Changed and removed some functions related to combinators, since they are Isabelle constants now.
(* ID: $Id$
Author: Jia Meng, NICTA
FOL clauses translated from HOL formulae. Combinators are used to represent lambda terms.
*)
structure ResHolClause =
struct
(* theorems for combinators and function extensionality *)
val ext = thm "HOL.ext";
val comb_I = thm "Reconstruction.COMBI_def";
val comb_K = thm "Reconstruction.COMBK_def";
val comb_B = thm "Reconstruction.COMBB_def";
val comb_C = thm "Reconstruction.COMBC_def";
val comb_S = thm "Reconstruction.COMBS_def";
val comb_B' = thm "Reconstruction.COMBB'_def";
val comb_C' = thm "Reconstruction.COMBC'_def";
val comb_S' = thm "Reconstruction.COMBS'_def";
val fequal_imp_equal = thm "Reconstruction.fequal_imp_equal";
val equal_imp_fequal = thm "Reconstruction.equal_imp_fequal";
(* a flag to set if we use extra combinators B',C',S' *)
val use_combB'C'S' = ref true;
val combI_count = ref 0;
val combK_count = ref 0;
val combB_count = ref 0;
val combC_count = ref 0;
val combS_count = ref 0;
val combB'_count = ref 0;
val combC'_count = ref 0;
val combS'_count = ref 0;
fun increI count_comb = if count_comb then combI_count := !combI_count + 1 else ();
fun increK count_comb = if count_comb then combK_count := !combK_count + 1 else ();
fun increB count_comb = if count_comb then combB_count := !combB_count + 1 else ();
fun increC count_comb = if count_comb then combC_count := !combC_count + 1 else ();
fun increS count_comb = if count_comb then combS_count := !combS_count + 1 else ();
fun increB' count_comb = if count_comb then combB'_count := !combB'_count + 1 else ();
fun increC' count_comb = if count_comb then combC'_count := !combC'_count + 1 else ();
fun increS' count_comb = if count_comb then combS'_count := !combS'_count + 1 else ();
exception DECRE_COMB of string;
fun decreB count_comb n = if count_comb then (if !combB_count >= n then combB_count := !combB_count - n else raise (DECRE_COMB "COMBB")) else ();
fun decreC count_comb n = if count_comb then (if !combC_count >= n then combC_count := !combC_count - n else raise (DECRE_COMB "COMBC")) else ();
fun decreS count_comb n = if count_comb then (if !combS_count >= n then combS_count := !combS_count - n else raise (DECRE_COMB "COMBS")) else ();
val const_typargs = ref (Library.K [] : (string*typ -> typ list));
fun init thy = (combI_count:=0; combK_count:=0;combB_count:=0;combC_count:=0;combS_count:=0;combB'_count:=0;combC'_count:=0;combS'_count:=0;
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 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 mk_compact_comb (tm as (Const("COMBB",_)$p) $ (Const("COMBB",_)$q$r)) Bnds count_comb =
let val tp_p = Term.type_of1(Bnds,p)
val tp_q = Term.type_of1(Bnds,q)
val tp_r = Term.type_of1(Bnds,r)
val typ = Term.type_of1(Bnds,tm)
val typ_B' = [tp_p,tp_q,tp_r] ---> typ
val _ = increB' count_comb
val _ = decreB count_comb 2
in
Const("COMBB_e",typ_B') $ p $ q $ r
end
| mk_compact_comb (tm as (Const("COMBC",_) $ (Const("COMBB",_)$p$q) $ r)) Bnds count_comb =
let val tp_p = Term.type_of1(Bnds,p)
val tp_q = Term.type_of1(Bnds,q)
val tp_r = Term.type_of1(Bnds,r)
val typ = Term.type_of1(Bnds,tm)
val typ_C' = [tp_p,tp_q,tp_r] ---> typ
val _ = increC' count_comb
val _ = decreC count_comb 1
val _ = decreB count_comb 1
in
Const("COMBC_e",typ_C') $ p $ q $ r
end
| mk_compact_comb (tm as (Const("COMBS",_) $ (Const("COMBB",_)$p$q) $ r)) Bnds count_comb =
let val tp_p = Term.type_of1(Bnds,p)
val tp_q = Term.type_of1(Bnds,q)
val tp_r = Term.type_of1(Bnds,r)
val typ = Term.type_of1(Bnds,tm)
val typ_S' = [tp_p,tp_q,tp_r] ---> typ
val _ = increS' count_comb
val _ = decreS count_comb 1
val _ = decreB count_comb 1
in
Const("COMBS_e",typ_S') $ p $ q $ r
end
| mk_compact_comb tm _ _ = tm;
fun compact_comb t Bnds count_comb = if !use_combB'C'S' then mk_compact_comb t Bnds count_comb else t;
fun lam2comb (Abs(x,tp,Bound 0)) _ count_comb =
let val tpI = Type("fun",[tp,tp])
val _ = increI count_comb
in
Const("COMBI",tpI)
end
| lam2comb (Abs(x,tp,Bound n)) Bnds count_comb =
let val (Bound n') = decre_bndVar (Bound n)
val tb = List.nth(Bnds,n')
val tK = Type("fun",[tb,Type("fun",[tp,tb])])
val _ = increK count_comb
in
Const("COMBK",tK) $ (Bound n')
end
| lam2comb (Abs(x,t1,Const(c,t2))) _ count_comb =
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
val _ = increK count_comb
in
Const("COMBK",tK) $ Const(c,t2)
end
| lam2comb (Abs(x,t1,Free(v,t2))) _ count_comb =
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
val _ = increK count_comb
in
Const("COMBK",tK) $ Free(v,t2)
end
| lam2comb (Abs(x,t1,Var(ind,t2))) _ count_comb =
let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
val _ = increK count_comb
in
Const("COMBK",tK) $ Var(ind,t2)
end
| lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds count_comb =
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 count_comb
val tp' = Term.type_of1(Bnds,P')
val tS = Type("fun",[tp',Type("fun",[tI,tr])])
val _ = increI count_comb
val _ = increS count_comb
in
compact_comb (Const("COMBS",tS) $ P' $ Const("COMBI",tI)) Bnds count_comb
end)
end
| lam2comb (t as (Abs(x,t1,P$Q))) Bnds count_comb =
let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
val tpq = Term.type_of1(t1::Bnds, P$Q)
in
if(nfreeP andalso nfreeQ) then (
let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
val PQ' = decre_bndVar(P $ Q)
val _ = increK count_comb
in
Const("COMBK",tK) $ PQ'
end)
else (
if nfreeP then (
let val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb
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])])])
val _ = increB count_comb
in
compact_comb (Const("COMBB",tB) $ P' $ Q') Bnds count_comb
end)
else (
if nfreeQ then (
let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
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])])])
val _ = increC count_comb
in
compact_comb (Const("COMBC",tC) $ P' $ Q') Bnds count_comb
end)
else(
let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb
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])])])
val _ = increS count_comb
in
compact_comb (Const("COMBS",tS) $ P' $ Q') Bnds count_comb
end)))
end
| lam2comb (t as (Abs(x,t1,_))) _ _ = raise ResClause.CLAUSE("HOL CLAUSE",t);
(*********************)
fun to_comb (Abs(x,tp,b)) Bnds count_comb =
let val b' = to_comb b (tp::Bnds) count_comb
in lam2comb (Abs(x,tp,b')) Bnds count_comb end
| to_comb (P $ Q) Bnds count_comb = ((to_comb P Bnds count_comb) $ (to_comb Q Bnds count_comb))
| to_comb t _ _ = t;
fun comb_of t count_comb = to_comb t [] count_comb;
(* 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)) = x ^ "_" ^ (string_of_int n)
| string_of_term (P $ Q) =
"(" ^ string_of_term P ^ " " ^ string_of_term Q ^ ")"
| string_of_term t = raise TERM_COMB (t);
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
val typ_level = ref T_CONST;
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;
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;
datatype literal = Literal of polarity * combterm;
datatype clause =
Clause of {clause_id: clause_id,
axiom_name: axiom_name,
th: thm,
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;
(*********************************************************************)
(* 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 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 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 (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;
fun occurs a (CombVar(b,_)) = a = b
| occurs a (CombApp(t1,t2,_)) = (occurs a t1) orelse (occurs a t2)
| occurs _ _ = false
fun too_general_terms (CombVar(v,_), t) = not (occurs v t)
| too_general_terms _ = false;
fun too_general_lit (Literal(true,(Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))))) =
too_general_terms (t1,t2) orelse too_general_terms (t2,t1)
| too_general_lit _ = false;
(* forbid a clause that contains hBOOL(V) *)
fun too_general [] = false
| too_general (lit::lits) =
case lit of Literal(_,Bool(CombVar(_,_))) => true
| _ => too_general lits;
(* making axiom and conjecture clauses *)
exception MAKE_CLAUSE
fun make_clause(clause_id,axiom_name,kind,thm,is_user) =
let val term = prop_of thm
val term' = comb_of term is_user
val (lits,ctypes_sorts) = literals_of_term term'
val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts
in
if forall isFalse lits
then error "Problem too trivial for resolution (empty clause)"
else if too_general lits
then (Output.debug ("Omitting " ^ axiom_name ^ ": clause contains universal predicates");
raise MAKE_CLAUSE)
else
if (!typ_level <> T_FULL) andalso kind=Axiom andalso forall too_general_lit lits
then (Output.debug ("Omitting " ^ axiom_name ^ ": equalities are too general");
raise MAKE_CLAUSE)
else
Clause {clause_id = clause_id, axiom_name = axiom_name, th = thm, kind = kind,
literals = lits, ctypes_sorts = ctypes_sorts,
ctvar_type_literals = ctvar_lits,
ctfree_type_literals = ctfree_lits}
end;
fun make_axiom_clause thm (ax_name,cls_id,is_user) =
make_clause(cls_id,ax_name,Axiom,thm,is_user);
fun make_axiom_clauses [] user_lemmas = []
| make_axiom_clauses ((thm,(name,id))::thms) user_lemmas =
let val is_user = name mem user_lemmas
val cls = SOME (make_axiom_clause thm (name,id,is_user))
handle MAKE_CLAUSE => NONE
val clss = make_axiom_clauses thms user_lemmas
in
case cls of NONE => clss
| SOME(cls') => if isTaut cls' then clss
else (name,cls')::clss
end;
fun make_conjecture_clauses_aux _ [] = []
| make_conjecture_clauses_aux n (th::ths) =
make_clause(n,"conjecture",Conjecture,th,true) ::
make_conjecture_clauses_aux (n+1) ths;
val make_conjecture_clauses = make_conjecture_clauses_aux 0;
(**********************************************************************)
(* convert clause into ATP specific formats: *)
(* TPTP used by Vampire and E *)
(* DFG used by SPASS *)
(**********************************************************************)
val type_wrapper = "typeinfo";
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
val c' = if c = "equal" then "c_fequal" else c
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(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
if is_pred then
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
else
let val (t,_) = string_of_combterm1_aux false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
in
(t,bool_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;
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
val c' = if c = "equal" then "c_fequal" else c
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(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
if is_pred then
let val s1 = string_of_combterm2 false t1
val s2 = string_of_combterm2 false t2
in
("equal" ^ (ResClause.paren_pack [s1,s2]))
end
else
string_of_combterm2 false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
| 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;
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);
(* tptp format *)
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;
(* dfg format *)
fun dfg_literal (Literal(pol,pred)) = ResClause.dfg_sign pol (string_of_combterm true pred);
fun dfg_clause_aux (Clause{literals, ctypes_sorts, ...}) =
let val lits = map dfg_literal literals
val (tvar_lits,tfree_lits) = ResClause.add_typs_aux ctypes_sorts
val tvar_lits_strs =
case !typ_level of T_NONE => []
| _ => map ResClause.dfg_of_typeLit tvar_lits
val tfree_lits =
case !typ_level of T_NONE => []
| _ => map ResClause.dfg_of_typeLit tfree_lits
in
(tvar_lits_strs @ lits, tfree_lits)
end;
fun get_uvars (CombConst(_,_,_)) vars = vars
| get_uvars (CombFree(_,_)) vars = vars
| get_uvars (CombVar(v,tp)) vars = (v::vars)
| get_uvars (CombApp(P,Q,tp)) vars = get_uvars P (get_uvars Q vars)
| get_uvars (Bool(c)) vars = get_uvars c vars;
fun get_uvars_l (Literal(_,c)) = get_uvars c [];
fun dfg_vars (Clause {literals,...}) = ResClause.union_all (map get_uvars_l literals);
fun clause2dfg (cls as Clause{axiom_name,clause_id,kind,ctypes_sorts,...}) =
let val (lits,tfree_lits) = dfg_clause_aux cls
val vars = dfg_vars cls
val tvars = ResClause.get_tvar_strs ctypes_sorts
val knd = name_of_kind kind
val lits_str = commas lits
val cls_str = ResClause.gen_dfg_cls(clause_id, axiom_name, knd, lits_str, tvars@vars)
in (cls_str, tfree_lits) end;
fun init_funcs_tab funcs =
let val tp = !typ_level
val funcs1 = case tp of T_PARTIAL => Symtab.update ("hAPP",3) funcs
| _ => Symtab.update ("hAPP",2) funcs
val funcs2 = case tp of T_FULL => Symtab.update ("typeinfo",2) funcs1
| _ => funcs1
in
funcs2
end;
fun add_funcs (CombConst(c,_,tvars),funcs) =
if c = "equal" then foldl ResClause.add_foltype_funcs funcs tvars
else
(case !typ_level of T_CONST => foldl ResClause.add_foltype_funcs (Symtab.update(c,length tvars) funcs) tvars
| _ => foldl ResClause.add_foltype_funcs (Symtab.update(c,0) funcs) tvars)
| add_funcs (CombFree(v,ctp),funcs) = ResClause.add_foltype_funcs (ctp,Symtab.update (v,0) funcs)
| add_funcs (CombVar(_,ctp),funcs) = ResClause.add_foltype_funcs (ctp,funcs)
| add_funcs (CombApp(P,Q,_),funcs) = add_funcs(P,add_funcs (Q,funcs))
| add_funcs (Bool(t),funcs) = add_funcs (t,funcs);
fun add_literal_funcs (Literal(_,c), funcs) = add_funcs (c,funcs);
fun add_clause_funcs (Clause {literals, ...}, funcs) =
foldl add_literal_funcs funcs literals
handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")
fun funcs_of_clauses clauses arity_clauses =
Symtab.dest (foldl ResClause.add_arityClause_funcs
(foldl add_clause_funcs (init_funcs_tab Symtab.empty) clauses)
arity_clauses)
fun preds_of clsrel_clauses arity_clauses =
Symtab.dest
(foldl ResClause.add_classrelClause_preds
(foldl ResClause.add_arityClause_preds
(Symtab.update ("hBOOL",1) Symtab.empty)
arity_clauses)
clsrel_clauses)
(**********************************************************************)
(* write clauses to files *)
(**********************************************************************)
local
val cnf_helper_thms = ResAxioms.cnf_rules_pairs o (map ResAxioms.pairname)
in
fun get_helper_clauses () =
let val IK = if !combI_count > 0 orelse !combK_count > 0 then (Output.debug "Include combinator I K"; cnf_helper_thms [comb_I,comb_K]) else []
val BC = if !combB_count > 0 orelse !combC_count > 0 then (Output.debug "Include combinator B C"; cnf_helper_thms [comb_B,comb_C]) else []
val S = if !combS_count > 0 then (Output.debug "Include combinator S"; cnf_helper_thms [comb_S]) else []
val B'C' = if !combB'_count > 0 orelse !combC'_count > 0 then (Output.debug "Include combinator B' C'"; cnf_helper_thms [comb_B', comb_C']) else []
val S' = if !combS'_count > 0 then (Output.debug "Include combinator S'"; cnf_helper_thms [comb_S']) else []
val other = cnf_helper_thms [ext,fequal_imp_equal,equal_imp_fequal]
in
make_axiom_clauses (other @ IK @ BC @ S @ B'C' @ S') []
end
end
(* tptp format *)
(* write TPTP format to a single file *)
(* when "get_helper_clauses" is called, "include_combS" and "include_min_comb" should have correct values already *)
fun tptp_write_file thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas=
let val clss = make_conjecture_clauses thms
val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)
val tfree_clss = map ResClause.tptp_tfree_clause (foldl (op union_string) [] tfree_litss)
val out = TextIO.openOut filename
val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
in
List.app (curry TextIO.output out o #1 o clause2tptp) axclauses';
ResClause.writeln_strs out tfree_clss;
ResClause.writeln_strs out tptp_clss;
List.app (curry TextIO.output out o ResClause.tptp_classrelClause) classrel_clauses;
List.app (curry TextIO.output out o ResClause.tptp_arity_clause) arity_clauses;
List.app (curry TextIO.output out o #1 o clause2tptp) helper_clauses;
TextIO.closeOut out;
clnames
end;
(* dfg format *)
fun dfg_write_file thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas =
let val _ = Output.debug ("Preparing to write the DFG file " ^ filename)
val conjectures = make_conjecture_clauses thms
val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
val (dfg_clss,tfree_litss) = ListPair.unzip (map clause2dfg conjectures)
and probname = Path.pack (Path.base (Path.unpack filename))
val (axstrs,_) = ListPair.unzip (map clause2dfg axclauses')
val tfree_clss = map ResClause.dfg_tfree_clause (ResClause.union_all tfree_litss)
val out = TextIO.openOut filename
val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
val helper_clauses_strs = (#1 o ListPair.unzip o (map clause2dfg)) helper_clauses
val funcs = funcs_of_clauses (helper_clauses @ conjectures @ axclauses') arity_clauses
and preds = preds_of classrel_clauses arity_clauses
in
TextIO.output (out, ResClause.string_of_start probname);
TextIO.output (out, ResClause.string_of_descrip probname);
TextIO.output (out, ResClause.string_of_symbols (ResClause.string_of_funcs funcs) (ResClause.string_of_preds preds));
TextIO.output (out, "list_of_clauses(axioms,cnf).\n");
ResClause.writeln_strs out axstrs;
List.app (curry TextIO.output out o ResClause.dfg_classrelClause) classrel_clauses;
List.app (curry TextIO.output out o ResClause.dfg_arity_clause) arity_clauses;
ResClause.writeln_strs out helper_clauses_strs;
TextIO.output (out, "end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n");
ResClause.writeln_strs out tfree_clss;
ResClause.writeln_strs out dfg_clss;
TextIO.output (out, "end_of_list.\n\nend_problem.\n");
TextIO.closeOut out;
clnames
end;
end