(* 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.
*)
(* works for writeoutclasimp on typed *)
signature RES_CLAUSE =
sig
val keep_types : bool ref
val special_equal : bool ref
val tagged : bool ref
exception ARCLAUSE of string
exception CLAUSE of string * term
type arityClause
type classrelClause
type clause
val init : theory -> unit
val make_axiom_clause : Term.term -> string * int -> clause
val make_conjecture_clauses : term list -> clause list
val get_axiomName : clause -> string
val isTaut : clause -> bool
val num_of_clauses : clause -> int
val clause2dfg : clause -> string * string list
val clauses2dfg : clause list -> string -> clause list -> clause list ->
(string * int) list -> (string * int) list -> string
val tfree_dfg_clause : string -> string
val arity_clause_thy: theory -> arityClause list
val classrel_clauses_thy: theory -> classrelClause list
val tptp_arity_clause : arityClause -> string
val tptp_classrelClause : classrelClause -> string
val tptp_clause : clause -> string list
val clause2tptp : clause -> string * string list
val tfree_clause : string -> string
val schematic_var_prefix : string
val fixed_var_prefix : string
val tvar_prefix : string
val tfree_prefix : string
val clause_prefix : string
val arclause_prefix : string
val const_prefix : string
val tconst_prefix : string
val class_prefix : string
val union_all : ''a list list -> ''a list
val ascii_of : String.string -> String.string
val paren_pack : string list -> string
val bracket_pack : string list -> string
val make_schematic_var : String.string * int -> string
val make_fixed_var : String.string -> string
val make_schematic_type_var : string * int -> string
val make_fixed_type_var : string -> string
val make_fixed_const : String.string -> string
val make_fixed_type_const : String.string -> string
val make_type_class : String.string -> string
val isMeta : String.string -> bool
type typ_var
val mk_typ_var_sort : Term.typ -> typ_var * sort
type type_literal
val add_typs_aux2 : (typ_var * string list) list -> type_literal list * type_literal list
val gen_tptp_cls : int * string * string * string -> string
val gen_tptp_type_cls : int * string * string * string * int -> string
val tptp_of_typeLit : type_literal -> string
end;
structure ResClause: RES_CLAUSE =
struct
(* Added for typed equality *)
val special_equal = ref false; (* by default,equality does not carry type information *)
val eq_typ_wrapper = "typeinfo"; (* default string *)
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"),
("op <=", "lessequals"),
("op <", "less"),
("op &", "and"),
("op |", "or"),
("op +", "plus"),
("op -", "minus"),
("op *", "times"),
("op -->", "implies"),
("{}", "emptyset"),
("op :", "in"),
("op Un", "union"),
("op Int", "inter"),
("List.op @", "append")];
val type_const_trans_table =
Symtab.make [("*", "t_prod"),
("+", "t_sum"),
("~=>", "t_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 ^ ")";
fun bracket_pack strings = "[" ^ commas 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 make_fixed_const c =
case Symtab.lookup const_trans_table c of
SOME c' => c'
| NONE => const_prefix ^ ascii_of c;
fun make_fixed_type_const c =
case Symtab.lookup type_const_trans_table c of
SOME c' => c'
| NONE => tconst_prefix ^ ascii_of c;
fun make_type_class clas = class_prefix ^ ascii_of clas;
(***** definitions and functions for FOL clauses, prepared for conversion into TPTP format or SPASS format. *****)
val keep_types = ref true;
datatype kind = Axiom | Hypothesis | Conjecture;
fun name_of_kind Axiom = "axiom"
| name_of_kind Hypothesis = "hypothesis"
| name_of_kind Conjecture = "conjecture";
type clause_id = int;
type axiom_name = string;
type polarity = bool;
type indexname = Term.indexname;
(* "tag" is used for vampire specific syntax *)
type tag = bool;
(**** Isabelle FOL clauses ****)
val tagged = ref false;
type pred_name = string;
type sort = Term.sort;
type fol_type = string;
datatype type_literal = LTVar of string | LTFree of string;
datatype folTerm = UVar of string * fol_type
| Fun of string * fol_type list * folTerm list;
datatype predicate = Predicate of pred_name * fol_type list * folTerm list;
datatype literal = Literal of polarity * predicate * tag;
datatype typ_var = FOLTVar of indexname | FOLTFree of string;
fun mk_typ_var_sort (TFree(a,s)) = (FOLTFree a,s)
| mk_typ_var_sort (TVar(v,s)) = (FOLTVar v,s);
(* ML datatype used to repsent one single clause: disjunction of literals. *)
datatype clause =
Clause of {clause_id: clause_id,
axiom_name: axiom_name,
kind: kind,
literals: literal list,
types_sorts: (typ_var * sort) list,
tvar_type_literals: type_literal list,
tfree_type_literals: type_literal list ,
tvars: string list,
predicates: (string*int) list,
functions: (string*int) list};
exception CLAUSE of string * term;
(*** make clauses ***)
fun isFalse (Literal (pol,Predicate(a,_,[]),_)) =
(pol andalso a = "c_False") orelse
(not pol andalso a = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol,Predicate(a,_,[]),_)) =
(pol andalso a = "c_True") orelse
(not pol andalso a = "c_False")
| isTrue _ = false;
fun isTaut (Clause {literals,...}) = exists isTrue literals;
fun make_clause (clause_id,axiom_name,kind,literals,
types_sorts,tvar_type_literals,
tfree_type_literals,tvars, predicates, functions) =
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, types_sorts = types_sorts,
tvar_type_literals = tvar_type_literals,
tfree_type_literals = tfree_type_literals,
tvars = tvars, predicates = predicates,
functions = functions};
(** Some Clause destructor functions **)
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 funcs_of_cls (Clause cls) = #functions cls;
fun preds_of_cls (Clause cls) = #predicates cls;
(*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 string while accumulating sort constraints on the TFrees and
TVars it contains.*)
fun type_of (Type (a, Ts)) =
let val (folTyps, (ts, funcs)) = types_of Ts
val t = make_fixed_type_const a
in
((t ^ paren_pack folTyps), (ts, (t, length Ts)::funcs))
end
| type_of (TFree (a,s)) =
let val t = make_fixed_type_var a
in (t, ([((FOLTFree a),s)], [(t,0)])) end
| type_of (TVar (v, s)) = (make_schematic_type_var v, ([((FOLTVar v),s)], []))
and types_of Ts =
let val foltyps_ts = map type_of Ts
val (folTyps,ts_funcs) = ListPair.unzip foltyps_ts
val (ts, funcslist) = ListPair.unzip ts_funcs
in
(folTyps, (union_all ts, union_all funcslist))
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)) =
let val (contys,(folTyps,funcs)) = const_types_of (c,T)
in (make_fixed_const c, (contys,folTyps), funcs) end
| 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("op =",T)) args = (*FIXME: Is this special treatment of = needed??*)
let val t = make_fixed_const "op ="
in (t, ([eq_arg_type T], []), [(t,2)]) end
| fun_name_type (Const(c,T)) args =
let val t = make_fixed_const c
val (contys, (folTyps,funcs)) = const_types_of (c,T)
val arity = num_typargs(c,T) + length args
in
(t, (contys,folTyps), ((t,arity)::funcs))
end
| fun_name_type (Free(x,T)) args =
let val t = make_fixed_var x
in (t, ([],[]), [(t, length args)]) end
| fun_name_type f args = raise CLAUSE("Function Not First Order 1", f);
fun term_of (Var(ind_nm,T)) =
let val (folType,(ts,funcs)) = type_of T
in
(UVar(make_schematic_var ind_nm, folType), (ts, funcs))
end
| term_of (Free(x,T)) =
let val (folType, (ts,funcs)) = type_of T
in
if isMeta x then (UVar(make_schematic_var(x,0),folType),
(ts, ((make_schematic_var(x,0)),0)::funcs))
else
(Fun(make_fixed_var x, [folType], []),
(ts, ((make_fixed_var x),0)::funcs))
end
| term_of (Const(c,T)) = (* impossible to be equality *)
let val (contys, (folTyps,funcs)) = const_types_of (c,T)
in
(Fun(make_fixed_const c, contys, []),
(folTyps, ((make_fixed_const c),0)::funcs))
end
| term_of app =
let val (f,args) = strip_comb app
val _ = case f of Const(_,_) => ()
| Free(s,_) =>
if isMeta s
then raise CLAUSE("Function Not First Order 2", f)
else ()
| _ => raise CLAUSE("Function Not First Order 3", f);
val (funName,(contys,ts1),funcs) = fun_name_type f args
val (args',(ts2,funcs')) = terms_of args
in
(Fun(funName,contys,args'),
(union_all (ts1::ts2),
union_all(funcs::funcs')))
end
| term_of t = raise CLAUSE("Function Not First Order 4", t)
and terms_of ts =
let val (args, ts_funcs) = ListPair.unzip (map term_of ts)
in
(args, ListPair.unzip ts_funcs)
end
fun pred_of (Const("op =", typ), args) =
let val arg_typ = eq_arg_type typ
val (args',(ts,funcs)) = terms_of args
val equal_name = make_fixed_const "op ="
in
(Predicate(equal_name,[arg_typ],args'),
union_all ts,
[((make_fixed_var equal_name), 2)],
union_all funcs)
end
| pred_of (pred,args) =
let val (predName,(predType,ts1), pfuncs) = pred_name_type pred
val (args',(ts2,ffuncs)) = terms_of args
val ts3 = union_all (ts1::ts2)
val ffuncs' = union_all ffuncs
val newfuncs = pfuncs union ffuncs'
val arity =
case pred of
Const (c,T) => num_typargs(c,T) + length args
| _ => length args
in
(Predicate(predName,predType,args'), ts3,
[(predName, arity)], newfuncs)
end;
(*Treatment of literals, possibly negated or tagged*)
fun predicate_of ((Const("Not",_) $ P), polarity, tag) =
predicate_of (P, not polarity, tag)
| predicate_of ((Const("HOL.tag",_) $ P), polarity, tag) =
predicate_of (P, polarity, true)
| predicate_of (term,polarity,tag) =
(pred_of (strip_comb term), polarity, tag);
fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
| literals_of_term1 (args as (lits, ts, preds, funcs)) (Const("op |",_) $ P $ Q) =
let val (lits', ts', preds', funcs') = literals_of_term1 args P
in
literals_of_term1 (lits', ts', preds' union preds, funcs' union funcs) Q
end
| literals_of_term1 (lits, ts, preds, funcs) P =
let val ((pred, ts', preds', funcs'), pol, tag) = predicate_of (P,true,false)
val lits' = Literal(pol,pred,tag) :: lits
in
(lits', ts union ts', preds' union preds, funcs' union funcs)
end;
val literals_of_term = literals_of_term1 ([],[],[],[]);
(* FIX: not sure what to do with these funcs *)
(*Make literals for sorted type variables*)
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));
(*UGLY: seems to be parsing the "show sorts" output, removing anything that
starts with a left parenthesis.*)
fun remove_type str = hd (String.fields (fn c => c = #"(") str);
fun pred_of_sort (LTVar x) = ((remove_type x),1)
| pred_of_sort (LTFree x) = ((remove_type x),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 [] preds = ([],[], preds)
| add_typs_aux ((FOLTVar indx,s)::tss) preds =
let val vs = sorts_on_typs (FOLTVar indx, s)
val preds' = (map pred_of_sort vs)@preds
val (vss,fss, preds'') = add_typs_aux tss preds'
in
(vs union vss, fss, preds'')
end
| add_typs_aux ((FOLTFree x,s)::tss) preds =
let val fs = sorts_on_typs (FOLTFree x, s)
val preds' = (map pred_of_sort fs)@preds
val (vss,fss, preds'') = add_typs_aux tss preds'
in
(vss, fs union fss, preds'')
end;
fun add_typs_aux2 [] = ([],[])
| add_typs_aux2 ((FOLTVar indx,s)::tss) =
let val vs = sorts_on_typs (FOLTVar indx,s)
val (vss,fss) = add_typs_aux2 tss
in
(vs union vss,fss)
end
| add_typs_aux2 ((FOLTFree x,s)::tss) =
let val fs = sorts_on_typs (FOLTFree x,s)
val (vss,fss) = add_typs_aux2 tss
in
(vss,fs union fss)
end;
fun add_typs (Clause cls) preds = add_typs_aux (#types_sorts cls) preds
(** make axiom clauses, hypothesis clauses and conjecture clauses. **)
fun get_tvar_strs [] = []
| get_tvar_strs ((FOLTVar indx,s)::tss) =
let val vstr = make_schematic_type_var indx
in
vstr ins (get_tvar_strs tss)
end
| get_tvar_strs((FOLTFree x,s)::tss) = distinct (get_tvar_strs tss)
(* FIX add preds and funcs to add typs aux here *)
fun make_axiom_clause_thm thm (ax_name,cls_id) =
let val (lits,types_sorts, preds, funcs) = literals_of_term (prop_of thm)
val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds
val tvars = get_tvar_strs types_sorts
in
make_clause(cls_id,ax_name,Axiom,
lits,types_sorts,tvar_lits,tfree_lits,
tvars, preds, funcs)
end;
(* check if a clause is FOL first*)
fun make_conjecture_clause n t =
let val _ = check_is_fol_term t
handle TERM("check_is_fol_term",_) => raise CLAUSE("Goal is not FOL",t)
val (lits,types_sorts, preds, funcs) = literals_of_term t
val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds
val tvars = get_tvar_strs types_sorts
in
make_clause(n,"conjecture",Conjecture,
lits,types_sorts,tvar_lits,tfree_lits,
tvars, preds, funcs)
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
(*before converting an axiom clause to "clause" format, check if it is FOL*)
fun make_axiom_clause term (ax_name,cls_id) =
let val _ = check_is_fol_term term
handle TERM("check_is_fol_term",_) => raise CLAUSE("Axiom is not FOL", term)
val (lits,types_sorts, preds,funcs) = literals_of_term term
val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds
val tvars = get_tvar_strs types_sorts
in
make_clause(cls_id,ax_name,Axiom,
lits,types_sorts,tvar_lits,tfree_lits,
tvars, preds,funcs)
end;
(**** 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 {clause_id: clause_id,
axiom_name: axiom_name,
kind: kind,
conclLit: arLit,
premLits: arLit list};
fun get_TVars 0 = []
| get_TVars n = ("T_" ^ (Int.toString n)) :: get_TVars (n-1);
fun pack_sort(_,[]) = raise ARCLAUSE("Empty Sort Found")
| pack_sort(tvar, [cls]) = [(make_type_class cls, tvar)]
| 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));
fun make_axiom_arity_clause (tcons,n,(res,args)) =
let val nargs = length args
val tvars = get_TVars nargs
val tvars_srts = ListPair.zip (tvars,args)
val tvars_srts' = union_all(map pack_sort tvars_srts)
val false_tvars_srts' = map (pair false) tvars_srts'
in
ArityClause {clause_id = n, kind = Axiom,
axiom_name = tcons,
conclLit = make_TConsLit(true,(res,tcons,tvars)),
premLits = map make_TVarLit false_tvars_srts'}
end;
(*The number of clauses generated from cls, including type clauses*)
fun num_of_clauses (Clause cls) =
let val num_tfree_lits =
if !keep_types then length (#tfree_type_literals cls)
else 0
in 1 + num_tfree_lits end;
(**** Isabelle class relations ****)
datatype classrelClause =
ClassrelClause of {clause_id: clause_id,
subclass: class,
superclass: class option};
fun make_axiom_classrelClause n subclass superclass =
ClassrelClause {clause_id = n,
subclass = subclass, superclass = superclass};
fun classrelClauses_of_aux n sub [] = []
| classrelClauses_of_aux n sub (sup::sups) =
make_axiom_classrelClause n sub (SOME sup) :: classrelClauses_of_aux (n+1) sub sups;
fun classrelClauses_of (sub,sups) =
case sups of [] => [make_axiom_classrelClause 0 sub NONE]
| _ => classrelClauses_of_aux 0 sub sups;
(***** Isabelle arities *****)
fun arity_clause _ (tcons, []) = []
| arity_clause n (tcons, ar::ars) =
make_axiom_arity_clause (tcons,n,ar) ::
arity_clause (n+1) (tcons,ars);
fun multi_arity_clause [] = []
| multi_arity_clause (tcon_ar :: tcons_ars) =
arity_clause 0 tcon_ar @ multi_arity_clause tcons_ars
fun arity_clause_thy thy =
let val arities = #arities (Type.rep_tsig (Sign.tsig_of thy))
in multi_arity_clause (Symtab.dest arities) end;
(* Isabelle classes *)
type classrelClauses = classrelClause list Symtab.table;
val classrel_of = #2 o #classes o Type.rep_tsig o Sign.tsig_of;
fun classrel_clauses_classrel (C: Sorts.classes) = map classrelClauses_of (Graph.dest C);
val classrel_clauses_thy = List.concat o classrel_clauses_classrel o classrel_of;
(****!!!! Changed for typed equality !!!!****)
fun wrap_eq_type typ t = eq_typ_wrapper ^"(" ^ t ^ "," ^ typ ^ ")";
(*Only need to wrap equality's arguments with "typeinfo" if the output clauses are typed
and if we specifically ask for types to be included. *)
fun string_of_equality (typ,terms) =
let val [tstr1,tstr2] = map string_of_term terms
in
if !keep_types andalso !special_equal
then "equal(" ^ (wrap_eq_type typ tstr1) ^ "," ^
(wrap_eq_type typ tstr2) ^ ")"
else "equal(" ^ tstr1 ^ "," ^ tstr2 ^ ")"
end
and string_of_term (UVar(x,_)) = x
| string_of_term (Fun("equal",[typ],terms)) = string_of_equality(typ,terms)
| string_of_term (Fun (name,typs,[])) = name (*Overloaded consts like 0 don't get types!*)
| string_of_term (Fun (name,typs,terms)) =
let val terms_as_strings = map string_of_term terms
val typs' = if !keep_types then typs else []
in name ^ (paren_pack (terms_as_strings @ typs')) end
| string_of_term _ = error "string_of_term";
(* before output the string of the predicate, check if the predicate corresponds to an equality or not. *)
fun string_of_predicate (Predicate("equal",[typ],terms)) = string_of_equality(typ,terms)
| string_of_predicate (Predicate(name,typs,terms)) =
let val terms_as_strings = map string_of_term terms
val typs' = if !keep_types then typs else []
in name ^ (paren_pack (terms_as_strings @ typs')) end
| string_of_predicate _ = error "string_of_predicate";
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);
(********************************)
(* Code for producing DFG files *)
(********************************)
fun dfg_literal (Literal(pol,pred,tag)) =
let val pred_string = string_of_predicate pred
in
if pol then pred_string else "not(" ^pred_string ^ ")"
end;
(* FIX: what does this mean? *)
(*fun dfg_of_typeLit (LTVar x) = "not(" ^ x ^ ")"
| dfg_of_typeLit (LTFree x) = "(" ^ x ^ ")";*)
fun dfg_of_typeLit (LTVar x) = x
| dfg_of_typeLit (LTFree x) = x ;
(*Make the string of universal quantifiers for a clause*)
fun forall_open ([],[]) = ""
| forall_open (vars,tvars) = "forall([" ^ (commas (tvars@vars))^ "],\n"
fun forall_close ([],[]) = ""
| forall_close (vars,tvars) = ")"
fun gen_dfg_cls (cls_id,ax_name,knd,lits,tvars,vars) =
"clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^
"or(" ^ lits ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^
string_of_clausename (cls_id,ax_name) ^ ").";
fun gen_dfg_type_cls (cls_id,ax_name,knd,tfree_lit,idx,tvars,vars) =
"clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^
"or( " ^ tfree_lit ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^
string_of_type_clsname (cls_id,ax_name,idx) ^ ").";
fun dfg_clause_aux (Clause cls) =
let val lits = map dfg_literal (#literals cls)
val tvar_lits_strs =
if !keep_types then map dfg_of_typeLit (#tvar_type_literals cls)
else []
val tfree_lits =
if !keep_types then map dfg_of_typeLit (#tfree_type_literals cls)
else []
in
(tvar_lits_strs @ lits, tfree_lits)
end;
fun dfg_folterms (Literal(pol,pred,tag)) =
let val Predicate (predname, _, folterms) = pred
in folterms end
fun get_uvars (UVar(a,typ)) = [a]
| get_uvars (Fun (_,typ,tlist)) = union_all(map get_uvars tlist)
fun is_uvar (UVar _) = true
| is_uvar (Fun _) = false;
fun uvar_name (UVar(a,_)) = a
| uvar_name (Fun (a,_,_)) = raise CLAUSE("Not a variable", Const(a,dummyT));
fun dfg_vars (Clause cls) =
let val lits = #literals cls
val folterms = List.concat (map dfg_folterms lits)
in
union_all(map get_uvars folterms)
end
fun dfg_tvars (Clause cls) =(#tvars cls)
(* make this return funcs and preds too? *)
fun string_of_predname (Predicate("equal",_,terms)) = "EQUALITY"
| string_of_predname (Predicate(name,_,terms)) = name
fun concat_with sep [] = ""
| concat_with sep [x] = "(" ^ x ^ ")"
| concat_with sep (x::xs) = "(" ^ x ^ ")" ^ sep ^ (concat_with sep xs);
fun dfg_pred (Literal(pol,pred,tag)) ax_name =
(string_of_predname pred) ^ " " ^ ax_name
fun dfg_clause cls =
let val (lits,tfree_lits) = dfg_clause_aux cls
(*"lits" includes the typing assumptions (TVars)*)
val vars = dfg_vars cls
val tvars = dfg_tvars cls
val knd = string_of_kind cls
val lits_str = commas lits
val cls_id = get_clause_id cls
val axname = get_axiomName cls
val cls_str = gen_dfg_cls(cls_id,axname,knd,lits_str,tvars, vars)
fun typ_clss k [] = []
| typ_clss k (tfree :: tfrees) =
(gen_dfg_type_cls(cls_id,axname,knd,tfree,k, tvars,vars)) ::
(typ_clss (k+1) tfrees)
in
cls_str :: (typ_clss 0 tfree_lits)
end;
fun string_of_arity (name, num) = name ^ "," ^ (Int.toString num)
fun string_of_preds preds =
"predicates[" ^ (concat_with ", " (map string_of_arity preds)) ^ "].\n";
fun string_of_funcs funcs =
"functions[" ^ (concat_with ", " (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_axioms axstr =
"list_of_clauses(axioms,cnf).\n" ^ axstr ^ "end_of_list.\n\n";
fun string_of_conjectures conjstr =
"list_of_clauses(conjectures,cnf).\n" ^ conjstr ^ "end_of_list.\n\n";
fun string_of_descrip () =
"list_of_descriptions.\nname({*[ File : ],[ Names :]*}).\nauthor({*[ Source :]*}).\nstatus(unknown).\ndescription({*[ Refs :]*}).\nend_of_list.\n\n"
fun string_of_start name = "%------------------------------------------------------------------------------\nbegin_problem(" ^ name ^ ").\n\n";
fun string_of_end () = "end_problem.\n%------------------------------------------------------------------------------";
fun clause2dfg cls =
let val (lits,tfree_lits) = dfg_clause_aux cls
(*"lits" includes the typing assumptions (TVars)*)
val cls_id = get_clause_id cls
val ax_name = get_axiomName cls
val vars = dfg_vars cls
val tvars = dfg_tvars cls
val funcs = funcs_of_cls cls
val preds = preds_of_cls cls
val knd = string_of_kind cls
val lits_str = commas lits
val cls_str = gen_dfg_cls(cls_id,ax_name,knd,lits_str,tvars,vars)
in
(cls_str,tfree_lits)
end;
fun tfree_dfg_clause tfree_lit =
"clause( %(conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ")."
fun gen_dfg_file probname axioms conjectures funcs preds =
let val axstrs_tfrees = (map clause2dfg axioms)
val (axstrs, atfrees) = ListPair.unzip axstrs_tfrees
val axstr = (space_implode "\n" axstrs) ^ "\n\n"
val conjstrs_tfrees = (map clause2dfg conjectures)
val (conjstrs, atfrees) = ListPair.unzip conjstrs_tfrees
val tfree_clss = map tfree_dfg_clause (union_all atfrees)
val conjstr = (space_implode "\n" (tfree_clss@conjstrs)) ^ "\n\n"
val funcstr = string_of_funcs funcs
val predstr = string_of_preds preds
in
(string_of_start probname) ^ (string_of_descrip ()) ^
(string_of_symbols funcstr predstr) ^
(string_of_axioms axstr) ^
(string_of_conjectures conjstr) ^ (string_of_end ())
end;
fun clauses2dfg [] probname axioms conjectures funcs preds =
let val funcs' = (union_all(map funcs_of_cls axioms)) @ funcs
val preds' = (union_all(map preds_of_cls axioms)) @ preds
in
gen_dfg_file probname axioms conjectures funcs' preds'
end
| clauses2dfg (cls::clss) probname axioms conjectures funcs preds =
let val (lits,tfree_lits) = dfg_clause_aux cls
(*"lits" includes the typing assumptions (TVars)*)
val cls_id = get_clause_id cls
val ax_name = get_axiomName cls
val vars = dfg_vars cls
val tvars = dfg_tvars cls
val funcs' = (funcs_of_cls cls) union funcs
val preds' = (preds_of_cls cls) union preds
val knd = string_of_kind cls
val lits_str = concat_with ", " lits
val axioms' = if knd = "axiom" then (cls::axioms) else axioms
val conjectures' =
if knd = "conjecture" then (cls::conjectures) else conjectures
in
clauses2dfg clss probname axioms' conjectures' funcs' preds'
end;
fun string_of_arClauseID (ArityClause {clause_id,axiom_name,...}) =
arclause_prefix ^ ascii_of axiom_name ^ "_" ^ Int.toString clause_id;
fun string_of_arKind (ArityClause arcls) = name_of_kind(#kind arcls);
(*FIXME!!! currently is TPTP format!*)
fun dfg_of_arLit (TConsLit(b,(c,t,args))) =
let val pol = if b then "++" else "--"
val arg_strs = paren_pack args
in
pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"
end
| dfg_of_arLit (TVarLit(b,(c,str))) =
let val pol = if b then "++" else "--"
in
pol ^ c ^ "(" ^ str ^ ")"
end;
fun dfg_of_conclLit (ArityClause arcls) = dfg_of_arLit (#conclLit arcls);
fun dfg_of_premLits (ArityClause arcls) = map dfg_of_arLit (#premLits arcls);
(*FIXME: would this have variables in a forall? *)
fun dfg_arity_clause arcls =
let val arcls_id = string_of_arClauseID arcls
val concl_lit = dfg_of_conclLit arcls
val prems_lits = dfg_of_premLits arcls
val knd = string_of_arKind arcls
val all_lits = concl_lit :: prems_lits
in
"clause( %(" ^ knd ^ ")\n" ^ "or( " ^ (bracket_pack all_lits) ^ ")),\n" ^
arcls_id ^ ")."
end;
(********************************)
(* code to produce TPTP files *)
(********************************)
fun tptp_literal (Literal(pol,pred,tag)) =
let val pred_string = string_of_predicate pred
val tagged_pol =
if (tag andalso !tagged) then (if pol then "+++" else "---")
else (if pol then "++" else "--")
in
tagged_pol ^ pred_string
end;
fun tptp_of_typeLit (LTVar x) = "--" ^ x
| tptp_of_typeLit (LTFree x) = "++" ^ x;
fun gen_tptp_cls (cls_id,ax_name,knd,lits) =
"input_clause(" ^ string_of_clausename (cls_id,ax_name) ^ "," ^
knd ^ "," ^ lits ^ ").";
fun gen_tptp_type_cls (cls_id,ax_name,knd,tfree_lit,idx) =
"input_clause(" ^ string_of_type_clsname (cls_id,ax_name,idx) ^ "," ^
knd ^ ",[" ^ tfree_lit ^ "]).";
fun tptp_type_lits (Clause cls) =
let val lits = map tptp_literal (#literals cls)
val tvar_lits_strs =
if !keep_types
then (map tptp_of_typeLit (#tvar_type_literals cls))
else []
val tfree_lits =
if !keep_types
then (map tptp_of_typeLit (#tfree_type_literals cls))
else []
in
(tvar_lits_strs @ lits, tfree_lits)
end;
fun tptp_clause cls =
let val (lits,tfree_lits) = tptp_type_lits cls
(*"lits" includes the typing assumptions (TVars)*)
val cls_id = get_clause_id cls
val ax_name = get_axiomName cls
val knd = string_of_kind cls
val lits_str = bracket_pack lits
val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str)
fun typ_clss k [] = []
| typ_clss k (tfree :: tfrees) =
gen_tptp_type_cls(cls_id,ax_name,knd,tfree,k) ::
typ_clss (k+1) tfrees
in
cls_str :: (typ_clss 0 tfree_lits)
end;
fun clause2tptp cls =
let val (lits,tfree_lits) = tptp_type_lits cls
(*"lits" includes the typing assumptions (TVars)*)
val cls_id = get_clause_id cls
val ax_name = get_axiomName cls
val knd = string_of_kind cls
val lits_str = bracket_pack lits
val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str)
in
(cls_str,tfree_lits)
end;
fun tfree_clause tfree_lit =
"input_clause(" ^ "tfree_tcs," ^ "conjecture" ^ ",[" ^ tfree_lit ^ "]).";
fun tptp_of_arLit (TConsLit(b,(c,t,args))) =
let val pol = if b then "++" else "--"
val arg_strs = paren_pack args
in
pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"
end
| tptp_of_arLit (TVarLit(b,(c,str))) =
let val pol = if b then "++" else "--"
in
pol ^ c ^ "(" ^ str ^ ")"
end;
fun tptp_of_conclLit (ArityClause arcls) = tptp_of_arLit (#conclLit arcls);
fun tptp_of_premLits (ArityClause arcls) = map tptp_of_arLit (#premLits arcls);
fun tptp_arity_clause arcls =
let val arcls_id = string_of_arClauseID arcls
val concl_lit = tptp_of_conclLit arcls
val prems_lits = tptp_of_premLits arcls
val knd = string_of_arKind arcls
val all_lits = concl_lit :: prems_lits
in
"input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^
(bracket_pack all_lits) ^ ")."
end;
fun tptp_classrelLits sub sup =
let val tvar = "(T)"
in
case sup of NONE => "[++" ^ sub ^ tvar ^ "]"
| (SOME supcls) => "[--" ^ sub ^ tvar ^ ",++" ^ supcls ^ tvar ^ "]"
end;
fun tptp_classrelClause (ClassrelClause {clause_id,subclass,superclass,...}) =
let val relcls_id = clrelclause_prefix ^ ascii_of subclass ^ "_" ^
Int.toString clause_id
val lits = tptp_classrelLits (make_type_class subclass)
(Option.map make_type_class superclass)
in
"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."
end;
end;