%% %% %CopyrightBegin% %% %% Copyright Ericsson AB 1996-2012. All Rights Reserved. %% %% The contents of this file are subject to the Erlang Public License, %% Version 1.1, (the "License"); you may not use this file except in %% compliance with the License. You should have received a copy of the %% Erlang Public License along with this software. If not, it can be %% retrieved online at http://www.erlang.org/. %% %% Software distributed under the License is distributed on an "AS IS" %% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See %% the License for the specific language governing rights and limitations %% under the License. %% %% %CopyrightEnd% %% %% Purpose : Expand some source Erlang constructions. This is part of the %% pre-processing phase. %% N.B. Although structs (tagged tuples) are not yet allowed in the %% language there is code included in pattern/2 and expr/3 (commented out) %% that handles them by transforming them to tuples. -module(sys_pre_expand). %% Main entry point. -export([module/2]). -import(ordsets, [from_list/1,union/2]). -import(lists, [member/2,foldl/3,foldr/3]). -include("../include/erl_bits.hrl"). -record(expand, {module=[], %Module name exports=[], %Exports imports=[], %Imports compile=[], %Compile flags attributes=[], %Attributes callbacks=[], %Callbacks defined, %Defined functions (gb_set) vcount=0, %Variable counter func=[], %Current function arity=[], %Arity for current function fcount=0, %Local fun count bitdefault, bittypes }). %% module(Forms, CompileOptions) %% {ModuleName,Exports,TransformedForms,CompileOptions'} %% Expand the forms in one module. N.B.: the lists of predefined %% exports and imports are really ordsets! %% CompileOptions is augmented with options from -compile attributes. module(Fs0, Opts0) -> %% Expand records. Normalise guard tests. Fs = erl_expand_records:module(Fs0, Opts0), Opts = compiler_options(Fs) ++ Opts0, %% Set pre-defined exported functions. PreExp = [{module_info,0},{module_info,1}], %% Build initial expand record. St0 = #expand{exports=PreExp, compile=Opts, defined=PreExp, bitdefault = erl_bits:system_bitdefault(), bittypes = erl_bits:system_bittypes() }, %% Expand the functions. {Tfs,St1} = forms(Fs, define_functions(Fs, St0)), %% Get the correct list of exported functions. Exports = case member(export_all, St1#expand.compile) of true -> gb_sets:to_list(St1#expand.defined); false -> St1#expand.exports end, %% Generate all functions from stored info. {Ats,St3} = module_attrs(St1#expand{exports = Exports}), {Mfs,St4} = module_predef_funcs(St3), {St4#expand.module, St4#expand.exports, Ats ++ Tfs ++ Mfs, St4#expand.compile}. compiler_options(Forms) -> lists:flatten([C || {attribute,_,compile,C} <- Forms]). %% define_function(Form, State) -> State. %% Add function to defined if form is a function. define_functions(Forms, #expand{defined=Predef}=St) -> Fs = foldl(fun({function,_,N,A,_Cs}, Acc) -> [{N,A}|Acc]; (_, Acc) -> Acc end, Predef, Forms), St#expand{defined=gb_sets:from_list(Fs)}. module_attrs(#expand{attributes=Attributes}=St) -> Attrs = [{attribute,Line,Name,Val} || {Name,Line,Val} <- Attributes], Callbacks = [Callback || {_,_,callback,_}=Callback <- Attrs], {Attrs,St#expand{callbacks=Callbacks}}. module_predef_funcs(St) -> {Mpf1,St1}=module_predef_func_beh_info(St), {Mpf2,St2}=module_predef_funcs_mod_info(St1), {Mpf1++Mpf2,St2}. module_predef_func_beh_info(#expand{callbacks=[]}=St) -> {[], St}; module_predef_func_beh_info(#expand{callbacks=Callbacks,defined=Defined, exports=Exports}=St) -> PreDef=[{behaviour_info,1}], PreExp=PreDef, {[gen_beh_info(Callbacks)], St#expand{defined=gb_sets:union(gb_sets:from_list(PreDef), Defined), exports=union(from_list(PreExp), Exports)}}. gen_beh_info(Callbacks) -> List = make_list(Callbacks), {function,0,behaviour_info,1, [{clause,0,[{atom,0,callbacks}],[], [List]}]}. make_list([]) -> {nil,0}; make_list([{_,_,_,[{{Name,Arity},_}]}|Rest]) -> {cons,0, {tuple,0, [{atom,0,Name}, {integer,0,Arity}]}, make_list(Rest)}. module_predef_funcs_mod_info(St) -> PreDef = [{module_info,0},{module_info,1}], PreExp = PreDef, {[{function,0,module_info,0, [{clause,0,[],[], [{call,0,{remote,0,{atom,0,erlang},{atom,0,get_module_info}}, [{atom,0,St#expand.module}]}]}]}, {function,0,module_info,1, [{clause,0,[{var,0,'X'}],[], [{call,0,{remote,0,{atom,0,erlang},{atom,0,get_module_info}}, [{atom,0,St#expand.module},{var,0,'X'}]}]}]}], St#expand{defined=gb_sets:union(gb_sets:from_list(PreDef), St#expand.defined), exports=union(from_list(PreExp), St#expand.exports)}}. %% forms(Forms, State) -> %% {TransformedForms,State'} %% Process the forms. Attributes are lost and just affect the state. %% Ignore uninteresting forms like eof and type. forms([{attribute,_,file,_File}=F|Fs0], St0) -> {Fs,St1} = forms(Fs0, St0), {[F|Fs],St1}; forms([{attribute,Line,Name,Val}|Fs0], St0) -> St1 = attribute(Name, Val, Line, St0), forms(Fs0, St1); forms([{function,L,N,A,Cs}|Fs0], St0) -> {Ff,St1} = function(L, N, A, Cs, St0), {Fs,St2} = forms(Fs0, St1), {[Ff|Fs],St2}; forms([_|Fs], St) -> forms(Fs, St); forms([], St) -> {[],St}. %% attribute(Attribute, Value, Line, State) -> State'. %% Process an attribute, this just affects the state. attribute(module, Module, _L, St) -> true = is_atom(Module), St#expand{module=Module}; attribute(export, Es, _L, St) -> St#expand{exports=union(from_list(Es), St#expand.exports)}; attribute(import, Is, _L, St) -> import(Is, St); attribute(compile, _C, _L, St) -> St; attribute(Name, Val, Line, St) when is_list(Val) -> St#expand{attributes=St#expand.attributes ++ [{Name,Line,Val}]}; attribute(Name, Val, Line, St) -> St#expand{attributes=St#expand.attributes ++ [{Name,Line,[Val]}]}. function(L, N, A, Cs0, St0) -> {Cs,St} = clauses(Cs0, St0#expand{func=N,arity=A,fcount=0}), {{function,L,N,A,Cs},St}. %% clauses([Clause], State) -> %% {[TransformedClause],State}. %% Expand function clauses. clauses([{clause,Line,H0,G0,B0}|Cs0], St0) -> {H,St1} = head(H0, St0), {G,St2} = guard(G0, St1), {B,St3} = exprs(B0, St2), {Cs,St4} = clauses(Cs0, St3), {[{clause,Line,H,G,B}|Cs],St4}; clauses([], St) -> {[],St}. %% head(HeadPatterns, State) -> %% {TransformedPatterns,Variables,UsedVariables,State'} head(As, St) -> pattern_list(As, St). %% pattern(Pattern, State) -> %% {TransformedPattern,State'} %% pattern({var,_,'_'}=Var, St) -> %Ignore anonymous variable. {Var,St}; pattern({var,_,_}=Var, St) -> {Var,St}; pattern({char,_,_}=Char, St) -> {Char,St}; pattern({integer,_,_}=Int, St) -> {Int,St}; pattern({float,_,_}=Float, St) -> {Float,St}; pattern({atom,_,_}=Atom, St) -> {Atom,St}; pattern({string,_,_}=String, St) -> {String,St}; pattern({nil,_}=Nil, St) -> {Nil,St}; pattern({cons,Line,H,T}, St0) -> {TH,St1} = pattern(H, St0), {TT,St2} = pattern(T, St1), {{cons,Line,TH,TT},St2}; pattern({tuple,Line,Ps}, St0) -> {TPs,St1} = pattern_list(Ps, St0), {{tuple,Line,TPs},St1}; pattern({map,Line,Ps}, St0) -> {TPs,St1} = pattern_list(Ps, St0), {{map,Line,TPs},St1}; pattern({map_field,Line,K0,V0}, St0) -> {K,St1} = pattern(K0, St0), {V,St2} = pattern(V0, St1), {{map_field,Line,K,V},St2}; %%pattern({struct,Line,Tag,Ps}, St0) -> %% {TPs,TPsvs,St1} = pattern_list(Ps, St0), %% {{tuple,Line,[{atom,Line,Tag}|TPs]},TPsvs,St1}; pattern({bin,Line,Es0}, St0) -> {Es1,St1} = pattern_bin(Es0, St0), {{bin,Line,Es1},St1}; pattern({op,_,'++',{nil,_},R}, St) -> pattern(R, St); pattern({op,_,'++',{cons,Li,H,T},R}, St) -> pattern({cons,Li,H,{op,Li,'++',T,R}}, St); pattern({op,_,'++',{string,Li,L},R}, St) -> pattern(string_to_conses(Li, L, R), St); pattern({match,Line,Pat1, Pat2}, St0) -> {TH,St1} = pattern(Pat2, St0), {TT,St2} = pattern(Pat1, St1), {{match,Line,TT,TH},St2}; %% Compile-time pattern expressions, including unary operators. pattern({op,_Line,_Op,_A}=Op, St) -> {erl_eval:partial_eval(Op),St}; pattern({op,_Line,_Op,_L,_R}=Op, St) -> {erl_eval:partial_eval(Op),St}. pattern_list([P0|Ps0], St0) -> {P,St1} = pattern(P0, St0), {Ps,St2} = pattern_list(Ps0, St1), {[P|Ps],St2}; pattern_list([], St) -> {[],St}. %% guard(Guard, State) -> %% {TransformedGuard,State'} %% Transform a list of guard tests. We KNOW that this has been checked %% and what the guards test are. Use expr for transforming the guard %% expressions. guard([G0|Gs0], St0) -> {G,St1} = guard_tests(G0, St0), {Gs,St2} = guard(Gs0, St1), {[G|Gs],St2}; guard([], St) -> {[],St}. guard_tests([Gt0|Gts0], St0) -> {Gt1,St1} = guard_test(Gt0, St0), {Gts1,St2} = guard_tests(Gts0, St1), {[Gt1|Gts1],St2}; guard_tests([], St) -> {[],St}. guard_test(Test, St) -> expr(Test, St). %% exprs(Expressions, State) -> %% {TransformedExprs,State'} exprs([E0|Es0], St0) -> {E,St1} = expr(E0, St0), {Es,St2} = exprs(Es0, St1), {[E|Es],St2}; exprs([], St) -> {[],St}. %% expr(Expression, State) -> %% {TransformedExpression,State'} expr({var,_,_}=Var, St) -> {Var,St}; expr({char,_,_}=Char, St) -> {Char,St}; expr({integer,_,_}=Int, St) -> {Int,St}; expr({float,_,_}=Float, St) -> {Float,St}; expr({atom,_,_}=Atom, St) -> {Atom,St}; expr({string,_,_}=String, St) -> {String,St}; expr({nil,_}=Nil, St) -> {Nil,St}; expr({cons,Line,H0,T0}, St0) -> {H,St1} = expr(H0, St0), {T,St2} = expr(T0, St1), {{cons,Line,H,T},St2}; expr({lc,Line,E0,Qs0}, St0) -> {Qs1,St1} = lc_tq(Line, Qs0, St0), {E1,St2} = expr(E0, St1), {{lc,Line,E1,Qs1},St2}; expr({bc,Line,E0,Qs0}, St0) -> {Qs1,St1} = lc_tq(Line, Qs0, St0), {E1,St2} = expr(E0, St1), {{bc,Line,E1,Qs1},St2}; expr({tuple,Line,Es0}, St0) -> {Es1,St1} = expr_list(Es0, St0), {{tuple,Line,Es1},St1}; %%expr({struct,Line,Tag,Es0}, Vs, St0) -> %% {Es1,Esvs,Esus,St1} = expr_list(Es0, Vs, St0), %% {{tuple,Line,[{atom,Line,Tag}|Es1]},Esvs,Esus,St1}; expr({map,Line,Es0}, St0) -> {Es1,St1} = expr_list(Es0, St0), {{map,Line,Es1},St1}; expr({map,Line,Var,Es0}, St0) -> {Es1,St1} = expr_list(Es0, St0), {{map,Line,Var,Es1},St1}; expr({map_field,Line,K0,V0}, St0) -> {K,St1} = expr(K0, St0), {V,St2} = expr(V0, St1), {{map_field,Line,K,V},St2}; expr({bin,Line,Es0}, St0) -> {Es1,St1} = expr_bin(Es0, St0), {{bin,Line,Es1},St1}; expr({block,Line,Es0}, St0) -> {Es,St1} = exprs(Es0, St0), {{block,Line,Es},St1}; expr({'if',Line,Cs0}, St0) -> {Cs,St1} = icr_clauses(Cs0, St0), {{'if',Line,Cs},St1}; expr({'case',Line,E0,Cs0}, St0) -> {E,St1} = expr(E0, St0), {Cs,St2} = icr_clauses(Cs0, St1), {{'case',Line,E,Cs},St2}; expr({'receive',Line,Cs0}, St0) -> {Cs,St1} = icr_clauses(Cs0, St0), {{'receive',Line,Cs},St1}; expr({'receive',Line,Cs0,To0,ToEs0}, St0) -> {To,St1} = expr(To0, St0), {ToEs,St2} = exprs(ToEs0, St1), {Cs,St3} = icr_clauses(Cs0, St2), {{'receive',Line,Cs,To,ToEs},St3}; expr({'fun',Line,Body}, St) -> fun_tq(Line, Body, St); expr({named_fun,Line,Name,Cs}, St) -> fun_tq(Line, Cs, St, Name); expr({call,Line,{atom,La,N}=Atom,As0}, St0) -> {As,St1} = expr_list(As0, St0), Ar = length(As), case defined(N,Ar,St1) of true -> {{call,Line,Atom,As},St1}; _ -> case imported(N, Ar, St1) of {yes,Mod} -> {{call,Line,{remote,La,{atom,La,Mod},Atom},As},St1}; no -> case erl_internal:bif(N, Ar) of true -> {{call,Line,{remote,La,{atom,La,erlang},Atom},As},St1}; false -> %% This should have been handled by erl_lint {{call,Line,Atom,As},St1} end end end; expr({call,Line,{remote,Lr,M0,F},As0}, St0) -> {[M1,F1|As1],St1} = expr_list([M0,F|As0], St0), {{call,Line,{remote,Lr,M1,F1},As1},St1}; expr({call,Line,F,As0}, St0) -> {[Fun1|As1],St1} = expr_list([F|As0], St0), {{call,Line,Fun1,As1},St1}; expr({'try',Line,Es0,Scs0,Ccs0,As0}, St0) -> {Es1,St1} = exprs(Es0, St0), {Scs1,St2} = icr_clauses(Scs0, St1), {Ccs1,St3} = icr_clauses(Ccs0, St2), {As1,St4} = exprs(As0, St3), {{'try',Line,Es1,Scs1,Ccs1,As1},St4}; expr({'catch',Line,E0}, St0) -> %% Catch exports no new variables. {E,St1} = expr(E0, St0), {{'catch',Line,E},St1}; expr({match,Line,P0,E0}, St0) -> {E,St1} = expr(E0, St0), {P,St2} = pattern(P0, St1), {{match,Line,P,E},St2}; expr({op,Line,Op,A0}, St0) -> {A,St1} = expr(A0, St0), {{op,Line,Op,A},St1}; expr({op,Line,Op,L0,R0}, St0) -> {L,St1} = expr(L0, St0), {R,St2} = expr(R0, St1), {{op,Line,Op,L,R},St2}. expr_list([E0|Es0], St0) -> {E,St1} = expr(E0, St0), {Es,St2} = expr_list(Es0, St1), {[E|Es],St2}; expr_list([], St) -> {[],St}. %% icr_clauses([Clause], State) -> {[TransformedClause],State'} %% Be very careful here to return the variables that are really used %% and really new. icr_clauses([], St) -> {[],St}; icr_clauses(Clauses, St) -> icr_clauses2(Clauses, St). icr_clauses2([{clause,Line,H0,G0,B0}|Cs0], St0) -> {H,St1} = head(H0, St0), {G,St2} = guard(G0, St1), {B,St3} = exprs(B0, St2), {Cs,St4} = icr_clauses2(Cs0, St3), {[{clause,Line,H,G,B}|Cs],St4}; icr_clauses2([], St) -> {[],St}. %% lc_tq(Line, Qualifiers, State) -> %% {[TransQual],State'} lc_tq(Line, [{generate,Lg,P0,G0} | Qs0], St0) -> {G1,St1} = expr(G0, St0), {P1,St2} = pattern(P0, St1), {Qs1,St3} = lc_tq(Line, Qs0, St2), {[{generate,Lg,P1,G1} | Qs1],St3}; lc_tq(Line, [{b_generate,Lg,P0,G0}|Qs0], St0) -> {G1,St1} = expr(G0, St0), {P1,St2} = pattern(P0, St1), {Qs1,St3} = lc_tq(Line, Qs0, St2), {[{b_generate,Lg,P1,G1}|Qs1],St3}; lc_tq(Line, [F0 | Qs0], St0) -> case erl_lint:is_guard_test(F0) of true -> {F1,St1} = guard_test(F0, St0), {Qs1,St2} = lc_tq(Line, Qs0, St1), {[F1|Qs1],St2}; false -> {F1,St1} = expr(F0, St0), {Qs1,St2} = lc_tq(Line, Qs0, St1), {[F1 | Qs1],St2} end; lc_tq(_Line, [], St0) -> {[],St0}. %% fun_tq(Line, Body, State) -> %% {Fun,State'} %% Transform an "explicit" fun {'fun', Line, {clauses, Cs}} into an %% extended form {'fun', Line, {clauses, Cs}, Info}, unless it is the %% name of a BIF (erl_lint has checked that it is not an import). %% "Implicit" funs {'fun', Line, {function, F, A}} are not changed. fun_tq(Lf, {function,F,A}=Function, St0) -> case erl_internal:bif(F, A) of true -> {As,St1} = new_vars(A, Lf, St0), Cs = [{clause,Lf,As,[],[{call,Lf,{atom,Lf,F},As}]}], fun_tq(Lf, {clauses,Cs}, St1); false -> {Fname,St1} = new_fun_name(St0), Index = Uniq = 0, {{'fun',Lf,Function,{Index,Uniq,Fname}},St1} end; fun_tq(L, {function,M,F,A}, St) when is_atom(M), is_atom(F), is_integer(A) -> %% This is the old format for external funs, generated by a pre-R15 %% compiler. That means that a tool, such as the debugger or xref, %% directly invoked this module with the abstract code from a %% pre-R15 BEAM file. Be helpful, and translate it to the new format. fun_tq(L, {function,{atom,L,M},{atom,L,F},{integer,L,A}}, St); fun_tq(Lf, {function,_,_,_}=ExtFun, St) -> {{'fun',Lf,ExtFun},St}; fun_tq(Lf, {clauses,Cs0}, St0) -> {Cs1,St1} = fun_clauses(Cs0, St0), {Fname,St2} = new_fun_name(St1), %% Set dummy values for Index and Uniq -- the real values will %% be assigned by beam_asm. Index = Uniq = 0, {{'fun',Lf,{clauses,Cs1},{Index,Uniq,Fname}},St2}. fun_tq(Line, Cs0, St0, Name) -> {Cs1,St1} = fun_clauses(Cs0, St0), {Fname,St2} = new_fun_name(St1, Name), {{named_fun,Line,Name,Cs1,{0,0,Fname}},St2}. fun_clauses([{clause,L,H0,G0,B0}|Cs0], St0) -> {H,St1} = head(H0, St0), {G,St2} = guard(G0, St1), {B,St3} = exprs(B0, St2), {Cs,St4} = fun_clauses(Cs0, St3), {[{clause,L,H,G,B}|Cs],St4}; fun_clauses([], St) -> {[],St}. %% new_fun_name(State) -> {FunName,State}. new_fun_name(St) -> new_fun_name(St, 'fun'). new_fun_name(#expand{func=F,arity=A,fcount=I}=St, FName) -> Name = "-" ++ atom_to_list(F) ++ "/" ++ integer_to_list(A) ++ "-" ++ atom_to_list(FName) ++ "-" ++ integer_to_list(I) ++ "-", {list_to_atom(Name),St#expand{fcount=I+1}}. %% pattern_bin([Element], State) -> {[Element],[Variable],[UsedVar],State}. pattern_bin(Es0, St) -> Es1 = bin_expand_strings(Es0), foldr(fun (E, Acc) -> pattern_element(E, Acc) end, {[],St}, Es1). pattern_element({bin_element,Line,Expr0,Size0,Type0}, {Es,St0}) -> {Expr1,St1} = pattern(Expr0, St0), {Size1,St2} = pat_bit_size(Size0, St1), {Size,Type} = make_bit_type(Line, Size1, Type0), Expr = coerce_to_float(Expr1, Type0), {[{bin_element,Line,Expr,Size,Type}|Es],St2}. pat_bit_size(default, St) -> {default,St}; pat_bit_size({atom,_La,all}=All, St) -> {All,St}; pat_bit_size({var,_Lv,_V}=Var, St) -> {Var,St}; pat_bit_size(Size, St) -> Line = element(2, Size), {value,Sz,_} = erl_eval:expr(Size, erl_eval:new_bindings()), {{integer,Line,Sz},St}. make_bit_type(Line, default, Type0) -> case erl_bits:set_bit_type(default, Type0) of {ok,all,Bt} -> {{atom,Line,all},erl_bits:as_list(Bt)}; {ok,undefined,Bt} -> {{atom,Line,undefined},erl_bits:as_list(Bt)}; {ok,Size,Bt} -> {{integer,Line,Size},erl_bits:as_list(Bt)} end; make_bit_type(_Line, Size, Type0) -> %Integer or 'all' {ok,Size,Bt} = erl_bits:set_bit_type(Size, Type0), {Size,erl_bits:as_list(Bt)}. coerce_to_float({integer,L,I}=E, [float|_]) -> try {float,L,float(I)} catch error:badarg -> E; error:badarith -> E end; coerce_to_float(E, _) -> E. %% expr_bin([Element], State) -> {[Element],State}. expr_bin(Es0, St) -> Es1 = bin_expand_strings(Es0), foldr(fun (E, Acc) -> bin_element(E, Acc) end, {[],St}, Es1). bin_element({bin_element,Line,Expr,Size,Type}, {Es,St0}) -> {Expr1,St1} = expr(Expr, St0), {Size1,St2} = if Size == default -> {default,St1}; true -> expr(Size, St1) end, {Size2,Type1} = make_bit_type(Line, Size1, Type), {[{bin_element,Line,Expr1,Size2,Type1}|Es],St2}. bin_expand_strings(Es) -> foldr(fun ({bin_element,Line,{string,_,S},Sz,Ts}, Es1) -> foldr(fun (C, Es2) -> [{bin_element,Line,{char,Line,C},Sz,Ts}|Es2] end, Es1, S); (E, Es1) -> [E|Es1] end, [], Es). %% new_var_name(State) -> {VarName,State}. new_var_name(St) -> C = St#expand.vcount, {list_to_atom("pre" ++ integer_to_list(C)),St#expand{vcount=C+1}}. %% new_var(Line, State) -> {Var,State}. new_var(L, St0) -> {New,St1} = new_var_name(St0), {{var,L,New},St1}. %% new_vars(Count, Line, State) -> {[Var],State}. %% Make Count new variables. new_vars(N, L, St) -> new_vars(N, L, St, []). new_vars(N, L, St0, Vs) when N > 0 -> {V,St1} = new_var(L, St0), new_vars(N-1, L, St1, [V|Vs]); new_vars(0, _L, St, Vs) -> {Vs,St}. string_to_conses(Line, Cs, Tail) -> foldr(fun (C, T) -> {cons,Line,{char,Line,C},T} end, Tail, Cs). %% import(Line, Imports, State) -> %% State' %% imported(Name, Arity, State) -> %% {yes,Module} | no %% Handle import declarations and test for imported functions. No need to %% check when building imports as code is correct. import({Mod,Fs}, St) -> true = is_atom(Mod), Mfs = from_list(Fs), St#expand{imports=add_imports(Mod, Mfs, St#expand.imports)}. add_imports(Mod, [F|Fs], Is) -> add_imports(Mod, Fs, orddict:store(F, Mod, Is)); add_imports(_, [], Is) -> Is. imported(F, A, St) -> case orddict:find({F,A}, St#expand.imports) of {ok,Mod} -> {yes,Mod}; error -> no end. defined(F, A, St) -> gb_sets:is_element({F,A}, St#expand.defined).