replaced old_style infixes eq_set, subset, union, inter and variants by generic versions
(*
Author: Jia Meng, NICTA
FOL clauses translated from HOL formulae.
*)
signature RES_HOL_CLAUSE =
sig
val ext: thm
val comb_I: thm
val comb_K: thm
val comb_B: thm
val comb_C: thm
val comb_S: thm
val minimize_applies: bool
type axiom_name = string
type polarity = bool
type clause_id = int
datatype combterm =
CombConst of string * ResClause.fol_type * ResClause.fol_type list (*Const and Free*)
| CombVar of string * ResClause.fol_type
| CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm
datatype clause = Clause of {clause_id: clause_id, axiom_name: axiom_name, th: thm,
kind: ResClause.kind,literals: literal list, ctypes_sorts: typ list}
val type_of_combterm: combterm -> ResClause.fol_type
val strip_comb: combterm -> combterm * combterm list
val literals_of_term: theory -> term -> literal list * typ list
exception TOO_TRIVIAL
val make_conjecture_clauses: bool -> theory -> thm list -> clause list
val make_axiom_clauses: bool ->
theory ->
(thm * (axiom_name * clause_id)) list -> (axiom_name * clause) list
val get_helper_clauses: bool ->
theory ->
bool ->
clause list * (thm * (axiom_name * clause_id)) list * string list ->
clause list
val tptp_write_file: bool -> Path.T ->
clause list * clause list * clause list * clause list *
ResClause.classrelClause list * ResClause.arityClause list ->
int * int
val dfg_write_file: bool -> Path.T ->
clause list * clause list * clause list * clause list *
ResClause.classrelClause list * ResClause.arityClause list ->
int * int
end
structure ResHolClause: RES_HOL_CLAUSE =
struct
structure RC = ResClause;
(* theorems for combinators and function extensionality *)
val ext = thm "HOL.ext";
val comb_I = thm "ATP_Linkup.COMBI_def";
val comb_K = thm "ATP_Linkup.COMBK_def";
val comb_B = thm "ATP_Linkup.COMBB_def";
val comb_C = thm "ATP_Linkup.COMBC_def";
val comb_S = thm "ATP_Linkup.COMBS_def";
val fequal_imp_equal = thm "ATP_Linkup.fequal_imp_equal";
val equal_imp_fequal = thm "ATP_Linkup.equal_imp_fequal";
(* Parameter t_full below indicates that full type information is to be
exported *)
(*If true, each function will be directly applied to as many arguments as possible, avoiding
use of the "apply" operator. Use of hBOOL is also minimized.*)
val minimize_applies = true;
fun min_arity_of const_min_arity c = getOpt (Symtab.lookup const_min_arity c, 0);
(*True if the constant ever appears outside of the top-level position in literals.
If false, the constant always receives all of its arguments and is used as a predicate.*)
fun needs_hBOOL const_needs_hBOOL c = not minimize_applies orelse
getOpt (Symtab.lookup const_needs_hBOOL c, false);
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
type axiom_name = string;
type polarity = bool;
type clause_id = int;
datatype combterm = CombConst of string * RC.fol_type * RC.fol_type list (*Const and Free*)
| CombVar of string * RC.fol_type
| CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm;
datatype clause =
Clause of {clause_id: clause_id,
axiom_name: axiom_name,
th: thm,
kind: RC.kind,
literals: literal list,
ctypes_sorts: typ list};
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
fun isFalse (Literal(pol, CombConst(c,_,_))) =
(pol andalso c = "c_False") orelse
(not pol andalso c = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol, CombConst(c,_,_))) =
(pol andalso c = "c_True") orelse
(not pol andalso c = "c_False")
| isTrue _ = false;
fun isTaut (Clause {literals,...}) = exists isTrue literals;
fun type_of dfg (Type (a, Ts)) =
let val (folTypes,ts) = types_of dfg Ts
in (RC.Comp(RC.make_fixed_type_const dfg a, folTypes), ts) end
| type_of _ (tp as TFree (a, _)) =
(RC.AtomF (RC.make_fixed_type_var a), [tp])
| type_of _ (tp as TVar (v, _)) =
(RC.AtomV (RC.make_schematic_type_var v), [tp])
and types_of dfg Ts =
let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
in (folTyps, RC.union_all ts) end;
(* same as above, but no gathering of sort information *)
fun simp_type_of dfg (Type (a, Ts)) =
RC.Comp(RC.make_fixed_type_const dfg a, map (simp_type_of dfg) Ts)
| simp_type_of _ (TFree (a, _)) = RC.AtomF(RC.make_fixed_type_var a)
| simp_type_of _ (TVar (v, _)) = RC.AtomV(RC.make_schematic_type_var v);
fun const_type_of dfg thy (c,t) =
let val (tp,ts) = type_of dfg t
in (tp, ts, map (simp_type_of dfg) (Sign.const_typargs thy (c,t))) end;
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
fun combterm_of dfg thy (Const(c,t)) =
let val (tp,ts,tvar_list) = const_type_of dfg thy (c,t)
val c' = CombConst(RC.make_fixed_const dfg c, tp, tvar_list)
in (c',ts) end
| combterm_of dfg _ (Free(v,t)) =
let val (tp,ts) = type_of dfg t
val v' = CombConst(RC.make_fixed_var v, tp, [])
in (v',ts) end
| combterm_of dfg _ (Var(v,t)) =
let val (tp,ts) = type_of dfg t
val v' = CombVar(RC.make_schematic_var v,tp)
in (v',ts) end
| combterm_of dfg thy (P $ Q) =
let val (P',tsP) = combterm_of dfg thy P
val (Q',tsQ) = combterm_of dfg thy Q
in (CombApp(P',Q'), gen_union (op =) (tsP, tsQ)) end
| combterm_of _ _ (t as Abs _) = raise RC.CLAUSE ("HOL CLAUSE", t);
fun predicate_of dfg thy ((Const("Not",_) $ P), polarity) = predicate_of dfg thy (P, not polarity)
| predicate_of dfg thy (t,polarity) = (combterm_of dfg thy (Envir.eta_contract t), polarity);
fun literals_of_term1 dfg thy args (Const("Trueprop",_) $ P) = literals_of_term1 dfg thy args P
| literals_of_term1 dfg thy args (Const("op |",_) $ P $ Q) =
literals_of_term1 dfg thy (literals_of_term1 dfg thy args P) Q
| literals_of_term1 dfg thy (lits,ts) P =
let val ((pred,ts'),pol) = predicate_of dfg thy (P,true)
in
(Literal(pol,pred)::lits, gen_union (op =) (ts, ts'))
end;
fun literals_of_term_dfg dfg thy P = literals_of_term1 dfg thy ([],[]) P;
val literals_of_term = literals_of_term_dfg false;
(* Problem too trivial for resolution (empty clause) *)
exception TOO_TRIVIAL;
(* making axiom and conjecture clauses *)
fun make_clause dfg thy (clause_id,axiom_name,kind,th) =
let val (lits,ctypes_sorts) = literals_of_term_dfg dfg thy (prop_of th)
in
if forall isFalse lits
then raise TOO_TRIVIAL
else
Clause {clause_id = clause_id, axiom_name = axiom_name, th = th, kind = kind,
literals = lits, ctypes_sorts = ctypes_sorts}
end;
fun add_axiom_clause dfg thy ((th,(name,id)), pairs) =
let val cls = make_clause dfg thy (id, name, RC.Axiom, th)
in
if isTaut cls then pairs else (name,cls)::pairs
end;
fun make_axiom_clauses dfg thy = List.foldl (add_axiom_clause dfg thy) [];
fun make_conjecture_clauses_aux _ _ _ [] = []
| make_conjecture_clauses_aux dfg thy n (th::ths) =
make_clause dfg thy (n,"conjecture", RC.Conjecture, th) ::
make_conjecture_clauses_aux dfg thy (n+1) ths;
fun make_conjecture_clauses dfg thy = make_conjecture_clauses_aux dfg thy 0;
(**********************************************************************)
(* convert clause into ATP specific formats: *)
(* TPTP used by Vampire and E *)
(* DFG used by SPASS *)
(**********************************************************************)
(*Result of a function type; no need to check that the argument type matches.*)
fun result_type (RC.Comp ("tc_fun", [_, tp2])) = tp2
| result_type _ = error "result_type"
fun type_of_combterm (CombConst (_, tp, _)) = tp
| type_of_combterm (CombVar (_, tp)) = tp
| type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1);
(*gets the head of a combinator application, along with the list of arguments*)
fun strip_comb u =
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
| stripc x = x
in stripc(u,[]) end;
val type_wrapper = "ti";
fun head_needs_hBOOL const_needs_hBOOL (CombConst(c,_,_)) = needs_hBOOL const_needs_hBOOL c
| head_needs_hBOOL _ _ = true;
fun wrap_type t_full (s, tp) =
if t_full then
type_wrapper ^ RC.paren_pack [s, RC.string_of_fol_type tp]
else s;
fun apply ss = "hAPP" ^ RC.paren_pack ss;
fun rev_apply (v, []) = v
| rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
fun string_apply (v, args) = rev_apply (v, rev args);
(*Apply an operator to the argument strings, using either the "apply" operator or
direct function application.*)
fun string_of_applic t_full cma (CombConst (c, _, tvars), args) =
let val c = if c = "equal" then "c_fequal" else c
val nargs = min_arity_of cma c
val args1 = List.take(args, nargs)
handle Subscript => error ("string_of_applic: " ^ c ^ " has arity " ^
Int.toString nargs ^ " but is applied to " ^
space_implode ", " args)
val args2 = List.drop(args, nargs)
val targs = if not t_full then map RC.string_of_fol_type tvars
else []
in
string_apply (c ^ RC.paren_pack (args1@targs), args2)
end
| string_of_applic _ _ (CombVar (v, _), args) = string_apply (v, args)
| string_of_applic _ _ _ = error "string_of_applic";
fun wrap_type_if t_full cnh (head, s, tp) =
if head_needs_hBOOL cnh head then wrap_type t_full (s, tp) else s;
fun string_of_combterm (params as (t_full, cma, cnh)) t =
let val (head, args) = strip_comb t
in wrap_type_if t_full cnh (head,
string_of_applic t_full cma (head, map (string_of_combterm (params)) args),
type_of_combterm t)
end;
(*Boolean-valued terms are here converted to literals.*)
fun boolify params t =
"hBOOL" ^ RC.paren_pack [string_of_combterm params t];
fun string_of_predicate (params as (_,_,cnh)) t =
case t of
(CombApp(CombApp(CombConst("equal",_,_), t1), t2)) =>
(*DFG only: new TPTP prefers infix equality*)
("equal" ^ RC.paren_pack [string_of_combterm params t1, string_of_combterm params t2])
| _ =>
case #1 (strip_comb t) of
CombConst(c,_,_) => if needs_hBOOL cnh c then boolify params t else string_of_combterm params t
| _ => boolify params t;
(*** tptp format ***)
fun tptp_of_equality params pol (t1,t2) =
let val eqop = if pol then " = " else " != "
in string_of_combterm params t1 ^ eqop ^ string_of_combterm params t2 end;
fun tptp_literal params (Literal(pol, CombApp(CombApp(CombConst("equal",_,_), t1), t2))) =
tptp_of_equality params pol (t1,t2)
| tptp_literal params (Literal(pol,pred)) =
RC.tptp_sign pol (string_of_predicate params pred);
(*Given a clause, returns its literals paired with a list of literals concerning TFrees;
the latter should only occur in conjecture clauses.*)
fun tptp_type_lits params pos (Clause{literals, ctypes_sorts, ...}) =
(map (tptp_literal params) literals,
map (RC.tptp_of_typeLit pos) (RC.add_typs ctypes_sorts));
fun clause2tptp params (cls as Clause {axiom_name, clause_id, kind, ...}) =
let val (lits,tylits) = tptp_type_lits params (kind = RC.Conjecture) cls
in
(RC.gen_tptp_cls(clause_id,axiom_name,kind,lits,tylits), tylits)
end;
(*** dfg format ***)
fun dfg_literal params (Literal(pol,pred)) = RC.dfg_sign pol (string_of_predicate params pred);
fun dfg_type_lits params pos (Clause{literals, ctypes_sorts, ...}) =
(map (dfg_literal params) literals,
map (RC.dfg_of_typeLit pos) (RC.add_typs ctypes_sorts));
fun get_uvars (CombConst _) vars = vars
| get_uvars (CombVar(v,_)) vars = (v::vars)
| get_uvars (CombApp(P,Q)) vars = get_uvars P (get_uvars Q vars);
fun get_uvars_l (Literal(_,c)) = get_uvars c [];
fun dfg_vars (Clause {literals,...}) = RC.union_all (map get_uvars_l literals);
fun clause2dfg params (cls as Clause{axiom_name,clause_id,kind,ctypes_sorts,...}) =
let val (lits,tylits) = dfg_type_lits params (kind = RC.Conjecture) cls
val vars = dfg_vars cls
val tvars = RC.get_tvar_strs ctypes_sorts
in
(RC.gen_dfg_cls(clause_id, axiom_name, kind, lits, tylits, tvars@vars), tylits)
end;
(** For DFG format: accumulate function and predicate declarations **)
fun addtypes tvars tab = List.foldl RC.add_foltype_funcs tab tvars;
fun add_decls (t_full, cma, cnh) (CombConst (c, _, tvars), (funcs, preds)) =
if c = "equal" then (addtypes tvars funcs, preds)
else
let val arity = min_arity_of cma c
val ntys = if not t_full then length tvars else 0
val addit = Symtab.update(c, arity+ntys)
in
if needs_hBOOL cnh c then (addtypes tvars (addit funcs), preds)
else (addtypes tvars funcs, addit preds)
end
| add_decls _ (CombVar(_,ctp), (funcs,preds)) =
(RC.add_foltype_funcs (ctp,funcs), preds)
| add_decls params (CombApp(P,Q),decls) = add_decls params (P,add_decls params (Q,decls));
fun add_literal_decls params (Literal(_,c), decls) = add_decls params (c,decls);
fun add_clause_decls params (Clause {literals, ...}, decls) =
List.foldl (add_literal_decls params) decls literals
handle Symtab.DUP a => error ("function " ^ a ^ " has multiple arities")
fun decls_of_clauses params clauses arity_clauses =
let val init_functab = Symtab.update (type_wrapper,2) (Symtab.update ("hAPP",2) RC.init_functab)
val init_predtab = Symtab.update ("hBOOL",1) Symtab.empty
val (functab,predtab) = (List.foldl (add_clause_decls params) (init_functab, init_predtab) clauses)
in
(Symtab.dest (List.foldl RC.add_arityClause_funcs functab arity_clauses),
Symtab.dest predtab)
end;
fun add_clause_preds (Clause {ctypes_sorts, ...}, preds) =
List.foldl RC.add_type_sort_preds preds ctypes_sorts
handle Symtab.DUP a => error ("predicate " ^ a ^ " has multiple arities")
(*Higher-order clauses have only the predicates hBOOL and type classes.*)
fun preds_of_clauses clauses clsrel_clauses arity_clauses =
Symtab.dest
(List.foldl RC.add_classrelClause_preds
(List.foldl RC.add_arityClause_preds
(List.foldl add_clause_preds Symtab.empty clauses)
arity_clauses)
clsrel_clauses)
(**********************************************************************)
(* write clauses to files *)
(**********************************************************************)
val init_counters =
Symtab.make [("c_COMBI", 0), ("c_COMBK", 0),
("c_COMBB", 0), ("c_COMBC", 0),
("c_COMBS", 0)];
fun count_combterm (CombConst (c, _, _), ct) =
(case Symtab.lookup ct c of NONE => ct (*no counter*)
| SOME n => Symtab.update (c,n+1) ct)
| count_combterm (CombVar _, ct) = ct
| count_combterm (CombApp(t1,t2), ct) = count_combterm(t1, count_combterm(t2, ct));
fun count_literal (Literal(_,t), ct) = count_combterm(t,ct);
fun count_clause (Clause{literals,...}, ct) = List.foldl count_literal ct literals;
fun count_user_clause user_lemmas (Clause{axiom_name,literals,...}, ct) =
if axiom_name mem_string user_lemmas then List.foldl count_literal ct literals
else ct;
fun cnf_helper_thms thy =
ResAxioms.cnf_rules_pairs thy o map ResAxioms.pairname
fun get_helper_clauses dfg thy isFO (conjectures, axcls, user_lemmas) =
if isFO then [] (*first-order*)
else
let
val axclauses = map #2 (make_axiom_clauses dfg thy axcls)
val ct0 = List.foldl count_clause init_counters conjectures
val ct = List.foldl (count_user_clause user_lemmas) ct0 axclauses
fun needed c = valOf (Symtab.lookup ct c) > 0
val IK = if needed "c_COMBI" orelse needed "c_COMBK"
then cnf_helper_thms thy [comb_I,comb_K]
else []
val BC = if needed "c_COMBB" orelse needed "c_COMBC"
then cnf_helper_thms thy [comb_B,comb_C]
else []
val S = if needed "c_COMBS"
then cnf_helper_thms thy [comb_S]
else []
val other = cnf_helper_thms thy [fequal_imp_equal,equal_imp_fequal]
in
map #2 (make_axiom_clauses dfg thy (other @ IK @ BC @ S))
end;
(*Find the minimal arity of each function mentioned in the term. Also, note which uses
are not at top level, to see if hBOOL is needed.*)
fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
let val (head, args) = strip_comb t
val n = length args
val (const_min_arity, const_needs_hBOOL) = fold (count_constants_term false) args (const_min_arity, const_needs_hBOOL)
in
case head of
CombConst (a,_,_) => (*predicate or function version of "equal"?*)
let val a = if a="equal" andalso not toplev then "c_fequal" else a
val const_min_arity = Symtab.map_default (a,n) (curry Int.min n) const_min_arity
in
if toplev then (const_min_arity, const_needs_hBOOL)
else (const_min_arity, Symtab.update (a,true) (const_needs_hBOOL))
end
| _ => (const_min_arity, const_needs_hBOOL)
end;
(*A literal is a top-level term*)
fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
count_constants_term true t (const_min_arity, const_needs_hBOOL);
fun count_constants_clause (Clause{literals,...}) (const_min_arity, const_needs_hBOOL) =
fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
fun display_arity const_needs_hBOOL (c,n) =
ResAxioms.trace_msg (fn () => "Constant: " ^ c ^ " arity:\t" ^ Int.toString n ^
(if needs_hBOOL const_needs_hBOOL c then " needs hBOOL" else ""));
fun count_constants (conjectures, _, extra_clauses, helper_clauses, _, _) =
if minimize_applies then
let val (const_min_arity, const_needs_hBOOL) =
fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
|> fold count_constants_clause extra_clauses
|> fold count_constants_clause helper_clauses
val _ = List.app (display_arity const_needs_hBOOL) (Symtab.dest (const_min_arity))
in (const_min_arity, const_needs_hBOOL) end
else (Symtab.empty, Symtab.empty);
(* tptp format *)
fun tptp_write_file t_full file clauses =
let
val (conjectures, axclauses, _, helper_clauses,
classrel_clauses, arity_clauses) = clauses
val (cma, cnh) = count_constants clauses
val params = (t_full, cma, cnh)
val (tptp_clss,tfree_litss) = ListPair.unzip (map (clause2tptp params) conjectures)
val tfree_clss = map RC.tptp_tfree_clause (List.foldl (gen_union (op =)) [] tfree_litss)
val _ =
File.write_list file (
map (#1 o (clause2tptp params)) axclauses @
tfree_clss @
tptp_clss @
map RC.tptp_classrelClause classrel_clauses @
map RC.tptp_arity_clause arity_clauses @
map (#1 o (clause2tptp params)) helper_clauses)
in (length axclauses + 1, length tfree_clss + length tptp_clss)
end;
(* dfg format *)
fun dfg_write_file t_full file clauses =
let
val (conjectures, axclauses, _, helper_clauses,
classrel_clauses, arity_clauses) = clauses
val (cma, cnh) = count_constants clauses
val params = (t_full, cma, cnh)
val (dfg_clss, tfree_litss) = ListPair.unzip (map (clause2dfg params) conjectures)
and probname = Path.implode (Path.base file)
val axstrs = map (#1 o (clause2dfg params)) axclauses
val tfree_clss = map RC.dfg_tfree_clause (RC.union_all tfree_litss)
val helper_clauses_strs = map (#1 o (clause2dfg params)) helper_clauses
val (funcs,cl_preds) = decls_of_clauses params (helper_clauses @ conjectures @ axclauses) arity_clauses
and ty_preds = preds_of_clauses axclauses classrel_clauses arity_clauses
val _ =
File.write_list file (
RC.string_of_start probname ::
RC.string_of_descrip probname ::
RC.string_of_symbols (RC.string_of_funcs funcs)
(RC.string_of_preds (cl_preds @ ty_preds)) ::
"list_of_clauses(axioms,cnf).\n" ::
axstrs @
map RC.dfg_classrelClause classrel_clauses @
map RC.dfg_arity_clause arity_clauses @
helper_clauses_strs @
["end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n"] @
tfree_clss @
dfg_clss @
["end_of_list.\n\n",
(*VarWeight=3 helps the HO problems, probably by counteracting the presence of hAPP*)
"list_of_settings(SPASS).\n{*\nset_flag(VarWeight,3).\n*}\nend_of_list.\n\n",
"end_problem.\n"])
in (length axclauses + length classrel_clauses + length arity_clauses +
length helper_clauses + 1, length tfree_clss + length dfg_clss)
end;
end