(* Author: Jia Meng, Cambridge University Computer Laboratory ID: $Id: res_clause.ML,v 1.105 2007/10/30 14:28:53 paulson Exp $ 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 dfg_format: bool ref val make_fixed_const : string -> string val make_fixed_type_const : 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: 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 :-(( *) val dfg_format = ref false; (*32-bit hash,so we expect no collisions unless there are around 65536 long identifiers...*) fun controlled_length s = if size s > 60 andalso !dfg_format then Word.toString (Polyhash.hashw_string(s,0w0)) else s; fun lookup_const c = case Symtab.lookup const_trans_table c of SOME c' => c' | NONE => controlled_length (ascii_of c); fun lookup_type_const c = case Symtab.lookup type_const_trans_table c of SOME c' => c' | NONE => controlled_length (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. *****) 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 (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 T = (atomic_type T, [T]) and types_of Ts = let val (folTyps,ts) = ListPair.unzip (map type_of 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); (** 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 (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 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 _ _ (tcons, []) = [] | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*) arity_clause seen n (tcons,ars) | arity_clause seen n (tcons, (ar as (class,_)) :: ars) = if class mem_string seen then (*multiple arities for the same tycon, class pair*) make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) :: arity_clause seen (n+1) (tcons,ars) else make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class, ar) :: arity_clause (class::seen) n (tcons,ars) fun multi_arity_clause [] = [] | multi_arity_clause ((tcons,ars) :: tc_arlists) = arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy 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 thy tycons classes = let val (classes', cpairs) = iter_type_class_pairs thy tycons classes in (classes', multi_arity_clause cpairs) end; (**** 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;