(* 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 clauses2dfg : string -> clause list -> clause 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_aux : (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
(*for hashing*)
val clause_eq : clause * clause -> bool
val hash_clause : clause -> int
val list_ord : ('a * 'b -> order) -> 'a list * 'b list -> order
type fol_type
val types_ord : fol_type list * fol_type list -> order
val string_of_fol_type : fol_type -> string
val mk_fol_type: string * string * fol_type list -> fol_type
val types_eq :fol_type list * fol_type list ->
(string * string) list * (string * string) list -> bool * ((string * string) list * (string * string) list)
val check_var_pairs: ''a * ''b -> (''a * ''b) list -> int
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"),
("Divides.op div", "div"),
("HOL.divide", "divide"),
("op -->", "implies"),
("{}", "emptyset"),
("op :", "in"),
("op Un", "union"),
("op Int", "inter"),
("List.op @", "append")];
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 ^ ")";
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 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 | 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;
(* "tag" is used for vampire specific syntax *)
type tag = bool;
(**** Isabelle FOL clauses ****)
val tagged = ref false;
type pred_name = string;
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 pred_name * fol_type list * fol_term list;
datatype literal = Literal of polarity * predicate * tag;
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,
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 * 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;
fun make_clause (clause_id,axiom_name,kind,literals,
types_sorts,tvar_type_literals,tfree_type_literals) =
if forall isFalse literals
then error "Problem too trivial for resolution (empty clause)"
else
Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,
literals = literals, types_sorts = types_sorts,
tvar_type_literals = tvar_type_literals,
tfree_type_literals = tfree_type_literals};
(** 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;
(*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, [folType], []), ts)
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 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 (Const("op |",_) $ P $ Q) =
literals_of_term1 (literals_of_term1 args P) Q
| literals_of_term1 (lits, ts) P =
let val ((pred, ts'), polarity, tag) = predicate_of (P,true,false)
val lits' = Literal(polarity,pred,tag) :: 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) =
let val xy_ord = ord(x,y)
in
case xy_ord of EQUAL => list_ord ord (xs,ys)
| _ => xy_ord
end;
fun type_ord (AtomV(_),AtomV(_)) = EQUAL
| type_ord (AtomV(_),_) = LESS
| type_ord (AtomF(_),AtomV(_)) = GREATER
| type_ord (AtomF(f1),AtomF(f2)) = string_ord (f1,f2)
| type_ord (AtomF(_),_) = LESS
| type_ord (Comp(_,_),AtomV(_)) = GREATER
| type_ord (Comp(_,_),AtomF(_)) = GREATER
| type_ord (Comp(con1,args1),Comp(con2,args2)) =
let val con_ord = string_ord(con1,con2)
in
case con_ord of EQUAL => types_ord (args1,args2)
| _ => con_ord
end
and
types_ord ([],[]) = EQUAL
| types_ord (tps1,tps2) = list_ord type_ord (tps1,tps2);
fun term_ord (UVar(_,_),UVar(_,_)) = EQUAL
| term_ord (UVar(_,_),_) = LESS
| term_ord (Fun(_,_,_),UVar(_)) = GREATER
| term_ord (Fun(f1,tps1,tms1),Fun(f2,tps2,tms2)) =
(case string_ord (f1,f2) of
EQUAL =>
(case terms_ord (tms1,tms2) of EQUAL => types_ord (tps1,tps2)
| tms_ord => tms_ord)
| fn_ord => fn_ord)
and
terms_ord ([],[]) = EQUAL
| terms_ord (tms1,tms2) = list_ord term_ord (tms1,tms2);
fun predicate_ord (Predicate(pname1,ftyps1,ftms1),Predicate(pname2,ftyps2,ftms2)) =
case string_ord (pname1,pname2) of
EQUAL => (case terms_ord(ftms1,ftms2) of EQUAL => types_ord(ftyps1,ftyps2)
| ftms_ord => ftms_ord)
| pname_ord => pname_ord
fun literal_ord (Literal(false,_,_),Literal(true,_,_)) = LESS
| literal_ord (Literal(true,_,_),Literal(false,_,_)) = GREATER
| literal_ord (Literal(_,pred1,_),Literal(_,pred2,_)) = predicate_ord(pred1,pred2);
fun sort_lits lits = sort literal_ord lits;
(********** clause equivalence ******************)
fun check_var_pairs (x,y) [] = 0
| check_var_pairs (x,y) ((u,v)::w) =
if (x,y) = (u,v) then 1
else
if (x = u) orelse (y = v) then 2 (*conflict*)
else check_var_pairs (x,y) w;
fun type_eq (AtomV(v1),AtomV(v2)) (vars,tvars) =
(case check_var_pairs (v1,v2) tvars of 0 => (true,(vars,(v1,v2)::tvars))
| 1 => (true,(vars,tvars))
| 2 => (false,(vars,tvars)))
| type_eq (AtomV(_),_) vtvars = (false,vtvars)
| type_eq (AtomF(f1),AtomF(f2)) vtvars = (f1=f2,vtvars)
| type_eq (AtomF(_),_) vtvars = (false,vtvars)
| type_eq (Comp(con1,args1),Comp(con2,args2)) vtvars =
let val (eq1,vtvars1) =
if con1 = con2 then types_eq (args1,args2) vtvars
else (false,vtvars)
in
(eq1,vtvars1)
end
| type_eq (Comp(_,_),_) vtvars = (false,vtvars)
and
types_eq ([],[]) vtvars = (true,vtvars)
| types_eq (tp1::tps1,tp2::tps2) vtvars =
let val (eq1,vtvars1) = type_eq (tp1,tp2) vtvars
val (eq2,vtvars2) = if eq1 then types_eq (tps1,tps2) vtvars1
else (eq1,vtvars1)
in
(eq2,vtvars2)
end;
fun term_eq (UVar(v1,tp1),UVar(v2,tp2)) (vars,tvars) =
(case check_var_pairs (v1,v2) vars of 0 => type_eq (tp1,tp2) (((v1,v2)::vars),tvars)
| 1 => type_eq (tp1,tp2) (vars,tvars)
| 2 => (false,(vars,tvars)))
| term_eq (UVar(_,_),_) vtvars = (false,vtvars)
| term_eq (Fun(f1,tps1,tms1),Fun(f2,tps2,tms2)) vtvars =
let val (eq1,vtvars1) =
if f1 = f2 then terms_eq (tms1,tms2) vtvars
else (false,vtvars)
val (eq2,vtvars2) =
if eq1 then types_eq (tps1,tps2) vtvars1
else (eq1,vtvars1)
in
(eq2,vtvars2)
end
| term_eq (Fun(_,_,_),_) vtvars = (false,vtvars)
and
terms_eq ([],[]) vtvars = (true,vtvars)
| terms_eq (tm1::tms1,tm2::tms2) vtvars =
let val (eq1,vtvars1) = term_eq (tm1,tm2) vtvars
val (eq2,vtvars2) = if eq1 then terms_eq (tms1,tms2) vtvars1
else (eq1,vtvars1)
in
(eq2,vtvars2)
end;
fun pred_eq (Predicate(pname1,tps1,tms1),Predicate(pname2,tps2,tms2)) vtvars =
let val (eq1,vtvars1) =
if (pname1 = pname2) then terms_eq (tms1,tms2) vtvars
else (false,vtvars)
val (eq2,vtvars2) =
if eq1 then types_eq (tps1,tps2) vtvars1
else (eq1,vtvars1)
in
(eq2,vtvars2)
end;
fun lit_eq (Literal(pol1,pred1,_),Literal(pol2,pred2,_)) vtvars =
if (pol1 = pol2) then pred_eq (pred1,pred2) vtvars
else (false,vtvars);
(*must have the same number of literals*)
fun lits_eq ([],[]) vtvars = (true,vtvars)
| lits_eq (l1::ls1,l2::ls2) vtvars =
let val (eq1,vtvars1) = lit_eq (l1,l2) vtvars
in
if eq1 then lits_eq (ls1,ls2) vtvars1
else (false,vtvars1)
end;
(*Equality of two clauses up to variable renaming*)
fun clause_eq (Clause{literals=lits1,...}, Clause{literals=lits2,...}) =
length lits1 = length lits2 andalso #1 (lits_eq (lits1,lits2) ([],[]));
(*** Hash function for clauses ***)
val xor_words = List.foldl Word.xorb 0w0;
fun hashw_term (UVar(_,_), w) = w
| hashw_term (Fun(f,tps,args), w) =
List.foldl hashw_term (Polyhash.hashw_string (f,w)) args;
fun hashw_pred (Predicate(pn,_,args), w) =
List.foldl hashw_term (Polyhash.hashw_string (pn,w)) args;
fun hash1_literal (Literal(true,pred,_)) = hashw_pred (pred, 0w0)
| hash1_literal (Literal(false,pred,_)) = Word.notb (hashw_pred (pred, 0w0));
fun hash_clause (Clause{literals,...}) =
Word.toIntX (xor_words (map hash1_literal literals));
(*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;
fun add_typs (Clause cls) = add_typs_aux (#types_sorts cls)
(** 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)
fun make_axiom_clause_thm thm (ax_name,cls_id) =
let val (lits,types_sorts) = literals_of_term (prop_of thm)
val lits' = sort_lits lits
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,ax_name,Axiom,
lits',types_sorts,tvar_lits,tfree_lits)
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) = literals_of_term t
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(n,"conjecture",Conjecture,
lits,types_sorts,tvar_lits,tfree_lits)
end;
fun make_conjecture_clauses_aux _ [] = []
| make_conjecture_clauses_aux n (t::ts) =
make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts
val make_conjecture_clauses = make_conjecture_clauses_aux 0
(*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) = literals_of_term term
val lits' = sort_lits lits
val (tvar_lits,tfree_lits) = add_typs_aux types_sorts
in
make_clause(cls_id,ax_name,Axiom,
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,
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, n, (res,args)) =
let val nargs = length args
val tvars = gen_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 = lookup_type_const 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. It's always 1
except for conjecture 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};
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 ("HOL.type"::sups) = (*Should be ignored*)
classrelClauses_of_aux n sub sups
| classrelClauses_of_aux n sub (sup::sups) =
ClassrelClause {clause_id = n, subclass = sub, superclass = sup}
:: classrelClauses_of_aux (n+1) sub sups;
fun classrelClauses_of (sub,sups) = classrelClauses_of_aux 0 sub sups;
(***** Isabelle arities *****)
fun arity_clause _ (tcons, []) = []
| arity_clause n (tcons, ("HOL.type",_)::ars) = (*Should be ignored*)
arity_clause n (tcons,ars)
| 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;
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
val typ' = string_of_fol_type typ
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 map string_of_fol_type typs else []
in name ^ (paren_pack (terms_as_strings @ typs')) end;
(* 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 map string_of_fol_type typs else []
in name ^ (paren_pack (terms_as_strings @ 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);
(********************************)
(* 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;
fun dfg_of_typeLit (LTVar (s,ty)) = "not(" ^ s ^ "(" ^ ty ^ "))"
| dfg_of_typeLit (LTFree (s,ty)) = s ^ "(" ^ ty ^ ")";
(*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) ^ ").";
(*FIXME: UNUSED*)
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 (_, _, 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 string_of_predname (Predicate("equal",_,terms)) = "EQUALITY"
| string_of_predname (Predicate(name,_,terms)) = name
fun dfg_pred (Literal(pol,pred,tag)) ax_name =
(string_of_predname pred) ^ " " ^ ax_name
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 knd = name_of_kind kind
val lits_str = commas lits
val cls_str = gen_dfg_cls(clause_id,axiom_name,knd,lits_str,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_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_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 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, atfrees) = ListPair.unzip (map clause2dfg conjectures)
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 probname ^
string_of_symbols funcstr predstr ^
string_of_axioms axstr ^
string_of_conjectures conjstr ^ "end_problem.\n"
end;
(*** Find all occurrences of predicates in types, terms, literals... ***)
(*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")
val preds_of_clauses = Symtab.dest o (foldl add_clause_preds Symtab.empty)
(*** Find all occurrences of functions in types, terms, literals... ***)
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 _, funcs) = funcs
| add_folterm_funcs (Fun(a,tys,[]), funcs) = Symtab.update (a,0) funcs
(*A constant is a special case: it has no type argument even if overloaded*)
| 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)
fun add_clause_funcs (Clause {literals, ...}, funcs) =
foldl add_literal_funcs funcs literals
handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")
val funcs_of_clauses = Symtab.dest o (foldl add_clause_funcs Symtab.empty)
fun clauses2dfg probname axioms conjectures =
let val clss = conjectures @ axioms
in
gen_dfg_file probname axioms conjectures
(funcs_of_clauses clss) (preds_of_clauses clss)
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 (s,ty)) = "--" ^ s ^ "(" ^ ty ^ ")"
| tptp_of_typeLit (LTFree (s,ty)) = "++" ^ s ^ "(" ^ ty ^ ")";
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
"[--" ^ sub ^ tvar ^ ",++" ^ sup ^ 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) (make_type_class superclass)
in
"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."
end;
end;