(* Author: Jia Meng, Cambridge University Computer Laboratory
ID: $Id$
Copyright 2004 University of Cambridge
Storing/printing FOL clauses and arity clauses.
Typed equality is treated differently.
*)
(*FIXME: combine with res_hol_clause!*)
signature RES_CLAUSE =
sig
val schematic_var_prefix: string
val fixed_var_prefix: string
val tvar_prefix: string
val tfree_prefix: string
val clause_prefix: string
val const_prefix: string
val tconst_prefix: string
val class_prefix: string
val union_all: ''a list list -> ''a list
val const_trans_table: string Symtab.table
val type_const_trans_table: string Symtab.table
val ascii_of: string -> string
val undo_ascii_of: string -> string
val paren_pack : string list -> string
val make_schematic_var : string * int -> string
val make_fixed_var : string -> string
val make_schematic_type_var : string * int -> string
val make_fixed_type_var : string -> string
val make_fixed_const : bool -> string -> string
val make_fixed_type_const : bool -> string -> string
val make_type_class : string -> string
datatype kind = Axiom | Conjecture
type axiom_name = string
datatype fol_type =
AtomV of string
| AtomF of string
| Comp of string * fol_type list
val string_of_fol_type : fol_type -> string
datatype type_literal = LTVar of string * string | LTFree of string * string
exception CLAUSE of string * term
val add_typs : typ list -> type_literal list
val get_tvar_strs: typ list -> string list
datatype arLit =
TConsLit of class * string * string list
| TVarLit of class * string
datatype arityClause = ArityClause of
{axiom_name: axiom_name, conclLit: arLit, premLits: arLit list}
datatype classrelClause = ClassrelClause of
{axiom_name: axiom_name, subclass: class, superclass: class}
val make_classrel_clauses: theory -> class list -> class list -> classrelClause list
val make_arity_clauses_dfg: bool -> theory -> string list -> class list -> class list * arityClause list
val make_arity_clauses: theory -> string list -> class list -> class list * arityClause list
val add_type_sort_preds: typ * int Symtab.table -> int Symtab.table
val add_classrelClause_preds : classrelClause * int Symtab.table -> int Symtab.table
val class_of_arityLit: arLit -> class
val add_arityClause_preds: arityClause * int Symtab.table -> int Symtab.table
val add_foltype_funcs: fol_type * int Symtab.table -> int Symtab.table
val add_arityClause_funcs: arityClause * int Symtab.table -> int Symtab.table
val init_functab: int Symtab.table
val writeln_strs: TextIO.outstream -> string list -> unit
val dfg_sign: bool -> string -> string
val dfg_of_typeLit: bool -> type_literal -> string
val gen_dfg_cls: int * string * kind * string list * string list * string list -> string
val string_of_preds: (string * Int.int) list -> string
val string_of_funcs: (string * int) list -> string
val string_of_symbols: string -> string -> string
val string_of_start: string -> string
val string_of_descrip : string -> string
val dfg_tfree_clause : string -> string
val dfg_classrelClause: classrelClause -> string
val dfg_arity_clause: arityClause -> string
val tptp_sign: bool -> string -> string
val tptp_of_typeLit : bool -> type_literal -> string
val gen_tptp_cls : int * string * kind * string list * string list -> string
val tptp_tfree_clause : string -> string
val tptp_arity_clause : arityClause -> string
val tptp_classrelClause : classrelClause -> string
end
structure ResClause: RES_CLAUSE =
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"),
(@{const_name HOL.less_eq}, "lessequals"),
(@{const_name HOL.less}, "less"),
("op &", "and"),
("op |", "or"),
(@{const_name HOL.plus}, "plus"),
(@{const_name HOL.minus}, "minus"),
(@{const_name HOL.times}, "times"),
(@{const_name Divides.div}, "div"),
(@{const_name HOL.divide}, "divide"),
("op -->", "implies"),
("{}", "emptyset"),
("op :", "in"),
("op Un", "union"),
("op Int", "inter"),
("List.append", "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.*)
val A_minus_space = Char.ord #"A" - Char.ord #" ";
fun stringN_of_int 0 _ = ""
| stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);
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 ("_" ^ stringN_of_int 3 (Char.ord c)) (*fixed width, in case more digits follow*)
else ""
val ascii_of = String.translate ascii_of_c;
(** Remove ASCII armouring from names in proof files **)
(*We don't raise error exceptions because this code can run inside the watcher.
Also, the errors are "impossible" (hah!)*)
fun undo_ascii_aux rcs [] = String.implode(rev rcs)
| undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) [] (*ERROR*)
(*Three types of _ escapes: __, _A to _P, _nnn*)
| undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs
| undo_ascii_aux rcs (#"_" :: c :: cs) =
if #"A" <= c andalso c<= #"P" (*translation of #" " to #"/"*)
then undo_ascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs
else
let val digits = List.take (c::cs, 3) handle Subscript => []
in
case Int.fromString (String.implode digits) of
NONE => undo_ascii_aux (c:: #"_"::rcs) cs (*ERROR*)
| SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))
end
| undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs;
val undo_ascii_of = undo_ascii_aux [] o String.explode;
(* 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));
(*HACK because SPASS truncates identifiers to 63 characters :-(( *)
(*32-bit hash,so we expect no collisions unless there are around 65536 long identifiers...*)
fun controlled_length dfg_format s =
if size s > 60 andalso dfg_format
then Word.toString (Polyhash.hashw_string(s,0w0))
else s;
fun lookup_const dfg c =
case Symtab.lookup const_trans_table c of
SOME c' => c'
| NONE => controlled_length dfg (ascii_of c);
fun lookup_type_const dfg c =
case Symtab.lookup type_const_trans_table c of
SOME c' => c'
| NONE => controlled_length dfg (ascii_of c);
fun make_fixed_const _ "op =" = "equal" (*MUST BE "equal" because it's built-in to ATPs*)
| make_fixed_const dfg c = const_prefix ^ lookup_const dfg c;
fun make_fixed_type_const dfg c = tconst_prefix ^ lookup_type_const dfg c;
fun make_type_class clas = class_prefix ^ ascii_of clas;
(***** definitions and functions for FOL clauses, for conversion to TPTP or DFG format. *****)
datatype kind = Axiom | Conjecture;
type axiom_name = string;
(**** Isabelle FOL clauses ****)
(*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));
(*First string is the type class; the second is a TVar or TFfree*)
datatype type_literal = LTVar of string * string | LTFree of string * string;
exception CLAUSE of string * term;
fun atomic_type (TFree (a,_)) = AtomF(make_fixed_type_var a)
| atomic_type (TVar (v,_)) = AtomV(make_schematic_type_var v);
(*Flatten a type to a fol_type while accumulating sort constraints on the TFrees and
TVars it contains.*)
fun type_of dfg (Type (a, Ts)) =
let val (folTyps, ts) = types_of dfg Ts
val t = make_fixed_type_const dfg a
in (Comp(t,folTyps), ts) end
| type_of dfg T = (atomic_type T, [T])
and types_of dfg Ts =
let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
in (folTyps, union_all ts) end;
(*Make literals for sorted type variables*)
fun sorts_on_typs_aux (_, []) = []
| sorts_on_typs_aux ((x,i), s::ss) =
let val sorts = sorts_on_typs_aux ((x,i), ss)
in
if s = "HOL.type" then sorts
else if i = ~1 then LTFree(make_type_class s, make_fixed_type_var x) :: sorts
else LTVar(make_type_class s, make_schematic_type_var (x,i)) :: sorts
end;
fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)
| sorts_on_typs (TVar (v,s)) = sorts_on_typs_aux (v,s);
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 a list of type literals.*)
fun add_typs Ts = foldl (op union) [] (map sorts_on_typs Ts);
(*The correct treatment of TFrees like 'a in lemmas (axiom clauses) is not clear.
* Ignoring them leads to unsound proofs, since we do nothing to ensure that 'a
in a lemma has the same sort as 'a in the conjecture.
* Deleting such clauses will lead to problems with locales in other use of local results
where 'a is fixed. Probably we should delete clauses unless the sorts agree.
* Currently we include a class constraint in the clause, exactly as with TVars.
*)
(** make axiom and conjecture clauses. **)
fun get_tvar_strs [] = []
| get_tvar_strs ((TVar (indx,s))::Ts) =
insert (op =) (make_schematic_type_var indx) (get_tvar_strs Ts)
| get_tvar_strs((TFree _)::Ts) = get_tvar_strs Ts
(**** Isabelle arities ****)
exception ARCLAUSE of string;
datatype arLit = TConsLit of class * string * string list
| TVarLit of class * string;
datatype arityClause =
ArityClause of {axiom_name: axiom_name,
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) = (cls, tvar) :: pack_sort(tvar, srt);
(*Arity of type constructor tcon :: (arg1,...,argN)res*)
fun make_axiom_arity_clause dfg (tcons, axiom_name, (cls,args)) =
let val tvars = gen_TVars (length args)
val tvars_srts = ListPair.zip (tvars,args)
in
ArityClause {axiom_name = axiom_name,
conclLit = TConsLit (cls, make_fixed_type_const dfg tcons, tvars),
premLits = map TVarLit (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 dfg _ _ (tcons, []) = []
| arity_clause dfg seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
arity_clause dfg seen n (tcons,ars)
| arity_clause dfg 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 dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::
arity_clause dfg seen (n+1) (tcons,ars)
else
make_axiom_arity_clause dfg (tcons, lookup_type_const dfg tcons ^ "_" ^ class, ar) ::
arity_clause dfg (class::seen) n (tcons,ars)
fun multi_arity_clause dfg [] = []
| multi_arity_clause dfg ((tcons,ars) :: tc_arlists) =
arity_clause dfg [] 1 (tcons, ars) @ multi_arity_clause dfg tc_arlists
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
provided its arguments have the corresponding sorts.*)
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;
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
fun iter_type_class_pairs thy tycons [] = ([], [])
| iter_type_class_pairs thy tycons classes =
let val cpairs = type_class_pairs thy tycons classes
val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs))) \\ classes \\ HOLogic.typeS
val _ = if null newclasses then ()
else Output.debug (fn _ => "New classes: " ^ space_implode ", " newclasses)
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
in (classes' union classes, cpairs' union cpairs) end;
fun make_arity_clauses_dfg dfg thy tycons classes =
let val (classes', cpairs) = iter_type_class_pairs thy tycons classes
in (classes', multi_arity_clause dfg cpairs) end;
val make_arity_clauses = make_arity_clauses_dfg false;
(**** 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_type_sort_preds (T, preds) =
update_many (preds, map pred_of_sort (sorts_on_typs T));
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 (make_type_class o class_of_arityLit) (conclLit::premLits)
fun upd (class,preds) = Symtab.update (class,1) preds
in foldl upd preds classes end;
(*** 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;
(*TFrees are recorded as constants*)
fun add_type_sort_funcs (TVar _, funcs) = funcs
| add_type_sort_funcs (TFree (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;
(*This type can be overlooked because it is built-in...*)
val init_functab = Symtab.update ("tc_itself", 1) Symtab.empty;
(**** String-oriented operations ****)
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);
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_of_typeLit pos (LTVar (s,ty)) = dfg_sign pos (s ^ "(" ^ ty ^ ")")
| dfg_of_typeLit pos (LTFree (s,ty)) = dfg_sign pos (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, Axiom, lits, tylits, vars) =
"clause( %(axiom)\n" ^
dfg_forall vars ("or(" ^ commas (tylits@lits) ^ ")") ^ ",\n" ^
string_of_clausename (cls_id,ax_name) ^ ").\n\n"
| gen_dfg_cls (cls_id, ax_name, Conjecture, lits, _, vars) =
"clause( %(negated_conjecture)\n" ^
dfg_forall vars ("or(" ^ commas lits ^ ")") ^ ",\n" ^
string_of_clausename (cls_id,ax_name) ^ ").\n\n";
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 (c,t,args)) =
dfg_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")
| dfg_of_arLit (TVarLit (c,str)) =
dfg_sign false (make_type_class 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,conclLit,premLits,...}) =
let val TConsLit (_,_,tvars) = conclLit
val lits = map dfg_of_arLit (conclLit :: premLits)
in
"clause( %(axiom)\n" ^
dfg_forall tvars ("or( " ^ commas lits ^ ")") ^ ",\n" ^
string_of_ar axiom_name ^ ").\n\n"
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_typeLit pos (LTVar (s,ty)) = tptp_sign pos (s ^ "(" ^ ty ^ ")")
| tptp_of_typeLit pos (LTFree (s,ty)) = tptp_sign pos (s ^ "(" ^ ty ^ ")");
fun gen_tptp_cls (cls_id,ax_name,Axiom,lits,tylits) =
"cnf(" ^ string_of_clausename (cls_id,ax_name) ^ ",axiom," ^
tptp_pack (tylits@lits) ^ ").\n"
| gen_tptp_cls (cls_id,ax_name,Conjecture,lits,_) =
"cnf(" ^ string_of_clausename (cls_id,ax_name) ^ ",negated_conjecture," ^
tptp_pack lits ^ ").\n";
fun tptp_tfree_clause tfree_lit =
"cnf(" ^ "tfree_tcs," ^ "negated_conjecture" ^ "," ^ tptp_pack[tfree_lit] ^ ").\n";
fun tptp_of_arLit (TConsLit (c,t,args)) =
tptp_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")
| tptp_of_arLit (TVarLit (c,str)) =
tptp_sign false (make_type_class c ^ "(" ^ str ^ ")")
fun tptp_arity_clause (ArityClause{axiom_name,conclLit,premLits,...}) =
"cnf(" ^ string_of_ar axiom_name ^ ",axiom," ^
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"
end;