(* Author: Jia Meng, Cambridge University Computer Laboratory
ID: $Id$
Copyright 2004 University of Cambridge
ML data structure for storing/printing FOL clauses and arity clauses.
Typed equality is treated differently.
*)
(*FIXME: is this signature necessary? Or maybe define and open a Basic_ResClause?*)
signature RES_CLAUSE =
sig
exception CLAUSE of string * term
type clause and arityClause and classrelClause
datatype fol_type = AtomV of string
| AtomF of string
| Comp of string * fol_type list;
datatype fol_term = UVar of string * fol_type
| Fun of string * fol_type list * fol_term list;
datatype predicate = Predicate of string * fol_type list * fol_term list;
datatype kind = Axiom | Conjecture;
val name_of_kind : kind -> string
type typ_var and type_literal and literal
val literals_of_term: Term.term -> literal list * (typ_var * Term.sort) list
val add_typs_aux : (typ_var * string list) list -> type_literal list * type_literal list
val arity_clause_thy: theory -> arityClause list
val ascii_of : string -> string
val tptp_pack : string list -> string
val make_classrel_clauses: theory -> class list -> class list -> classrelClause list
val clause_prefix : string
val clause2tptp : clause -> string * string list
val const_prefix : string
val dfg_write_file: thm list -> string ->
((thm * (string * int)) list * classrelClause list * arityClause list) -> string list
val fixed_var_prefix : string
val gen_tptp_cls : int * string * string * string list -> string
val get_axiomName : clause -> string
val get_literals : clause -> literal list
val init : theory -> unit
val isMeta : string -> bool
val isTaut : clause -> bool
val keep_types : bool ref
val list_ord : ('a * 'b -> order) -> 'a list * 'b list -> order
val make_axiom_clause : thm -> string * int -> clause option
val make_conjecture_clauses : thm list -> clause list
val make_fixed_const : string -> string
val make_fixed_type_const : string -> string
val make_fixed_type_var : string -> string
val make_fixed_var : string -> string
val make_schematic_type_var : string * int -> string
val make_schematic_var : string * int -> string
val make_type_class : string -> string
val mk_fol_type: string * string * fol_type list -> fol_type
val mk_typ_var_sort : Term.typ -> typ_var * sort
val paren_pack : string list -> string
val schematic_var_prefix : string
val string_of_fol_type : fol_type -> string
val tconst_prefix : string
val tfree_prefix : string
val tptp_arity_clause : arityClause -> string
val tptp_classrelClause : classrelClause -> string
val tptp_of_typeLit : type_literal -> string
val tptp_tfree_clause : string -> string
val tptp_write_file: thm list -> string ->
((thm * (string * int)) list * classrelClause list * arityClause list) -> string list
val tvar_prefix : string
val union_all : ''a list list -> ''a list
val writeln_strs: TextIO.outstream -> TextIO.vector list -> unit
val dfg_sign: bool -> string -> string
val dfg_of_typeLit: type_literal -> string
val get_tvar_strs: (typ_var * sort) list -> string list
val gen_dfg_cls: int * string * string * string * string list -> string
val add_foltype_funcs: fol_type * int Symtab.table -> int Symtab.table
val add_arityClause_funcs: arityClause * int Symtab.table -> int Symtab.table
val add_arityClause_preds: arityClause * int Symtab.table -> int Symtab.table
val add_classrelClause_preds : classrelClause * int Symtab.table -> int Symtab.table
val dfg_tfree_clause : string -> string
val string_of_start: string -> string
val string_of_descrip : string -> string
val string_of_symbols: string -> string -> string
val string_of_funcs: (string * int) list -> string
val string_of_preds: (string * Int.int) list -> string
val dfg_classrelClause: classrelClause -> string
val dfg_arity_clause: arityClause -> string
end;
structure ResClause =
struct
val schematic_var_prefix = "V_";
val fixed_var_prefix = "v_";
val tvar_prefix = "T_";
val tfree_prefix = "t_";
val clause_prefix = "cls_";
val arclause_prefix = "clsarity_"
val clrelclause_prefix = "clsrel_";
val const_prefix = "c_";
val tconst_prefix = "tc_";
val class_prefix = "class_";
fun union_all xss = foldl (op union) [] xss;
(*Provide readable names for the more common symbolic functions*)
val const_trans_table =
Symtab.make [("op =", "equal"),
("Orderings.less_eq", "lessequals"),
("Orderings.less", "less"),
("op &", "and"),
("op |", "or"),
("HOL.plus", "plus"),
("HOL.minus", "minus"),
("HOL.times", "times"),
("Divides.div", "div"),
("HOL.divide", "divide"),
("op -->", "implies"),
("{}", "emptyset"),
("op :", "in"),
("op Un", "union"),
("op Int", "inter"),
("List.op @", "append"),
("ATP_Linkup.fequal", "fequal"),
("ATP_Linkup.COMBI", "COMBI"),
("ATP_Linkup.COMBK", "COMBK"),
("ATP_Linkup.COMBB", "COMBB"),
("ATP_Linkup.COMBC", "COMBC"),
("ATP_Linkup.COMBS", "COMBS"),
("ATP_Linkup.COMBB'", "COMBB_e"),
("ATP_Linkup.COMBC'", "COMBC_e"),
("ATP_Linkup.COMBS'", "COMBS_e")];
val type_const_trans_table =
Symtab.make [("*", "prod"),
("+", "sum"),
("~=>", "map")];
(*Escaping of special characters.
Alphanumeric characters are left unchanged.
The character _ goes to __
Characters in the range ASCII space to / go to _A to _P, respectively.
Other printing characters go to _NNN where NNN is the decimal ASCII code.*)
local
val A_minus_space = Char.ord #"A" - Char.ord #" ";
fun ascii_of_c c =
if Char.isAlphaNum c then String.str c
else if c = #"_" then "__"
else if #" " <= c andalso c <= #"/"
then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
else if Char.isPrint c then ("_" ^ Int.toString (Char.ord c))
else ""
in
val ascii_of = String.translate ascii_of_c;
end;
(* convert a list of strings into one single string; surrounded by brackets *)
fun paren_pack [] = "" (*empty argument list*)
| paren_pack strings = "(" ^ commas strings ^ ")";
(*TSTP format uses (...) rather than the old [...]*)
fun tptp_pack strings = "(" ^ space_implode " | " strings ^ ")";
(*Remove the initial ' character from a type variable, if it is present*)
fun trim_type_var s =
if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
else error ("trim_type: Malformed type variable encountered: " ^ s);
fun ascii_of_indexname (v,0) = ascii_of v
| ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;
fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);
fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);
fun make_schematic_type_var (x,i) =
tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
fun lookup_const c =
case Symtab.lookup const_trans_table c of
SOME c' => c'
| NONE => ascii_of c;
fun lookup_type_const c =
case Symtab.lookup type_const_trans_table c of
SOME c' => c'
| NONE => ascii_of c;
fun make_fixed_const "op =" = "equal" (*MUST BE "equal" because it's built-in to ATPs*)
| make_fixed_const c = const_prefix ^ lookup_const c;
fun make_fixed_type_const c = tconst_prefix ^ lookup_type_const c;
fun make_type_class clas = class_prefix ^ ascii_of clas;
(***** definitions and functions for FOL clauses, for conversion to TPTP or DFG format. *****)
val keep_types = ref true;
datatype kind = Axiom | Conjecture;
fun name_of_kind Axiom = "axiom"
| name_of_kind Conjecture = "negated_conjecture";
type clause_id = int;
type axiom_name = string;
type polarity = bool;
(**** Isabelle FOL clauses ****)
datatype typ_var = FOLTVar of indexname | FOLTFree of string;
(*FIXME: give the constructors more sensible names*)
datatype fol_type = AtomV of string
| AtomF of string
| Comp of string * fol_type list;
fun string_of_fol_type (AtomV x) = x
| string_of_fol_type (AtomF x) = x
| string_of_fol_type (Comp(tcon,tps)) =
tcon ^ (paren_pack (map string_of_fol_type tps));
fun mk_fol_type ("Var",x,_) = AtomV(x)
| mk_fol_type ("Fixed",x,_) = AtomF(x)
| mk_fol_type ("Comp",con,args) = Comp(con,args)
(*First string is the type class; the second is a TVar or TFfree*)
datatype type_literal = LTVar of string * string | LTFree of string * string;
datatype fol_term = UVar of string * fol_type
| Fun of string * fol_type list * fol_term list;
datatype predicate = Predicate of string * fol_type list * fol_term list;
datatype literal = Literal of polarity * predicate;
fun mk_typ_var_sort (TFree(a,s)) = (FOLTFree a,s)
| mk_typ_var_sort (TVar(v,s)) = (FOLTVar v,s);
(*A clause has first-order literals and other, type-related literals*)
datatype clause =
Clause of {clause_id: clause_id,
axiom_name: axiom_name,
th: thm,
kind: kind,
literals: literal list,
types_sorts: (typ_var * sort) list};
fun get_axiomName (Clause cls) = #axiom_name cls;
fun get_literals (Clause cls) = #literals cls;
exception CLAUSE of string * term;
fun isFalse (Literal (pol, Predicate(pname,_,[]))) =
(pol andalso pname = "c_False") orelse
(not pol andalso pname = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol, Predicate(pname,_,[]))) =
(pol andalso pname = "c_True") orelse
(not pol andalso pname = "c_False")
| isTrue _ = false;
fun isTaut (Clause {literals,...}) = exists isTrue literals;
(*Declarations of the current theory--to allow suppressing types.*)
val const_typargs = ref (Library.K [] : (string*typ -> typ list));
fun num_typargs(s,T) = if !keep_types then length (!const_typargs (s,T)) else 0;
(*Initialize the type suppression mechanism with the current theory before
producing any clauses!*)
fun init thy = (const_typargs := Sign.const_typargs thy);
(*Flatten a type to a fol_type while accumulating sort constraints on the TFrees and
TVars it contains.*)
fun type_of (Type (a, Ts)) =
let val (folTyps, ts) = types_of Ts
val t = make_fixed_type_const a
in (Comp(t,folTyps), ts) end
| type_of (TFree (a,s)) = (AtomF(make_fixed_type_var a), [(FOLTFree a, s)])
| type_of (TVar (v, s)) = (AtomV(make_schematic_type_var v), [(FOLTVar v, s)])
and types_of Ts =
let val (folTyps,ts) = ListPair.unzip (map type_of Ts)
in (folTyps, union_all ts) end;
fun const_types_of (c,T) = types_of (!const_typargs (c,T));
(* Any variables created via the METAHYPS tactical should be treated as
universal vars, although it is represented as "Free(...)" by Isabelle *)
val isMeta = String.isPrefix "METAHYP1_"
fun pred_name_type (Const(c,T)) = (make_fixed_const c, const_types_of (c,T))
| pred_name_type (Free(x,T)) =
if isMeta x then raise CLAUSE("Predicate Not First Order 1", Free(x,T))
else (make_fixed_var x, ([],[]))
| pred_name_type (v as Var _) = raise CLAUSE("Predicate Not First Order 2", v)
| pred_name_type t = raise CLAUSE("Predicate input unexpected", t);
(* For typed equality *)
(* here "arg_typ" is the type of "="'s argument's type, not the type of the equality *)
(* Find type of equality arg *)
fun eq_arg_type (Type("fun",[T,_])) =
let val (folT,_) = type_of T;
in folT end;
fun fun_name_type (Const(c,T)) args = (make_fixed_const c, const_types_of (c,T))
| fun_name_type (Free(x,T)) args =
if isMeta x then raise CLAUSE("Function Not First Order", Free(x,T))
else (make_fixed_var x, ([],[]))
| fun_name_type f args = raise CLAUSE("Function Not First Order 1", f);
(*Convert a term to a fol_term while accumulating sort constraints on the TFrees and
TVars it contains.*)
fun term_of (Var(ind_nm,T)) =
let val (folType,ts) = type_of T
in (UVar(make_schematic_var ind_nm, folType), ts) end
| term_of (Free(x,T)) =
let val (folType, ts) = type_of T
in
if isMeta x then (UVar(make_schematic_var(x,0),folType), ts)
else (Fun(make_fixed_var x, [], []), ts) (*Frees don't need types!*)
end
| term_of app =
let val (f,args) = strip_comb app
val (funName,(contys,ts1)) = fun_name_type f args
val (args',ts2) = terms_of args
in
(Fun(funName,contys,args'), union_all (ts1::ts2))
end
and terms_of ts = ListPair.unzip (map term_of ts)
(*Create a predicate value, again accumulating sort constraints.*)
fun pred_of (Const("op =", typ), args) =
let val arg_typ = eq_arg_type typ
val (args',ts) = terms_of args
val equal_name = make_fixed_const "op ="
in
(Predicate(equal_name,[arg_typ],args'),
union_all ts)
end
| pred_of (pred,args) =
let val (pname, (predType,ts1)) = pred_name_type pred
val (args',ts2) = terms_of args
in
(Predicate(pname,predType,args'), union_all (ts1::ts2))
end;
(*Treatment of literals, possibly negated*)
fun predicate_of ((Const("Not",_) $ P), polarity) = predicate_of (P, not polarity)
| predicate_of (term,polarity) = (pred_of (strip_comb term), polarity);
fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
| literals_of_term1 args (Const("op |",_) $ P $ Q) =
literals_of_term1 (literals_of_term1 args P) Q
| literals_of_term1 (lits, ts) P =
let val ((pred, ts'), polarity) = predicate_of (P,true)
val lits' = Literal(polarity,pred) :: lits
in
(lits', ts union ts')
end;
val literals_of_term = literals_of_term1 ([],[]);
fun list_ord _ ([],[]) = EQUAL
| list_ord _ ([],_) = LESS
| list_ord _ (_,[]) = GREATER
| list_ord ord (x::xs, y::ys) =
(case ord(x,y) of EQUAL => list_ord ord (xs,ys)
| xy_ord => xy_ord);
(*Make literals for sorted type variables. FIXME: can it use map?*)
fun sorts_on_typs (_, []) = ([])
| sorts_on_typs (v, "HOL.type" :: s) =
sorts_on_typs (v,s) (*IGNORE sort "type"*)
| sorts_on_typs ((FOLTVar indx), s::ss) =
LTVar(make_type_class s, make_schematic_type_var indx) ::
sorts_on_typs ((FOLTVar indx), ss)
| sorts_on_typs ((FOLTFree x), s::ss) =
LTFree(make_type_class s, make_fixed_type_var x) ::
sorts_on_typs ((FOLTFree x), ss);
fun pred_of_sort (LTVar (s,ty)) = (s,1)
| pred_of_sort (LTFree (s,ty)) = (s,1)
(*Given a list of sorted type variables, return two separate lists.
The first is for TVars, the second for TFrees.*)
fun add_typs_aux [] = ([],[])
| add_typs_aux ((FOLTVar indx,s)::tss) =
let val vs = sorts_on_typs (FOLTVar indx, s)
val (vss,fss) = add_typs_aux tss
in
(vs union vss, fss)
end
| add_typs_aux ((FOLTFree x,s)::tss) =
let val fs = sorts_on_typs (FOLTFree x, s)
val (vss,fss) = add_typs_aux tss
in
(vss, fs union fss)
end;
(** make axiom and conjecture clauses. **)
exception MAKE_CLAUSE;
fun make_clause (clause_id, axiom_name, th, kind) =
let val (lits,types_sorts) = literals_of_term (prop_of th)
in if forall isFalse lits
then error "Problem too trivial for resolution (empty clause)"
else Clause {clause_id = clause_id, axiom_name = axiom_name, th = th,
kind = kind, literals = lits, types_sorts = types_sorts}
end;
fun get_tvar_strs [] = []
| get_tvar_strs ((FOLTVar indx,s)::tss) =
insert (op =) (make_schematic_type_var indx) (get_tvar_strs tss)
| get_tvar_strs((FOLTFree x,s)::tss) = get_tvar_strs tss
(* check if a clause is first-order before making a conjecture clause*)
fun make_conjecture_clause n th =
if Meson.is_fol_term (prop_of th) then make_clause(n, "conjecture", th, Conjecture)
else raise CLAUSE("Goal is not FOL", prop_of th);
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
(*before converting an axiom clause to "clause" format, check if it is FOL*)
fun make_axiom_clause thm (ax_name,cls_id) =
if Meson.is_fol_term (prop_of thm)
then (SOME (make_clause(cls_id, ax_name, thm, Axiom)) handle MAKE_CLAUSE => NONE)
else (Output.debug ("Omitting " ^ ax_name ^ ": Axiom is not FOL"); NONE)
fun make_axiom_clauses [] = []
| make_axiom_clauses ((thm,(name,id))::thms) =
case make_axiom_clause thm (name,id) of
SOME cls => if isTaut cls then make_axiom_clauses thms
else (name,cls) :: make_axiom_clauses thms
| NONE => make_axiom_clauses thms;
(**** Isabelle arities ****)
exception ARCLAUSE of string;
type class = string;
type tcons = string;
datatype arLit = TConsLit of bool * (class * tcons * string list)
| TVarLit of bool * (class * string);
datatype arityClause =
ArityClause of {axiom_name: axiom_name,
kind: kind,
conclLit: arLit,
premLits: arLit list};
fun gen_TVars 0 = []
| gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n-1);
fun pack_sort(_,[]) = []
| pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt) (*IGNORE sort "type"*)
| pack_sort(tvar, cls::srt) = (make_type_class cls, tvar) :: pack_sort(tvar, srt);
fun make_TVarLit b (cls,str) = TVarLit(b, (cls,str));
fun make_TConsLit b (cls,tcons,tvars) =
TConsLit(b, (make_type_class cls, make_fixed_type_const tcons, tvars));
(*Arity of type constructor tcon :: (arg1,...,argN)res*)
fun make_axiom_arity_clause (tcons, axiom_name, (res,args)) =
let val tvars = gen_TVars (length args)
val tvars_srts = ListPair.zip (tvars,args)
in
ArityClause {axiom_name = axiom_name, kind = Axiom,
conclLit = make_TConsLit true (res,tcons,tvars),
premLits = map (make_TVarLit false) (union_all(map pack_sort tvars_srts))}
end;
(**** Isabelle class relations ****)
datatype classrelClause =
ClassrelClause of {axiom_name: axiom_name,
subclass: class,
superclass: class};
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
fun class_pairs thy [] supers = []
| class_pairs thy subs supers =
let val class_less = Sorts.class_less(Sign.classes_of thy)
fun add_super sub (super,pairs) =
if class_less (sub,super) then (sub,super)::pairs else pairs
fun add_supers (sub,pairs) = foldl (add_super sub) pairs supers
in foldl add_supers [] subs end;
fun make_classrelClause (sub,super) =
ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of sub ^ "_" ^ ascii_of super,
subclass = make_type_class sub,
superclass = make_type_class super};
fun make_classrel_clauses thy subs supers =
map make_classrelClause (class_pairs thy subs supers);
(** Isabelle arities **)
fun arity_clause _ _ (tcons, []) = []
| arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
arity_clause seen n (tcons,ars)
| arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
if class mem_string seen then (*multiple arities for the same tycon, class pair*)
make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::
arity_clause seen (n+1) (tcons,ars)
else
make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class, ar) ::
arity_clause (class::seen) n (tcons,ars)
fun multi_arity_clause [] = []
| multi_arity_clause ((tcons,ars) :: tc_arlists) =
arity_clause [] 1 (tcons, ars) @
multi_arity_clause tc_arlists
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy.*)
fun type_class_pairs thy tycons classes =
let val alg = Sign.classes_of thy
fun domain_sorts (tycon,class) = Sorts.mg_domain alg tycon [class]
fun add_class tycon (class,pairs) =
(class, domain_sorts(tycon,class))::pairs
handle Sorts.CLASS_ERROR _ => pairs
fun try_classes tycon = (tycon, foldl (add_class tycon) [] classes)
in map try_classes tycons end;
fun arity_clause_thy thy tycons classes =
multi_arity_clause (type_class_pairs thy tycons classes);
(**** Find occurrences of predicates in clauses ****)
(*FIXME: multiple-arity checking doesn't work, as update_new is the wrong
function (it flags repeated declarations of a function, even with the same arity)*)
fun update_many (tab, keypairs) = foldl (uncurry Symtab.update) tab keypairs;
fun add_predicate_preds (Predicate(pname,tys,tms), preds) =
if pname = "equal" then preds (*equality is built-in and requires no declaration*)
else Symtab.update (pname, length tys + length tms) preds
fun add_literal_preds (Literal(_,pred), preds) = add_predicate_preds (pred,preds)
fun add_type_sort_preds ((FOLTVar indx,s), preds) =
update_many (preds, map pred_of_sort (sorts_on_typs (FOLTVar indx, s)))
| add_type_sort_preds ((FOLTFree x,s), preds) =
update_many (preds, map pred_of_sort (sorts_on_typs (FOLTFree x, s)));
fun add_clause_preds (Clause {literals, types_sorts, ...}, preds) =
foldl add_literal_preds (foldl add_type_sort_preds preds types_sorts) literals
handle Symtab.DUP a => raise ERROR ("predicate " ^ a ^ " has multiple arities")
fun add_classrelClause_preds (ClassrelClause {subclass,superclass,...}, preds) =
Symtab.update (subclass,1) (Symtab.update (superclass,1) preds);
fun class_of_arityLit (TConsLit(_, (tclass, _, _))) = tclass
| class_of_arityLit (TVarLit(_, (tclass, _))) = tclass;
fun add_arityClause_preds (ArityClause {conclLit,premLits,...}, preds) =
let val classes = map class_of_arityLit (conclLit::premLits)
fun upd (class,preds) = Symtab.update (class,1) preds
in foldl upd preds classes end;
fun preds_of_clauses clauses clsrel_clauses arity_clauses =
Symtab.dest
(foldl add_classrelClause_preds
(foldl add_arityClause_preds
(foldl add_clause_preds Symtab.empty clauses)
arity_clauses)
clsrel_clauses)
(*** Find occurrences of functions in clauses ***)
fun add_foltype_funcs (AtomV _, funcs) = funcs
| add_foltype_funcs (AtomF a, funcs) = Symtab.update (a,0) funcs
| add_foltype_funcs (Comp(a,tys), funcs) =
foldl add_foltype_funcs (Symtab.update (a, length tys) funcs) tys;
fun add_folterm_funcs (UVar(_,ty), funcs) = add_foltype_funcs (ty, funcs)
| add_folterm_funcs (Fun(a,tys,tms), funcs) =
foldl add_foltype_funcs
(foldl add_folterm_funcs (Symtab.update (a, length tys + length tms) funcs)
tms)
tys
fun add_predicate_funcs (Predicate(_,tys,tms), funcs) =
foldl add_foltype_funcs (foldl add_folterm_funcs funcs tms) tys;
fun add_literal_funcs (Literal(_,pred), funcs) = add_predicate_funcs (pred,funcs)
(*TFrees are recorded as constants*)
fun add_type_sort_funcs ((FOLTVar _, _), funcs) = funcs
| add_type_sort_funcs ((FOLTFree a, _), funcs) =
Symtab.update (make_fixed_type_var a, 0) funcs
fun add_arityClause_funcs (ArityClause {conclLit,...}, funcs) =
let val TConsLit(_, (_, tcons, tvars)) = conclLit
in Symtab.update (tcons, length tvars) funcs end;
fun add_clause_funcs (Clause {literals, types_sorts, ...}, funcs) =
foldl add_literal_funcs (foldl add_type_sort_funcs funcs types_sorts)
literals
handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")
fun funcs_of_clauses clauses arity_clauses =
Symtab.dest (foldl add_arityClause_funcs
(foldl add_clause_funcs Symtab.empty clauses)
arity_clauses)
(**** String-oriented operations ****)
fun string_of_term (UVar(x,_)) = x
| string_of_term (Fun (name,typs,[])) = name ^ (paren_pack (map string_of_fol_type typs))
| string_of_term (Fun (name,typs,terms)) =
let val typs' = if !keep_types then map string_of_fol_type typs else []
in name ^ (paren_pack (map string_of_term terms @ typs')) end;
fun string_of_pair [t1,t2] = (string_of_term t1, string_of_term t2)
| string_of_pair _ = raise ERROR ("equality predicate requires two arguments");
fun string_of_equality ts =
let val (s1,s2) = string_of_pair ts
in "equal(" ^ s1 ^ "," ^ s2 ^ ")" end;
(* before output the string of the predicate, check if the predicate corresponds to an equality or not. *)
fun string_of_predicate (Predicate("equal",_,ts)) = string_of_equality ts
| string_of_predicate (Predicate(name,typs,ts)) =
let val typs' = if !keep_types then map string_of_fol_type typs else []
in name ^ (paren_pack (map string_of_term ts @ typs')) end;
fun string_of_clausename (cls_id,ax_name) =
clause_prefix ^ 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);
(*Write a list of strings to a file*)
fun writeln_strs os = List.app (fn s => TextIO.output (os,s));
(**** Producing DFG files ****)
(*Attach sign in DFG syntax: false means negate.*)
fun dfg_sign true s = s
| dfg_sign false s = "not(" ^ s ^ ")"
fun dfg_literal (Literal(pol,pred)) = dfg_sign pol (string_of_predicate pred)
fun dfg_of_typeLit (LTVar (s,ty)) = "not(" ^ s ^ "(" ^ ty ^ "))"
| dfg_of_typeLit (LTFree (s,ty)) = s ^ "(" ^ ty ^ ")";
(*Enclose the clause body by quantifiers, if necessary*)
fun dfg_forall [] body = body
| dfg_forall vars body = "forall([" ^ commas vars ^ "],\n" ^ body ^ ")"
fun gen_dfg_cls (cls_id, ax_name, knd, lits, vars) =
"clause( %(" ^ knd ^ ")\n" ^
dfg_forall vars ("or(" ^ lits ^ ")") ^ ",\n" ^
string_of_clausename (cls_id,ax_name) ^ ").\n\n";
fun dfg_clause_aux (Clause{literals, types_sorts, ...}) =
let val lits = map dfg_literal literals
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
val tvar_lits_strs =
if !keep_types then map dfg_of_typeLit tvar_lits else []
val tfree_lits =
if !keep_types then map dfg_of_typeLit tfree_lits else []
in
(tvar_lits_strs @ lits, tfree_lits)
end;
fun dfg_folterms (Literal(pol,pred)) =
let val Predicate (_, _, folterms) = pred
in folterms end
fun get_uvars (UVar(a,typ)) = [a]
| get_uvars (Fun (_,typ,tlist)) = union_all(map get_uvars tlist)
fun dfg_vars (Clause {literals,...}) =
union_all (map get_uvars (List.concat (map dfg_folterms literals)))
fun clause2dfg (cls as Clause{axiom_name,clause_id,kind,types_sorts,...}) =
let val (lits,tfree_lits) = dfg_clause_aux cls
(*"lits" includes the typing assumptions (TVars)*)
val vars = dfg_vars cls
val tvars = get_tvar_strs types_sorts
val cls_str = gen_dfg_cls(clause_id, axiom_name, name_of_kind kind,
commas lits, tvars@vars)
in (cls_str, tfree_lits) end;
fun string_of_arity (name, num) = "(" ^ name ^ "," ^ Int.toString num ^ ")"
fun string_of_preds [] = ""
| string_of_preds preds = "predicates[" ^ commas(map string_of_arity preds) ^ "].\n";
fun string_of_funcs [] = ""
| string_of_funcs funcs = "functions[" ^ commas(map string_of_arity funcs) ^ "].\n" ;
fun string_of_symbols predstr funcstr =
"list_of_symbols.\n" ^ predstr ^ funcstr ^ "end_of_list.\n\n";
fun string_of_start name = "begin_problem(" ^ name ^ ").\n\n";
fun string_of_descrip name =
"list_of_descriptions.\nname({*" ^ name ^
"*}).\nauthor({*Isabelle*}).\nstatus(unknown).\ndescription({*auto-generated*}).\nend_of_list.\n\n"
fun dfg_tfree_clause tfree_lit =
"clause( %(negated_conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ").\n\n"
fun dfg_of_arLit (TConsLit(pol,(c,t,args))) =
dfg_sign pol (c ^ "(" ^ t ^ paren_pack args ^ ")")
| dfg_of_arLit (TVarLit(pol,(c,str))) =
dfg_sign pol (c ^ "(" ^ str ^ ")")
fun dfg_classrelLits sub sup = "not(" ^ sub ^ "(T)), " ^ sup ^ "(T)";
fun dfg_classrelClause (ClassrelClause {axiom_name,subclass,superclass,...}) =
"clause(forall([T],\nor( " ^ dfg_classrelLits subclass superclass ^ ")),\n" ^
axiom_name ^ ").\n\n";
fun string_of_ar axiom_name = arclause_prefix ^ ascii_of axiom_name;
fun dfg_arity_clause (ArityClause{axiom_name,kind,conclLit,premLits,...}) =
let val TConsLit(_, (_,_,tvars)) = conclLit
val lits = map dfg_of_arLit (conclLit :: premLits)
in
"clause( %(" ^ name_of_kind kind ^ ")\n" ^
dfg_forall tvars ("or( " ^ commas lits ^ ")") ^ ",\n" ^
string_of_ar axiom_name ^ ").\n\n"
end;
(* write out a subgoal in DFG format to the file "xxxx_N"*)
fun dfg_write_file thms filename (ax_tuples,classrel_clauses,arity_clauses) =
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 ax_tuples)
val (dfg_clss, tfree_litss) = ListPair.unzip (map clause2dfg conjectures)
val clss = conjectures @ axclauses
val funcs = funcs_of_clauses clss arity_clauses
and preds = preds_of_clauses clss classrel_clauses arity_clauses
and probname = Path.pack (Path.base (Path.unpack filename))
val (axstrs, _) = ListPair.unzip (map clause2dfg axclauses)
val tfree_clss = map dfg_tfree_clause (union_all tfree_litss)
val out = TextIO.openOut filename
in
TextIO.output (out, string_of_start probname);
TextIO.output (out, string_of_descrip probname);
TextIO.output (out, string_of_symbols (string_of_funcs funcs) (string_of_preds preds));
TextIO.output (out, "list_of_clauses(axioms,cnf).\n");
writeln_strs out axstrs;
List.app (curry TextIO.output out o dfg_classrelClause) classrel_clauses;
List.app (curry TextIO.output out o dfg_arity_clause) arity_clauses;
TextIO.output (out, "end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n");
writeln_strs out tfree_clss;
writeln_strs out dfg_clss;
TextIO.output (out, "end_of_list.\n\nend_problem.\n");
TextIO.closeOut out;
clnames
end;
(**** Produce TPTP files ****)
(*Attach sign in TPTP syntax: false means negate.*)
fun tptp_sign true s = s
| tptp_sign false s = "~ " ^ s
fun tptp_of_equality pol ts =
let val (s1,s2) = string_of_pair ts
val eqop = if pol then " = " else " != "
in s1 ^ eqop ^ s2 end;
fun tptp_literal (Literal(pol,Predicate("equal",_,ts))) = tptp_of_equality pol ts
| tptp_literal (Literal(pol,pred)) = tptp_sign pol (string_of_predicate pred);
fun tptp_of_typeLit (LTVar (s,ty)) = tptp_sign false (s ^ "(" ^ ty ^ ")")
| tptp_of_typeLit (LTFree (s,ty)) = tptp_sign true (s ^ "(" ^ ty ^ ")");
fun gen_tptp_cls (cls_id,ax_name,knd,lits) =
"cnf(" ^ string_of_clausename (cls_id,ax_name) ^ "," ^
name_of_kind knd ^ "," ^ tptp_pack lits ^ ").\n";
fun tptp_type_lits (Clause {literals, types_sorts, ...}) =
let val lits = map tptp_literal literals
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
val tvar_lits_strs =
if !keep_types then map tptp_of_typeLit tvar_lits else []
val tfree_lits =
if !keep_types then map tptp_of_typeLit tfree_lits else []
in
(tvar_lits_strs @ lits, tfree_lits)
end;
fun clause2tptp (cls as Clause {clause_id, axiom_name, kind, ...}) =
let val (lits,tfree_lits) = tptp_type_lits cls
(*"lits" includes the typing assumptions (TVars)*)
val cls_str = gen_tptp_cls(clause_id, axiom_name, kind, lits)
in
(cls_str,tfree_lits)
end;
fun tptp_tfree_clause tfree_lit =
"cnf(" ^ "tfree_tcs," ^ "negated_conjecture" ^ "," ^ tptp_pack[tfree_lit] ^ ").\n";
fun tptp_of_arLit (TConsLit(b,(c,t,args))) =
tptp_sign b (c ^ "(" ^ t ^ paren_pack args ^ ")")
| tptp_of_arLit (TVarLit(b,(c,str))) =
tptp_sign b (c ^ "(" ^ str ^ ")")
fun tptp_arity_clause (ArityClause{axiom_name,kind,conclLit,premLits,...}) =
"cnf(" ^ string_of_ar axiom_name ^ "," ^ name_of_kind kind ^ "," ^
tptp_pack (map tptp_of_arLit (conclLit :: premLits)) ^ ").\n";
fun tptp_classrelLits sub sup =
let val tvar = "(T)"
in tptp_pack [tptp_sign false (sub^tvar), tptp_sign true (sup^tvar)] end;
fun tptp_classrelClause (ClassrelClause {axiom_name,subclass,superclass,...}) =
"cnf(" ^ axiom_name ^ ",axiom," ^ tptp_classrelLits subclass superclass ^ ").\n"
(* write out a subgoal as tptp clauses to the file "xxxx_N"*)
fun tptp_write_file thms filename (ax_tuples,classrel_clauses,arity_clauses) =
let
val _ = Output.debug ("Preparing to write the TPTP file " ^ filename)
val clss = make_conjecture_clauses thms
val (clnames,axclauses) = ListPair.unzip (make_axiom_clauses ax_tuples)
val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)
val tfree_clss = map tptp_tfree_clause (foldl (op union_string) [] tfree_litss)
val out = TextIO.openOut filename
in
List.app (curry TextIO.output out o #1 o clause2tptp) axclauses;
writeln_strs out tfree_clss;
writeln_strs out tptp_clss;
List.app (curry TextIO.output out o tptp_classrelClause) classrel_clauses;
List.app (curry TextIO.output out o tptp_arity_clause) arity_clauses;
TextIO.closeOut out;
clnames
end;
end;