(* 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.
*)
signature RES_CLAUSE =
sig
exception ARCLAUSE of string
exception CLAUSE of string
type arityClause
type classrelClause
val classrelClauses_of :
string * string list -> classrelClause list
type clause
val keep_types : bool ref
val make_axiom_arity_clause :
string * (string * string list list) -> arityClause
val make_axiom_classrelClause :
string * string option -> classrelClause
val make_axiom_clause : Term.term -> string * int -> clause
val make_axiom_clause_thm : Thm.thm -> string * int -> clause
val make_conjecture_clause : Term.term -> clause
val make_conjecture_clause_thm : Thm.thm -> clause
val make_hypothesis_clause : Term.term -> clause
val make_hypothesis_clause_thm : Thm.thm -> clause
val special_equal : bool ref
val tptp_arity_clause : arityClause -> string
val tptp_classrelClause : classrelClause -> string
val tptp_clause : clause -> string list
val clause_info : clause -> string * string
val tptp_clauses2str : string list -> string
val typed : unit -> unit
val untyped : unit -> unit
val clause2tptp : clause -> string * string list
val tfree_clause : string -> 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 = "Typ_";
val tfree_prefix = "typ_";
val clause_prefix = "cls_";
val arclause_prefix = "arcls_"
val const_prefix = "const_";
val tconst_prefix = "tconst_";
val class_prefix = "class_";
(**** some useful functions ****)
val const_trans_table =
Symtab.make [("op =", "equal"),
("op <=", "lessequals"),
("op <", "less"),
("op &", "and"),
("op |", "or"),
("op -->", "implies"),
("op :", "in"),
("op Un", "union"),
("op Int", "inter")];
(*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;
(* another version of above functions that remove chars that may not be allowed by Vampire *)
fun make_schematic_var v = schematic_var_prefix ^ (ascii_of v);
fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);
fun make_schematic_type_var v = tvar_prefix ^ (ascii_of v);
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of x);
fun make_fixed_const c = const_prefix ^ (ascii_of c);
fun make_fixed_type_const c = tconst_prefix ^ (ascii_of c);
fun make_type_class clas = class_prefix ^ (ascii_of clas);
fun lookup_const c =
case Symtab.lookup (const_trans_table,c) of
SOME c' => c'
| NONE => make_fixed_const c;
(***** definitions and functions for FOL clauses, prepared for conversion into TPTP format or SPASS format. *****)
val keep_types = ref true; (* default is true *)
fun untyped () = (keep_types := false);
fun typed () = (keep_types := 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;
fun string_of_indexname (name,index) = name ^ "_" ^ (string_of_int index);
val id_ref = ref 0;
fun generate_id () =
let val id = !id_ref
in
(id_ref:=id + 1; id)
end;
(**** Isabelle FOL clauses ****)
(* by default it is false *)
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 * folTerm list;
datatype predicate = Predicate of pred_name * fol_type * folTerm list;
datatype literal = Literal of polarity * predicate * tag;
datatype typ_var = FOLTVar of indexname | FOLTFree of string;
(* 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 };
exception CLAUSE of string;
(*** make clauses ***)
fun make_clause (clause_id,axiom_name,kind,literals,types_sorts,tvar_type_literals,tfree_type_literals) =
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};
fun type_of (Type (a, [])) = (make_fixed_type_const a,[])
| type_of (Type (a, Ts)) =
let val foltyps_ts = map type_of Ts
val (folTyps,ts) = ListPair.unzip foltyps_ts
val ts' = ResLib.flat_noDup ts
in
(((make_fixed_type_const a) ^ (ResLib.list_to_string folTyps)),ts')
end
| type_of (TFree (a, s)) = (make_fixed_type_var a, [((FOLTFree a),s)])
| type_of (TVar (v, s)) = (make_schematic_type_var (string_of_indexname v), [((FOLTVar v),s)]);
(* added: checkMeta: string -> bool *)
(* Any meta vars like ?x should be treated as universal vars,although it is represented as "Free(...)" by Isabelle *)
fun checkMeta s =
let val chars = explode s
in
["M", "E", "T", "A", "H", "Y", "P", "1"] prefix chars
end;
fun pred_name_type (Const(c,T)) = (lookup_const c,type_of T)
| pred_name_type (Free(x,T)) =
let val is_meta = checkMeta x
in
if is_meta then (raise CLAUSE("Predicate Not First Order")) else
(make_fixed_var x,type_of T)
end
| pred_name_type (Var(_,_)) = raise CLAUSE("Predicate Not First Order")
| pred_name_type _ = raise CLAUSE("Predicate input unexpected");
(* For type 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)) = (lookup_const c,type_of T)
| fun_name_type (Free(x,T)) = (make_fixed_var x,type_of T)
| fun_name_type _ = raise CLAUSE("Function Not First Order");
fun term_of (Var(ind_nm,T)) =
let val (folType,ts) = type_of T
in
(UVar(make_schematic_var(string_of_indexname ind_nm),folType),ts)
end
| term_of (Free(x,T)) =
let val is_meta = checkMeta x
val (folType,ts) = type_of T
in
if is_meta then (UVar(make_schematic_var x,folType),ts)
else
(Fun(make_fixed_var x,folType,[]),ts)
end
| term_of (Const(c,T)) = (* impossible to be equality *)
let val (folType,ts) = type_of T
in
(Fun(lookup_const c,folType,[]),ts)
end
| term_of (app as (t $ a)) =
let val (f,args) = strip_comb app
fun term_of_aux () =
let val (funName,(funType,ts1)) = fun_name_type f
val (args',ts2) = ListPair.unzip (map term_of args)
val ts3 = ResLib.flat_noDup (ts1::ts2)
in
(Fun(funName,funType,args'),ts3)
end
fun term_of_eq ((Const ("op =", typ)),args) =
let val arg_typ = eq_arg_type typ
val (args',ts) = ListPair.unzip (map term_of args)
val equal_name = lookup_const ("op =")
in
(Fun(equal_name,arg_typ,args'),ResLib.flat_noDup ts)
end
in
case f of Const ("op =", typ) => term_of_eq (f,args)
| Const(_,_) => term_of_aux ()
| Free(s,_) => if (checkMeta s) then (raise CLAUSE("Function Not First Order")) else term_of_aux ()
| _ => raise CLAUSE("Function Not First Order")
end
| term_of _ = raise CLAUSE("Function Not First Order");
fun pred_of_eq ((Const ("op =", typ)),args) =
let val arg_typ = eq_arg_type typ
val (args',ts) = ListPair.unzip (map term_of args)
val equal_name = lookup_const "op ="
in
(Predicate(equal_name,arg_typ,args'),ResLib.flat_noDup ts)
end;
(* changed for non-equality predicate *)
(* The input "pred" cannot be an equality *)
fun pred_of_nonEq (pred,args) =
let val (predName,(predType,ts1)) = pred_name_type pred
val (args',ts2) = ListPair.unzip (map term_of args)
val ts3 = ResLib.flat_noDup (ts1::ts2)
in
(Predicate(predName,predType,args'),ts3)
end;
(* Changed for typed equality *)
(* First check if the predicate is an equality or not, then call different functions for equality and non-equalities *)
fun predicate_of term =
let val (pred,args) = strip_comb term
in
case pred of (Const ("op =", _)) => pred_of_eq (pred,args)
| _ => pred_of_nonEq (pred,args)
end;
fun literals_of_term ((Const("Trueprop",_) $ P),lits_ts) = literals_of_term(P,lits_ts)
| literals_of_term ((Const("op |",_) $ P $ Q),(lits,ts)) =
let val (lits',ts') = literals_of_term(P,(lits,ts))
in
literals_of_term(Q,(lits',ts'))
end
| literals_of_term ((Const("Not",_) $ P),(lits,ts)) =
let val (pred,ts') = predicate_of P
val lits' = Literal(false,pred,false) :: lits
val ts'' = ResLib.no_rep_app ts ts'
in
(lits',ts'')
end
| literals_of_term (P,(lits,ts)) =
let val (pred,ts') = predicate_of P
val lits' = Literal(true,pred,false) :: lits
val ts'' = ResLib.no_rep_app ts ts'
in
(lits',ts'')
end;
fun literals_of_thm thm = literals_of_term (prop_of thm, ([],[]));
(*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(string_of_indexname 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));
(*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
(ResLib.no_rep_app vs 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, ResLib.no_rep_app fs fss)
end;
fun add_typs (Clause cls) = add_typs_aux (#types_sorts cls)
(** make axiom clauses, hypothesis clauses and conjecture clauses. **)
local
fun replace_dot "." = "_"
| replace_dot c = c;
in
fun proper_ax_name ax_name =
let val chars = explode ax_name
in
implode (map replace_dot chars)
end;
end;
fun make_axiom_clause_thm thm (name,number)=
let val (lits,types_sorts) = literals_of_thm thm
val cls_id = number
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
val ax_name = proper_ax_name name
in
make_clause(cls_id,ax_name,Axiom,lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_hypothesis_clause_thm thm =
let val (lits,types_sorts) = literals_of_thm thm
val cls_id = generate_id()
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,"",Hypothesis,lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_conjecture_clause_thm thm =
let val (lits,types_sorts) = literals_of_thm thm
val cls_id = generate_id()
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,"",Conjecture,lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_axiom_clause term (name,number)=
let val (lits,types_sorts) = literals_of_term (term,([],[]))
val cls_id = number
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
val ax_name = proper_ax_name name
in
make_clause(cls_id,ax_name,Axiom,lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_hypothesis_clause term =
let val (lits,types_sorts) = literals_of_term (term,([],[]))
val cls_id = generate_id()
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,"",Hypothesis,lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_conjecture_clause term =
let val (lits,types_sorts) = literals_of_term (term,([],[]))
val cls_id = generate_id()
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,"",Conjecture,lits,types_sorts,tvar_lits,tfree_lits)
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,
kind: kind,
conclLit: arLit,
premLits: arLit list};
fun get_TVars 0 = []
| get_TVars n = ("T_" ^ (string_of_int 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_arity_clause (clause_id,kind,conclLit,premLits) =
ArityClause {clause_id = clause_id, kind = kind, conclLit = conclLit, premLits = premLits};
fun make_axiom_arity_clause (tcons,(res,args)) =
let val cls_id = generate_id()
val nargs = length args
val tvars = get_TVars nargs
val conclLit = make_TConsLit(true,(res,tcons,tvars))
val tvars_srts = ListPair.zip (tvars,args)
val tvars_srts' = ResLib.flat_noDup(map pack_sort tvars_srts)
val false_tvars_srts' = ResLib.pair_ins false tvars_srts'
val premLits = map make_TVarLit false_tvars_srts'
in
make_arity_clause (cls_id,Axiom,conclLit,premLits)
end;
(**** Isabelle class relations ****)
datatype classrelClause =
ClassrelClause of {clause_id: clause_id,
subclass: class,
superclass: class option};
fun make_classrelClause (clause_id,subclass,superclass) =
ClassrelClause {clause_id = clause_id,subclass = subclass, superclass = superclass};
fun make_axiom_classrelClause (subclass,superclass) =
let val cls_id = generate_id()
val sub = make_type_class subclass
val sup = case superclass of NONE => NONE
| SOME s => SOME (make_type_class s)
in
make_classrelClause(cls_id,sub,sup)
end;
fun classrelClauses_of_aux (sub,[]) = []
| classrelClauses_of_aux (sub,(sup::sups)) = make_axiom_classrelClause(sub,SOME sup) :: (classrelClauses_of_aux (sub,sups));
fun classrelClauses_of (sub,sups) =
case sups of [] => [make_axiom_classrelClause (sub,NONE)]
| _ => classrelClauses_of_aux (sub, sups);
(***** convert clauses to tptp format *****)
fun string_of_clauseID (Clause cls) = clause_prefix ^ (string_of_int (#clause_id cls));
fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
fun string_of_axiomName (Clause cls) = #axiom_name cls;
(****!!!! Changed for typed equality !!!!****)
fun wrap_eq_type typ t = eq_typ_wrapper ^"(" ^ t ^ "," ^ typ ^ ")";
(****!!!! Changed for typed equality !!!!****)
(* Only need to wrap equality's arguments with "typeinfo" if the output clauses are typed && 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,typ,[])) = name
| string_of_term (Fun (name,typ,terms)) =
let val terms' = map string_of_term terms
in
if (!keep_types) then name ^ (ResLib.list_to_string (typ :: terms'))
else name ^ (ResLib.list_to_string terms')
end;
(* Changed for typed equality *)
(* 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,_,[])) = name
| string_of_predicate (Predicate(name,typ,terms)) =
let val terms_as_strings = map string_of_term terms
in
if (!keep_types) then name ^ (ResLib.list_to_string (typ :: terms_as_strings))
else name ^ (ResLib.list_to_string terms_as_strings)
end;
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) =
let val ax_str = (if ax_name = "" then "" else ("_" ^ ax_name))
in
"input_clause(" ^ cls_id ^ ax_str ^ "," ^ knd ^ "," ^ lits ^ ")."
end;
fun gen_tptp_type_cls (cls_id,knd,tfree_lit,idx) = "input_clause(" ^ cls_id ^ "_tcs" ^ (string_of_int idx) ^ "," ^ knd ^ ",[" ^ tfree_lit ^ "]).";
fun tptp_clause_aux (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_clause_aux cls (*"lits" includes the typing assumptions (TVars)*)
val cls_id = string_of_clauseID cls
val ax_name = string_of_axiomName cls
val knd = string_of_kind cls
val lits_str = ResLib.list_to_string' 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,knd,tfree,k)) :: (typ_clss (k+1) tfrees)
in
cls_str :: (typ_clss 0 tfree_lits)
end;
fun clause_info cls =
let
val cls_id = string_of_clauseID cls
val ax_name = string_of_axiomName cls
in
((ax_name^""), cls_id)
end;
fun clause2tptp cls =
let val (lits,tfree_lits) = tptp_clause_aux cls (*"lits" includes the typing assumptions (TVars)*)
val cls_id = string_of_clauseID cls
val ax_name = string_of_axiomName cls
val knd = string_of_kind cls
val lits_str = ResLib.list_to_string' 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 ^ "]).";
val delim = "\n";
val tptp_clauses2str = ResLib.list2str_sep delim;
fun string_of_arClauseID (ArityClause arcls) = arclause_prefix ^ string_of_int(#clause_id arcls);
fun string_of_arLit (TConsLit(b,(c,t,args))) =
let val pol = if b then "++" else "--"
val arg_strs = (case args of [] => "" | _ => ResLib.list_to_string args)
in
pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"
end
| string_of_arLit (TVarLit(b,(c,str))) =
let val pol = if b then "++" else "--"
in
pol ^ c ^ "(" ^ str ^ ")"
end;
fun string_of_conclLit (ArityClause arcls) = string_of_arLit (#conclLit arcls);
fun strings_of_premLits (ArityClause arcls) = map string_of_arLit (#premLits arcls);
fun string_of_arKind (ArityClause arcls) = name_of_kind(#kind arcls);
fun tptp_arity_clause arcls =
let val arcls_id = string_of_arClauseID arcls
val concl_lit = string_of_conclLit arcls
val prems_lits = strings_of_premLits arcls
val knd = string_of_arKind arcls
val all_lits = concl_lit :: prems_lits
in
"input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^ (ResLib.list_to_string' all_lits) ^ ")."
end;
val clrelclause_prefix = "relcls_";
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 cls) =
let val relcls_id = clrelclause_prefix ^ string_of_int(#clause_id cls)
val sub = #subclass cls
val sup = #superclass cls
val lits = tptp_classrelLits sub sup
in
"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."
end;
end;