clauses;
filter (not o known) c_clauses
end;
(*Filter axiom clauses, but keep supplied clauses and clauses in whitelist.
Duplicates are removed later.*)
fun get_relevant_clauses thy cls_thms white_cls goals =
white_cls @ (ReduceAxiomsN.relevance_filter thy cls_thms goals);
fun display_thms [] = ()
| display_thms ((name,thm)::nthms) =
let val nthm = name ^ ": " ^ (string_of_thm thm)
in Output.debug nthm; display_thms nthms end;
fun all_valid_thms ctxt =
PureThy.thms_containing (ProofContext.theory_of ctxt) ([], []) @
filter (ProofContext.valid_thms ctxt)
(FactIndex.find (ProofContext.fact_index_of ctxt) ([], []));
fun multi_name a (th, (n,pairs)) =
(n+1, (a ^ "(" ^ Int.toString n ^ ")", th) :: pairs)
fun add_multi_names_aux ((a, []), pairs) = pairs
| add_multi_names_aux ((a, [th]), pairs) = (a,th)::pairs
| add_multi_names_aux ((a, ths), pairs) = #2 (foldl (multi_name a) (1,pairs) ths);
val multi_blacklist =
["Set.ball_simps", "Set.bex_simps", (*quantifier rewriting: useless*)
"Set.disjoint_insert", "Set.insert_disjoint", "Set.Inter_UNIV_conv"];
val multi_base_blacklist =
["defs","select_defs","update_defs","induct","inducts","split","splits","split_asm"];
(*Ignore blacklisted theorem lists*)
fun add_multi_names ((a, ths), pairs) =
if a mem_string multi_blacklist orelse (Sign.base_name a) mem_string multi_base_blacklist
then pairs
else add_multi_names_aux ((a, ths), pairs);
fun is_multi (a, ths) = length ths > 1 orelse String.isSuffix ".axioms" a;
(*The single theorems go BEFORE the multiple ones*)
fun name_thm_pairs ctxt =
let val (mults,singles) = List.partition is_multi (all_valid_thms ctxt)
in foldl add_multi_names (foldl add_multi_names [] mults) singles end;
fun check_named ("",th) = (warning ("No name for theorem " ^ string_of_thm th); false)
| check_named (_,th) = true;
(* get lemmas from claset, simpset, atpset and extra supplied rules *)
fun get_clasimp_atp_lemmas ctxt user_thms =
let val included_thms =
if !include_all
then (tap (fn ths => Output.debug
("Including all " ^ Int.toString (length ths) ^ " theorems"))
(name_thm_pairs ctxt))
else
let val claset_thms =
if !include_claset then ResAxioms.claset_rules_of ctxt
else []
val simpset_thms =
if !include_simpset then ResAxioms.simpset_rules_of ctxt
else []
val atpset_thms =
if !include_atpset then ResAxioms.atpset_rules_of ctxt
else []
val _ = if !Output.show_debug_msgs
then (Output.debug "ATP theorems: "; display_thms atpset_thms)
else ()
in claset_thms @ simpset_thms @ atpset_thms end
val user_rules = filter check_named
(map (ResAxioms.pairname)
(if null user_thms then !whitelist else user_thms))
in
(filter check_named included_thms, user_rules)
end;
(*Remove lemmas that are banned from the backlist. Also remove duplicates. *)
fun blacklist_filter ths =
if !run_blacklist_filter then
let val banned = make_banned_test (map #1 ths)
fun ok (a,_) = not (banned a)
val (good,bad) = List.partition ok ths
in if !Output.show_debug_msgs then
(Output.debug("blacklist filter gets " ^ Int.toString (length ths) ^ " theorems");
Output.debug("filtered: " ^ space_implode ", " (map #1 bad));
Output.debug("...and returns " ^ Int.toString (length good)))
else ();
good
end
else ths;
(***************************************************************)
(* Type Classes Present in the Axiom or Conjecture Clauses *)
(***************************************************************)
fun setinsert (x,s) = Symtab.update (x,()) s;
fun add_classes (sorts, cset) = foldl setinsert cset (List.concat sorts);
(*Remove this trivial type class*)
fun delete_type cset = Symtab.delete_safe "HOL.type" cset;
fun tvar_classes_of_terms ts =
let val sorts_list = map (map #2 o term_tvars) ts
in Symtab.keys (delete_type (foldl add_classes Symtab.empty sorts_list)) end;
fun tfree_classes_of_terms ts =
let val sorts_list = map (map #2 o term_tfrees) ts
in Symtab.keys (delete_type (foldl add_classes Symtab.empty sorts_list)) end;
(*fold type constructors*)
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
| fold_type_consts f T x = x;
val add_type_consts_in_type = fold_type_consts setinsert;
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
fun add_type_consts_in_term thy =
let val const_typargs = Sign.const_typargs thy
fun add_tcs (Const cT) x = fold add_type_consts_in_type (const_typargs cT) x
| add_tcs (Abs (_, T, u)) x = add_tcs u x
| add_tcs (t $ u) x = add_tcs t (add_tcs u x)
| add_tcs _ x = x
in add_tcs end
fun type_consts_of_terms thy ts =
Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
(***************************************************************)
(* ATP invocation methods setup *)
(***************************************************************)
fun cnf_hyps_thms ctxt =
let val ths = Assumption.prems_of ctxt
in fold (fold (insert Thm.eq_thm) o ResAxioms.skolem_thm) ths [] end;
(*Translation mode can be auto-detected, or forced to be first-order or higher-order*)
datatype mode = Auto | Fol | Hol;
val linkup_logic_mode = ref Auto;
(*Ensures that no higher-order theorems "leak out"*)
fun restrict_to_logic logic cls =
if is_fol_logic logic then filter (Meson.is_fol_term o prop_of o fst) cls
else cls;
(**** Predicates to detect unwanted clauses (prolific or likely to cause unsoundness) ****)
(** Too general means, positive equality literal with a variable X as one operand,
when X does not occur properly in the other operand. This rules out clearly
inconsistent clauses such as V=a|V=b, though it by no means guarantees soundness. **)
fun occurs ix =
let fun occ(Var (jx,_)) = (ix=jx)
| occ(t1$t2) = occ t1 orelse occ t2
| occ(Abs(_,_,t)) = occ t
| occ _ = false
in occ end;
fun is_recordtype T = not (null (RecordPackage.dest_recTs T));
(*Unwanted equalities include
(1) those between a variable that does not properly occur in the second operand,
(2) those between a variable and a record, since these seem to be prolific "cases" thms
*)
fun too_general_eqterms (Var (ix,T), t) = not (occurs ix t) orelse is_recordtype T
| too_general_eqterms _ = false;
fun too_general_equality (Const ("op =", _) $ x $ y) =
too_general_eqterms (x,y) orelse too_general_eqterms(y,x)
| too_general_equality _ = false;
(* tautologous? *)
fun is_taut (Const ("Trueprop", _) $ Const ("True", _)) = true
| is_taut _ = false;
(*True if the term contains a variable whose (atomic) type is in the given list.*)
fun has_typed_var tycons =
let fun var_tycon (Var (_, Type(a,_))) = a mem_string tycons
| var_tycon _ = false
in exists var_tycon o term_vars end;
fun unwanted t =
is_taut t orelse has_typed_var ["Product_Type.unit","bool"] t orelse
forall too_general_equality (dest_disj t);
(*Clauses containing variables of type "unit" or "bool" are unlikely to be useful and
likely to lead to unsound proofs.*)
fun remove_unwanted_clauses cls =
filter (not o unwanted o prop_of o fst) cls;
fun tptp_writer logic goals filename (axioms,classrels,arities) user_lemmas =
if is_fol_logic logic
then ResClause.tptp_write_file goals filename (axioms, classrels, arities)
else ResHolClause.tptp_write_file goals filename (axioms, classrels, arities) user_lemmas;
fun dfg_writer logic goals filename (axioms,classrels,arities) user_lemmas =
if is_fol_logic logic
then ResClause.dfg_write_file goals filename (axioms, classrels, arities)
else ResHolClause.dfg_write_file goals filename (axioms, classrels, arities) user_lemmas;
(*Called by the oracle-based methods declared in res_atp_methods.ML*)
fun write_subgoal_file dfg mode ctxt conjectures user_thms n =
let val conj_cls = make_clauses conjectures
|> ResAxioms.assume_abstract_list |> Meson.finish_cnf
val hyp_cls = cnf_hyps_thms ctxt
val goal_cls = conj_cls@hyp_cls
val goal_tms = map prop_of goal_cls
val logic = case mode of
Auto => problem_logic_goals [goal_tms]
| Fol => FOL
| Hol => HOL
val (included_thms,user_rules) = get_clasimp_atp_lemmas ctxt user_thms
val cla_simp_atp_clauses = included_thms |> blacklist_filter
|> ResAxioms.cnf_rules_pairs |> make_unique
|> restrict_to_logic logic
|> remove_unwanted_clauses
val user_cls = ResAxioms.cnf_rules_pairs user_rules
val thy = ProofContext.theory_of ctxt
val axclauses = make_unique (get_relevant_clauses thy cla_simp_atp_clauses user_cls goal_tms)
val subs = tfree_classes_of_terms goal_tms
and axtms = map (prop_of o #1) axclauses
val supers = tvar_classes_of_terms axtms
and tycons = type_consts_of_terms thy (goal_tms@axtms)
(*TFrees in conjecture clauses; TVars in axiom clauses*)
val classrel_clauses = ResClause.make_classrel_clauses thy subs supers
val arity_clauses = ResClause.arity_clause_thy thy tycons supers
val writer = if dfg then dfg_writer else tptp_writer
and file = atp_input_file()
and user_lemmas_names = map #1 user_rules
in
writer logic goal_cls file (axclauses,classrel_clauses,arity_clauses) user_lemmas_names;
Output.debug ("Writing to " ^ file);
file
end;
(**** remove tmp files ****)
fun cond_rm_tmp file =
if !Output.show_debug_msgs orelse !destdir <> "" then Output.debug "ATP input kept..."
else OS.FileSys.remove file;
(****** setup ATPs as Isabelle methods ******)
fun atp_meth tac ths ctxt =
let val thy = ProofContext.theory_of ctxt
val _ = ResClause.init thy
val _ = ResHolClause.init thy
in Method.SIMPLE_METHOD' (tac ctxt ths) end;
fun atp_method tac = Method.thms_ctxt_args (atp_meth tac);
(***************************************************************)
(* automatic ATP invocation *)
(***************************************************************)
(* call prover with settings and problem file for the current subgoal *)
fun watcher_call_provers sign sg_terms (childin, childout, pid) =
let
fun make_atp_list [] n = []
| make_atp_list (sg_term::xs) n =
let
val probfile = prob_pathname n
val time = Int.toString (!time_limit)
in
Output.debug ("problem file in watcher_call_provers is " ^ probfile);
(*options are separated by Watcher.setting_sep, currently #"%"*)
if !prover = "spass"
then
let val spass = helper_path "SPASS_HOME" "SPASS"
val sopts =
"-Auto%-SOS=1%-PGiven=0%-PProblem=0%-Splits=0%-FullRed=0%-DocProof%-TimeLimit=" ^ time
in
("spass", spass, sopts, probfile) :: make_atp_list xs (n+1)
end
else if !prover = "vampire"
then
let val vampire = helper_path "VAMPIRE_HOME" "vampire"
val vopts = "--mode casc%-t " ^ time (*what about -m 100000?*)
in
("vampire", vampire, vopts, probfile) :: make_atp_list xs (n+1)
end
else if !prover = "E"
then
let val Eprover = helper_path "E_HOME" "eproof"
in
("E", Eprover,
"--tstp-in%-l5%-xAutoDev%-tAutoDev%--silent%--cpu-limit=" ^ time, probfile) ::
make_atp_list xs (n+1)
end
else error ("Invalid prover name: " ^ !prover)
end
val atp_list = make_atp_list sg_terms 1
in
Watcher.callResProvers(childout,atp_list);
Output.debug "Sent commands to watcher!"
end
fun trace_array fname =
let val path = File.unpack_platform_path fname
in Array.app (File.append path o (fn s => s ^ "\n")) end;
(*Converting a subgoal into negated conjecture clauses*)
fun neg_clauses th n =
let val tacs = [rtac ccontr, ObjectLogic.atomize_tac, skolemize_tac]
val st = Seq.hd (EVERY' tacs n th)
val negs = Option.valOf (metahyps_thms n st)
in make_clauses negs |> ResAxioms.assume_abstract_list |> Meson.finish_cnf end;
(*We write out problem files for each subgoal. Argument probfile generates filenames,
and allows the suppression of the suffix "_1" in problem-generation mode.
FIXME: does not cope with &&, and it isn't easy because one could have multiple
subgoals, each involving &&.*)
fun write_problem_files probfile (ctxt,th) =
let val goals = Thm.prems_of th
val _ = Output.debug ("number of subgoals = " ^ Int.toString (length goals))
val thy = ProofContext.theory_of ctxt
fun get_neg_subgoals [] _ = []
| get_neg_subgoals (gl::gls) n = neg_clauses th n :: get_neg_subgoals gls (n+1)
val goal_cls = get_neg_subgoals goals 1
val logic = case !linkup_logic_mode of
Auto => problem_logic_goals (map ((map prop_of)) goal_cls)
| Fol => FOL
| Hol => HOL
val (included_thms,white_thms) = get_clasimp_atp_lemmas ctxt []
val included_cls = included_thms |> blacklist_filter
|> ResAxioms.cnf_rules_pairs |> make_unique
|> restrict_to_logic logic
|> remove_unwanted_clauses
val _ = Output.debug ("included clauses = " ^ Int.toString(length included_cls))
val white_cls = ResAxioms.cnf_rules_pairs white_thms
(*clauses relevant to goal gl*)
val axcls_list = map (fn ngcls => get_relevant_clauses thy included_cls white_cls (map prop_of ngcls)) goal_cls
val _ = app (fn axcls => Output.debug ("filtered clauses = " ^ Int.toString(length axcls)))
axcls_list
val writer = if !prover = "spass" then dfg_writer else tptp_writer
fun write_all [] [] _ = []
| write_all (ccls::ccls_list) (axcls::axcls_list) k =
let val fname = probfile k
val axcls = make_unique axcls
val ccls = subtract_cls ccls axcls
val ccltms = map prop_of ccls
and axtms = map (prop_of o #1) axcls
val subs = tfree_classes_of_terms ccltms
and supers = tvar_classes_of_terms axtms
and tycons = type_consts_of_terms thy (ccltms@axtms)
(*TFrees in conjecture clauses; TVars in axiom clauses*)
val classrel_clauses = ResClause.make_classrel_clauses thy subs supers
val _ = Output.debug ("classrel clauses = " ^ Int.toString (length classrel_clauses))
val arity_clauses = ResClause.arity_clause_thy thy tycons supers
val _ = Output.debug ("arity clauses = " ^ Int.toString (length arity_clauses))
val clnames = writer logic ccls fname (axcls,classrel_clauses,arity_clauses) []
val thm_names = Array.fromList clnames
val _ = if !Output.show_debug_msgs
then trace_array (fname ^ "_thm_names") thm_names else ()
in (thm_names,fname) :: write_all ccls_list axcls_list (k+1) end
val (thm_names_list, filenames) = ListPair.unzip (write_all goal_cls axcls_list 1)
in
(filenames, thm_names_list)
end;
val last_watcher_pid = ref (NONE : (TextIO.instream * TextIO.outstream *
Posix.Process.pid * string list) option);
fun kill_last_watcher () =
(case !last_watcher_pid of
NONE => ()
| SOME (_, _, pid, files) =>
(Output.debug ("Killing old watcher, pid = " ^ string_of_pid pid);
Watcher.killWatcher pid;
ignore (map (try cond_rm_tmp) files)))
handle OS.SysErr _ => Output.debug "Attempt to kill watcher failed";
(*writes out the current clasimpset to a tptp file;
turns off xsymbol at start of function, restoring it at end *)
fun isar_atp_body (ctxt, th) =
if Thm.no_prems th then ()
else
let
val _ = kill_last_watcher()
val (files,thm_names_list) = write_problem_files prob_pathname (ctxt,th)
val (childin, childout, pid) = Watcher.createWatcher (th, thm_names_list)
in
last_watcher_pid := SOME (childin, childout, pid, files);
Output.debug ("problem files: " ^ space_implode ", " files);
Output.debug ("pid: " ^ string_of_pid pid);
watcher_call_provers (sign_of_thm th) (Thm.prems_of th) (childin, childout, pid)
end;
val isar_atp = setmp print_mode [] isar_atp_body;
(*For ML scripts, and primarily, for debugging*)
fun callatp () =
let val th = topthm()
val ctxt = ProofContext.init (theory_of_thm th)
in isar_atp_body (ctxt, th) end;
val isar_atp_writeonly = setmp print_mode []
(fn (ctxt,th) =>
if Thm.no_prems th then ()
else
let val probfile = if Thm.nprems_of th = 1 then probfile_nosuffix
else prob_pathname
in ignore (write_problem_files probfile (ctxt,th)) end);
(** the Isar toplevel hook **)
fun invoke_atp_ml (ctxt, goal) =
let val thy = ProofContext.theory_of ctxt;
in
Output.debug ("subgoals in isar_atp:\n" ^
Pretty.string_of (ProofContext.pretty_term ctxt
(Logic.mk_conjunction_list (Thm.prems_of goal))));
Output.debug ("current theory: " ^ Context.theory_name thy);
inc hook_count;
Output.debug ("in hook for time: " ^ Int.toString (!hook_count));
ResClause.init thy;
ResHolClause.init thy;
if !time_limit > 0 then isar_atp (ctxt, goal)
else (warning "Writing problem file only"; isar_atp_writeonly (ctxt, goal))
end;
val invoke_atp = Toplevel.no_timing o Toplevel.unknown_proof o Toplevel.keep
(fn state =>
let val (ctxt, (_, goal)) = Proof.get_goal (Toplevel.proof_of state)
in invoke_atp_ml (ctxt, goal) end);
val call_atpP =
OuterSyntax.command
"ProofGeneral.call_atp"
"call automatic theorem provers"
OuterKeyword.diag
(Scan.succeed invoke_atp);
val _ = OuterSyntax.add_parsers [call_atpP];
end;