(* ID: $Id$
Author: Jia Meng, NICTA
FOL clauses translated from HOL formulae. Combinators are used to represent lambda terms.
*)
structure ResHolClause =
struct
val include_combS = ref false;
val include_min_comb = ref false;
val const_typargs = ref (Library.K [] : (string*typ -> typ list));
fun init thy = (include_combS:=false;include_min_comb:=false;const_typargs := Sign.const_typargs thy);
(**********************************************************************)
(* convert a Term.term with lambdas into a Term.term with combinators *)
(**********************************************************************)
fun is_free (Bound(a)) n = (a = n)
| is_free (Abs(x,_,b)) n = (is_free b (n+1))
| is_free (P $ Q) n = ((is_free P n) orelse (is_free Q n))
| is_free _ _ = false;
exception LAM2COMB of term;
exception BND of term;
fun decre_bndVar (Bound n) = Bound (n-1)
| decre_bndVar (P $ Q) = (decre_bndVar P) $ (decre_bndVar Q)
| decre_bndVar t =
case t of Const(_,_) => t
| Free(_,_) => t
| Var(_,_) => t
| Abs(_,_,_) => raise BND(t); (*should not occur*)
(*******************************************)
fun lam2comb (Abs(x,tp,Bound 0)) _ =
let val tpI = Type("fun",[tp,tp])
in
include_min_comb:=true;
Const("COMBI",tpI)
end
| lam2comb (Abs(x,tp,Bound n)) Bnds =
let val (Bound n') = decre_bndVar (Bound n)
val tb = List.nth(Bnds,n')
val tK = Type("fun",[tb,Type("fun",[tp,tb])])
in
include_min_comb:=true;
Const("COMBK",tK) $ (Bound n')
end
| lam2comb (Abs(x,t1,Const(c,t2))) _ =
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
in
include_min_comb:=true;
Const("COMBK",tK) $ Const(c,t2)
end
| lam2comb (Abs(x,t1,Free(v,t2))) _ =
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
in
include_min_comb:=true;
Const("COMBK",tK) $ Free(v,t2)
end
| lam2comb (Abs(x,t1,Var(ind,t2))) _=
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
in
include_min_comb:=true;
Const("COMBK",tK) $ Var(ind,t2)
end
| lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds =
let val nfreeP = not(is_free P 0)
val tr = Term.type_of1(t1::Bnds,P)
in
if nfreeP then (decre_bndVar P)
else (
let val tI = Type("fun",[t1,t1])
val P' = lam2comb (Abs(x,t1,P)) Bnds
val tp' = Term.type_of1(Bnds,P')
val tS = Type("fun",[tp',Type("fun",[tI,tr])])
in
include_min_comb:=true;
include_combS:=true;
Const("COMBS",tS) $ P' $ Const("COMBI",tI)
end)
end
| lam2comb (t as (Abs(x,t1,P$Q))) Bnds =
let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
val tpq = Term.type_of1(t1::Bnds, P$Q)
in
if(nfreeP andalso nfreeQ) then (
let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
val PQ' = decre_bndVar(P $ Q)
in
include_min_comb:=true;
Const("COMBK",tK) $ PQ'
end)
else (
if nfreeP then (
let val Q' = lam2comb (Abs(x,t1,Q)) Bnds
val P' = decre_bndVar P
val tp = Term.type_of1(Bnds,P')
val tq' = Term.type_of1(Bnds, Q')
val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])
in
include_min_comb:=true;
Const("COMBB",tB) $ P' $ Q'
end)
else (
if nfreeQ then (
let val P' = lam2comb (Abs(x,t1,P)) Bnds
val Q' = decre_bndVar Q
val tq = Term.type_of1(Bnds,Q')
val tp' = Term.type_of1(Bnds, P')
val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])
in
include_min_comb:=true;
Const("COMBC",tC) $ P' $ Q'
end)
else(
let val P' = lam2comb (Abs(x,t1,P)) Bnds
val Q' = lam2comb (Abs(x,t1,Q)) Bnds
val tp' = Term.type_of1(Bnds,P')
val tq' = Term.type_of1(Bnds,Q')
val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])
in
include_min_comb:=true;
include_combS:=true;
Const("COMBS",tS) $ P' $ Q'
end)))
end
| lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);
(*********************)
fun to_comb (Abs(x,tp,b)) Bnds =
let val b' = to_comb b (tp::Bnds)
in lam2comb (Abs(x,tp,b')) Bnds end
| to_comb (P $ Q) Bnds = ((to_comb P Bnds) $ (to_comb Q Bnds))
| to_comb t _ = t;
fun comb_of t = to_comb t [];
(* print a term containing combinators, used for debugging *)
exception TERM_COMB of term;
fun string_of_term (Const(c,t)) = c
| string_of_term (Free(v,t)) = v
| string_of_term (Var((x,n),t)) =
let val xn = x ^ "_" ^ (string_of_int n)
in xn end
| string_of_term (P $ Q) =
let val P' = string_of_term P
val Q' = string_of_term Q
in
"(" ^ P' ^ " " ^ Q' ^ ")" end
| string_of_term t = raise TERM_COMB (t);
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
type axiom_name = string;
datatype kind = Axiom | Conjecture;
fun name_of_kind Axiom = "axiom"
| name_of_kind Conjecture = "conjecture";
type polarity = bool;
type indexname = Term.indexname;
type clause_id = int;
type csort = Term.sort;
type ctyp = ResClause.fol_type;
val string_of_ctyp = ResClause.string_of_fol_type;
type ctyp_var = ResClause.typ_var;
type ctype_literal = ResClause.type_literal;
datatype combterm = CombConst of string * ctyp * ctyp list
| CombFree of string * ctyp
| CombVar of string * ctyp
| CombApp of combterm * combterm * ctyp
| Bool of combterm
| Equal of combterm * combterm;
datatype literal = Literal of polarity * combterm;
datatype clause =
Clause of {clause_id: clause_id,
axiom_name: axiom_name,
kind: kind,
literals: literal list,
ctypes_sorts: (ctyp_var * csort) list,
ctvar_type_literals: ctype_literal list,
ctfree_type_literals: ctype_literal list};
fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
fun get_axiomName (Clause cls) = #axiom_name cls;
fun get_clause_id (Clause cls) = #clause_id cls;
fun get_literals (c as Clause(cls)) = #literals cls;
exception TERM_ORD of string
fun term_ord (CombVar(_,_),CombVar(_,_)) = EQUAL
| term_ord (CombVar(_,_),_) = LESS
| term_ord (CombFree(_,_),CombVar(_,_)) = GREATER
| term_ord (CombFree(f1,tp1),CombFree(f2,tp2)) =
let val ord1 = string_ord(f1,f2)
in
case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])
| _ => ord1
end
| term_ord (CombFree(_,_),_) = LESS
| term_ord (CombConst(_,_,_),CombVar(_,_)) = GREATER
| term_ord (CombConst(_,_,_),CombFree(_,_)) = GREATER
| term_ord (CombConst(c1,tp1,_),CombConst(c2,tp2,_)) =
let val ord1 = string_ord (c1,c2)
in
case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])
| _ => ord1
end
| term_ord (CombConst(_,_,_),_) = LESS
| term_ord (CombApp(_,_,_),Bool(_)) = raise TERM_ORD("bool")
| term_ord (CombApp(_,_,_),Equal(_,_)) = LESS
| term_ord (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) =
let val ord1 = term_ord (f1,f2)
val ord2 = case ord1 of EQUAL => term_ord (arg1,arg2)
| _ => ord1
in
case ord2 of EQUAL => ResClause.types_ord ([tp1],[tp2])
| _ => ord2
end
| term_ord (CombApp(_,_,_),_) = GREATER
| term_ord (Bool(_),_) = raise TERM_ORD("bool")
| term_ord (Equal(t1,t2),Equal(t3,t4)) = ResClause.list_ord term_ord ([t1,t2],[t3,t4])
| term_ord (Equal(_,_),_) = GREATER;
fun predicate_ord (Equal(_,_),Bool(_)) = LESS
| predicate_ord (Equal(t1,t2),Equal(t3,t4)) =
ResClause.list_ord term_ord ([t1,t2],[t3,t4])
| predicate_ord (Bool(_),Equal(_,_)) = GREATER
| predicate_ord (Bool(t1),Bool(t2)) = term_ord (t1,t2)
fun literal_ord (Literal(false,_),Literal(true,_)) = LESS
| literal_ord (Literal(true,_),Literal(false,_)) = GREATER
| literal_ord (Literal(_,pred1),Literal(_,pred2)) = predicate_ord(pred1,pred2);
fun sort_lits lits = sort literal_ord lits;
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =
(pol andalso c = "c_False") orelse
(not pol andalso c = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =
(pol andalso c = "c_True") orelse
(not pol andalso c = "c_False")
| isTrue _ = false;
fun isTaut (Clause {literals,...}) = exists isTrue literals;
fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =
if forall isFalse literals
then error "Problem too trivial for resolution (empty clause)"
else
Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,
literals = literals, ctypes_sorts = ctypes_sorts,
ctvar_type_literals = ctvar_type_literals,
ctfree_type_literals = ctfree_type_literals};
fun type_of (Type (a, Ts)) =
let val (folTypes,ts) = types_of Ts
val t = ResClause.make_fixed_type_const a
in
(ResClause.mk_fol_type("Comp",t,folTypes),ts)
end
| type_of (tp as (TFree(a,s))) =
let val t = ResClause.make_fixed_type_var a
in
(ResClause.mk_fol_type("Fixed",t,[]),[ResClause.mk_typ_var_sort tp])
end
| type_of (tp as (TVar(v,s))) =
let val t = ResClause.make_schematic_type_var v
in
(ResClause.mk_fol_type("Var",t,[]),[ResClause.mk_typ_var_sort tp])
end
and types_of Ts =
let val foltyps_ts = map type_of Ts
val (folTyps,ts) = ListPair.unzip foltyps_ts
in
(folTyps,ResClause.union_all ts)
end;
(* same as above, but no gathering of sort information *)
fun simp_type_of (Type (a, Ts)) =
let val typs = map simp_type_of Ts
val t = ResClause.make_fixed_type_const a
in
ResClause.mk_fol_type("Comp",t,typs)
end
| simp_type_of (TFree (a,s)) = ResClause.mk_fol_type("Fixed",ResClause.make_fixed_type_var a,[])
| simp_type_of (TVar (v,s)) = ResClause.mk_fol_type("Var",ResClause.make_schematic_type_var v,[]);
fun comb_typ ("COMBI",t) =
let val t' = domain_type t
in
[simp_type_of t']
end
| comb_typ ("COMBK",t) =
let val a = domain_type t
val b = domain_type (range_type t)
in
map simp_type_of [a,b]
end
| comb_typ ("COMBS",t) =
let val t' = domain_type t
val a = domain_type t'
val b = domain_type (range_type t')
val c = range_type (range_type t')
in
map simp_type_of [a,b,c]
end
| comb_typ ("COMBB",t) =
let val ab = domain_type t
val ca = domain_type (range_type t)
val a = domain_type ab
val b = range_type ab
val c = domain_type ca
in
map simp_type_of [a,b,c]
end
| comb_typ ("COMBC",t) =
let val t1 = domain_type t
val a = domain_type t1
val b = domain_type (range_type t1)
val c = range_type (range_type t1)
in
map simp_type_of [a,b,c]
end;
fun const_type_of ("COMBI",t) =
let val (tp,ts) = type_of t
val I_var = comb_typ ("COMBI",t)
in
(tp,ts,I_var)
end
| const_type_of ("COMBK",t) =
let val (tp,ts) = type_of t
val K_var = comb_typ ("COMBK",t)
in
(tp,ts,K_var)
end
| const_type_of ("COMBS",t) =
let val (tp,ts) = type_of t
val S_var = comb_typ ("COMBS",t)
in
(tp,ts,S_var)
end
| const_type_of ("COMBB",t) =
let val (tp,ts) = type_of t
val B_var = comb_typ ("COMBB",t)
in
(tp,ts,B_var)
end
| const_type_of ("COMBC",t) =
let val (tp,ts) = type_of t
val C_var = comb_typ ("COMBC",t)
in
(tp,ts,C_var)
end
| const_type_of (c,t) =
let val (tp,ts) = type_of t
val tvars = !const_typargs(c,t)
val tvars' = map simp_type_of tvars
in
(tp,ts,tvars')
end;
fun is_bool_type (Type("bool",[])) = true
| is_bool_type _ = false;
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
fun combterm_of (Const(c,t)) =
let val (tp,ts,tvar_list) = const_type_of (c,t)
val is_bool = is_bool_type t
val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)
val c'' = if is_bool then Bool(c') else c'
in
(c'',ts)
end
| combterm_of (Free(v,t)) =
let val (tp,ts) = type_of t
val is_bool = is_bool_type t
val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
else CombFree(ResClause.make_fixed_var v,tp)
val v'' = if is_bool then Bool(v') else v'
in
(v'',ts)
end
| combterm_of (Var(v,t)) =
let val (tp,ts) = type_of t
val is_bool = is_bool_type t
val v' = CombVar(ResClause.make_schematic_var v,tp)
val v'' = if is_bool then Bool(v') else v'
in
(v'',ts)
end
| combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)
let val (P',tsP) = combterm_of P
val (Q',tsQ) = combterm_of Q
in
(Equal(P',Q'),tsP union tsQ)
end
| combterm_of (t as (P $ Q)) =
let val (P',tsP) = combterm_of P
val (Q',tsQ) = combterm_of Q
val tp = Term.type_of t
val tp' = simp_type_of tp
val is_bool = is_bool_type tp
val t' = CombApp(P',Q',tp')
val t'' = if is_bool then Bool(t') else t'
in
(t'',tsP union tsQ)
end;
fun predicate_of ((Const("Not",_) $ P), polarity) =
predicate_of (P, not polarity)
| predicate_of (term,polarity) = (combterm_of term,polarity);
fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
| literals_of_term1 args (Const("op |",_) $ P $ Q) =
let val args' = literals_of_term1 args P
in
literals_of_term1 args' Q
end
| literals_of_term1 (lits,ts) P =
let val ((pred,ts'),pol) = predicate_of (P,true)
val lits' = Literal(pol,pred)::lits
in
(lits',ts union ts')
end;
fun literals_of_term P = literals_of_term1 ([],[]) P;
(* making axiom and conjecture clauses *)
fun make_axiom_clause term (ax_name,cls_id) =
let val term' = comb_of term
val (lits,ctypes_sorts) = literals_of_term term'
val lits' = sort_lits lits
val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
in
make_clause(cls_id,ax_name,Axiom,
lits',ctypes_sorts,ctvar_lits,ctfree_lits)
end;
fun make_conjecture_clause n t =
let val t' = comb_of t
val (lits,ctypes_sorts) = literals_of_term t'
val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
in
make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)
end;
fun make_conjecture_clauses_aux _ [] = []
| make_conjecture_clauses_aux n (t::ts) =
make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;
val make_conjecture_clauses = make_conjecture_clauses_aux 0;
(**********************************************************************)
(* convert clause into ATP specific formats: *)
(* TPTP used by Vampire and E *)
(**********************************************************************)
val type_wrapper = "typeinfo";
datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
val typ_level = ref T_PARTIAL;
fun full_types () = (typ_level:=T_FULL);
fun partial_types () = (typ_level:=T_PARTIAL);
fun const_types_only () = (typ_level:=T_CONST);
fun no_types () = (typ_level:=T_NONE);
fun find_typ_level () = !typ_level;
fun wrap_type (c,t) =
case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [c,t])
| _ => c;
val bool_tp = ResClause.make_fixed_type_const "bool";
val app_str = "hAPP";
val bool_str = "hBOOL";
exception STRING_OF_COMBTERM of int;
(* convert literals of clauses into strings *)
fun string_of_combterm1_aux _ (CombConst(c,tp,_)) =
let val tp' = string_of_ctyp tp
in
(wrap_type (c,tp'),tp')
end
| string_of_combterm1_aux _ (CombFree(v,tp)) =
let val tp' = string_of_ctyp tp
in
(wrap_type (v,tp'),tp')
end
| string_of_combterm1_aux _ (CombVar(v,tp)) =
let val tp' = string_of_ctyp tp
in
(wrap_type (v,tp'),tp')
end
| string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =
let val (s1,tp1) = string_of_combterm1_aux is_pred t1
val (s2,tp2) = string_of_combterm1_aux is_pred t2
val tp' = ResClause.string_of_fol_type tp
val r = case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [(app_str ^ (ResClause.paren_pack [s1,s2])),tp'])
| T_PARTIAL => app_str ^ (ResClause.paren_pack [s1,s2,tp1])
| T_NONE => app_str ^ (ResClause.paren_pack [s1,s2])
| T_CONST => raise STRING_OF_COMBTERM (1) (*should not happen, if happened may be a bug*)
in (r,tp')
end
| string_of_combterm1_aux is_pred (Bool(t)) =
let val (t',_) = string_of_combterm1_aux false t
val r = if is_pred then bool_str ^ (ResClause.paren_pack [t'])
else t'
in
(r,bool_tp)
end
| string_of_combterm1_aux _ (Equal(t1,t2)) =
let val (s1,_) = string_of_combterm1_aux false t1
val (s2,_) = string_of_combterm1_aux false t2
in
("equal" ^ (ResClause.paren_pack [s1,s2]),bool_tp)
end;
fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);
fun string_of_combterm2 _ (CombConst(c,tp,tvars)) =
let val tvars' = map string_of_ctyp tvars
in
c ^ (ResClause.paren_pack tvars')
end
| string_of_combterm2 _ (CombFree(v,tp)) = v
| string_of_combterm2 _ (CombVar(v,tp)) = v
| string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =
let val s1 = string_of_combterm2 is_pred t1
val s2 = string_of_combterm2 is_pred t2
in
app_str ^ (ResClause.paren_pack [s1,s2])
end
| string_of_combterm2 is_pred (Bool(t)) =
let val t' = string_of_combterm2 false t
in
if is_pred then bool_str ^ (ResClause.paren_pack [t'])
else t'
end
| string_of_combterm2 _ (Equal(t1,t2)) =
let val s1 = string_of_combterm2 false t1
val s2 = string_of_combterm2 false t2
in
("equal" ^ (ResClause.paren_pack [s1,s2]))
end;
fun string_of_combterm is_pred term =
case !typ_level of T_CONST => string_of_combterm2 is_pred term
| _ => string_of_combterm1 is_pred term;
fun string_of_clausename (cls_id,ax_name) =
ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
fun string_of_type_clsname (cls_id,ax_name,idx) =
string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
fun tptp_literal (Literal(pol,pred)) =
let val pred_string = string_of_combterm true pred
val pol_str = if pol then "++" else "--"
in
pol_str ^ pred_string
end;
fun tptp_type_lits (Clause cls) =
let val lits = map tptp_literal (#literals cls)
val ctvar_lits_strs =
case !typ_level of T_NONE => []
| _ => (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls))
val ctfree_lits =
case !typ_level of T_NONE => []
| _ => (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls))
in
(ctvar_lits_strs @ lits, ctfree_lits)
end;
fun clause2tptp cls =
let val (lits,ctfree_lits) = tptp_type_lits cls
val cls_id = get_clause_id cls
val ax_name = get_axiomName cls
val knd = string_of_kind cls
val lits_str = ResClause.bracket_pack lits
val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
in
(cls_str,ctfree_lits)
end;
(**********************************************************************)
(* clause equalities and hashing functions *)
(**********************************************************************)
fun combterm_eq (CombConst(c1,tp1,tps1),CombConst(c2,tp2,tps2)) vtvars =
let val (eq1,vtvars1) = if c1 = c2 then ResClause.types_eq (tps1,tps2) vtvars
else (false,vtvars)
in
(eq1,vtvars1)
end
| combterm_eq (CombConst(_,_,_),_) vtvars = (false,vtvars)
| combterm_eq (CombFree(a1,tp1),CombFree(a2,tp2)) vtvars =
if a1 = a2 then ResClause.types_eq ([tp1],[tp2]) vtvars
else (false,vtvars)
| combterm_eq (CombFree(_,_),_) vtvars = (false,vtvars)
| combterm_eq (CombVar(v1,tp1),CombVar(v2,tp2)) (vars,tvars) =
(case ResClause.check_var_pairs(v1,v2) vars of 0 => ResClause.types_eq ([tp1],[tp2]) ((v1,v2)::vars,tvars)
| 1 => ResClause.types_eq ([tp1],[tp2]) (vars,tvars)
| 2 => (false,(vars,tvars)))
| combterm_eq (CombVar(_,_),_) vtvars = (false,vtvars)
| combterm_eq (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) vtvars =
let val (eq1,vtvars1) = combterm_eq (f1,f2) vtvars
val (eq2,vtvars2) = if eq1 then combterm_eq (arg1,arg2) vtvars1
else (eq1,vtvars1)
in
if eq2 then ResClause.types_eq ([tp1],[tp2]) vtvars2
else (eq2,vtvars2)
end
| combterm_eq (CombApp(_,_,_),_) vtvars = (false,vtvars)
| combterm_eq (Bool(t1),Bool(t2)) vtvars = combterm_eq (t1,t2) vtvars
| combterm_eq (Bool(_),_) vtvars = (false,vtvars)
| combterm_eq (Equal(t1,t2),Equal(t3,t4)) vtvars =
let val (eq1,vtvars1) = combterm_eq (t1,t3) vtvars
in
if eq1 then combterm_eq (t2,t4) vtvars1
else (eq1,vtvars1)
end
| combterm_eq (Equal(t1,t2),_) vtvars = (false,vtvars);
fun lit_eq (Literal(pol1,pred1),Literal(pol2,pred2)) vtvars =
if (pol1 = pol2) then combterm_eq (pred1,pred2) vtvars
else (false,vtvars);
fun lits_eq ([],[]) vtvars = (true,vtvars)
| lits_eq (l1::ls1,l2::ls2) vtvars =
let val (eq1,vtvars1) = lit_eq (l1,l2) vtvars
in
if eq1 then lits_eq (ls1,ls2) vtvars1
else (false,vtvars1)
end;
fun clause_eq (cls1,cls2) =
let val lits1 = get_literals cls1
val lits2 = get_literals cls2
in
length lits1 = length lits2 andalso #1 (lits_eq (lits1,lits2) ([],[]))
end;
val xor_words = List.foldl Word.xorb 0w0;
fun hash_combterm (CombVar(_,_),w) = w
| hash_combterm (CombFree(f,_),w) = Polyhash.hashw_string(f,w)
| hash_combterm (CombConst(c,tp,tps),w) = Polyhash.hashw_string(c,w)
| hash_combterm (CombApp(f,arg,tp),w) = hash_combterm (arg, hash_combterm (f,w))
| hash_combterm (Bool(t),w) = hash_combterm (t,w)
| hash_combterm (Equal(t1,t2),w) =
List.foldl hash_combterm (Polyhash.hashw_string ("equal",w)) [t1,t2]
fun hash_literal (Literal(true,pred)) = hash_combterm(pred,0w0)
| hash_literal (Literal(false,pred)) = Word.notb(hash_combterm(pred,0w0));
fun hash_clause clause = xor_words (map hash_literal (get_literals clause));
end