%%
%% %CopyrightBegin%
%%
  Copyright Ericsson AB 2004 - 2017 . All Rights Reserved .
%%
  Licensed under the Apache License , Version 2.0 ( the " License " ) ;
%% you may not use this file except in compliance with the License.
%% You may obtain a copy of the License at
%%
%%     -2.0
%%
%% Unless required by applicable law or agreed to in writing, software
  distributed under the License is distributed on an " AS IS " BASIS ,
%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
%% See the License for the specific language governing permissions and
%% limitations under the License.
%%
%% %CopyrightEnd%
%%
-module(qlc_pt).

%%% Purpose: Implements the qlc Parse Transform.

-export([parse_transform/2, transform_from_evaluator/2, 
         transform_expression/2]).

-include_lib("stdlib/include/ms_transform.hrl").

-define(APIMOD, qlc).
-define(Q, q).

%% Also in qlc.erl.
-define(QLC_Q(L1, L2, L3, L4, LC, Os), 
        {call,L1,{remote,L2,{atom,L3,?APIMOD},{atom,L4,?Q}},[LC | Os]}).
-define(IMP_Q(L1, L2, LC, Os), {call,L,{atom,L2,?Q},[LC | Os]}).

%% Also in qlc.erl.
  qlc : q/1,2 , a query handle
        {lc,
         opt        % #qlc_opt
        }).

-record(state, {imp,
		overridden,
                maxargs,
                records,
                xwarnings = [],
                intro_vars,
                node_info}).

%-define(debug, true).

-ifdef(debug).
-define(DEBUG(S, A), io:format(S, A)).
-else.
-define(DEBUG(S, A), ok).
-endif.

  erl_eval can not interpret funs with more than 20 arguments :
-define(EVAL_MAX_NUM_OF_ARGS, 20).
  Currently the compiler can handle at most 255 arguments .
-define(COMPILE_MAX_NUM_OF_ARGS, 250).

-define(QLC_FILE, qlc_current_file).

%%%
%%% Exported functions
%%%

-spec(parse_transform(Forms, Options) -> Forms2 when
      Forms :: [erl_parse:abstract_form() | erl_parse:form_info()],
      Forms2 :: [erl_parse:abstract_form() | erl_parse:form_info()],
      Options :: [Option],
      Option :: type_checker | compile:option()).

parse_transform(Forms0, Options) ->
    ?DEBUG("qlc Parse Transform~n", []),
    Imported = is_qlc_q_imported(Forms0),
    {Forms, FormsNoShadows, State} = initiate(Forms0, Imported),
    NodeInfo = State#state.node_info,
    try
        case called_from_type_checker(Options) of
            true ->
                %% The returned value should conform to the types, but
                %% need not evaluate to anything meaningful.
                L = anno0(),
                {tuple,_,Fs0} = abstr(#qlc_lc{}, L),
                F = fun(_Id, LC, A) ->
                            Init = simple(L, 'V', LC, L),
                            {{tuple,L,set_field(#qlc_lc.lc, Fs0, Init)}, A}
                    end,
                {Forms1,ok} = qlc_mapfold(F, ok, Forms, State),
                Forms1;
            false ->
                case
                    compile_messages(Forms, FormsNoShadows, Options, State)
                of
                    {[],Warnings} ->
                        ?DEBUG("node info1 ~p~n",
                               [lists:sort(ets:tab2list(NodeInfo))]),
                        {NewForms, State1} =
                            transform(FormsNoShadows, State),
                        ExtraWs = State1#state.xwarnings,
                        {[],WForms} = no_duplicates(NewForms, [], Warnings,
                                                    ExtraWs, Options),
                        (restore_locations(WForms, State) ++
                         restore_anno(NewForms, NodeInfo));
                    {Errors,Warnings} ->
                        ?DEBUG("node info2 ~p~n",
                               [lists:sort(ets:tab2list(NodeInfo))]),
                        {EForms,WForms} = no_duplicates(FormsNoShadows, Errors,
                                                        Warnings, [],
                                                        Options),
                        restore_locations(EForms ++ WForms, State) ++ Forms0
                end
        end
    after
        true = ets:delete(NodeInfo)
    end.

-spec(transform_from_evaluator(LC, Bs) -> Return when
      LC :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct(),
      Return :: {ok, erl_parse:abstract_expr()}
              | {not_ok, {error, module(), Reason :: term()}}).

transform_from_evaluator(LC, Bindings) ->
    ?DEBUG("qlc Parse Transform (Evaluator Version)~n", []),
    transform_expression(LC, Bindings, false).

-spec(transform_expression(LC, Bs) -> Return when
      LC :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct(),
      Return :: {ok, erl_parse:abstract_expr()}
              | {not_ok, [{error, Reason :: term()}]}).

transform_expression(LC, Bindings) ->
    transform_expression(LC, Bindings, true).

%%%
%%% Local functions
%%%

called_from_type_checker(Options) ->
    lists:member(type_checker, Options).

transform_expression(LC, Bs0, WithLintErrors) ->
    L = anno1(),
    As = [{var,L,V} || {V,_Val} <- Bs0],
    Ar = length(As),
    F = {function,L,bar,Ar,[{clause,L,As,[],[?QLC_Q(L, L, L, L, LC, [])]}]},
    Forms0 = [{attribute,L,file,{"foo",L}},
              {attribute,L,module,foo}, F],
    {Forms, FormsNoShadows, State} = initiate(Forms0, false),
    NodeInfo = State#state.node_info,
    Options = [],
    try compile_messages(Forms, FormsNoShadows, Options, State) of
        {Errors0,_Warnings} ->
            case restore_locations(Errors0, State) of
                [] ->
                    {NewForms,_State1} = transform(FormsNoShadows, State),
                    NewForms1 = restore_anno(NewForms, NodeInfo),
                    {function,L,bar,Ar,[{clause,L,As,[],[NF]}]} =
                        lists:last(NewForms1),
                    {ok,NF};
                Errors when WithLintErrors ->
                    {not_ok,mforms(error, Errors)};
                Errors ->
                    [{error,Reason} | _] = mforms(error, Errors),
                    {not_ok, {error, ?APIMOD, Reason}}
            end
    after
        true = ets:delete(NodeInfo)
    end.

-ifdef(DEBUG).
-define(ILIM, 0).
-else.
-define(ILIM, 255).
-endif.

initiate(Forms0, Imported) ->
    NodeInfo = ets:new(?APIMOD, []),
    true = ets:insert(NodeInfo, {var_n, ?ILIM}),
    exclude_integers_from_unique_line_numbers(Forms0, NodeInfo),
    ?DEBUG("node info0 ~p~n",
           [lists:sort(ets:tab2list(NodeInfo))]),
    IsOverridden = set_up_overridden(Forms0),
    State0 = #state{imp = Imported,
		    overridden = IsOverridden,
                    maxargs = ?EVAL_MAX_NUM_OF_ARGS,
                    records = record_attributes(Forms0),
                    node_info = NodeInfo},
    Forms = save_anno(Forms0, NodeInfo),
    FormsNoShadows = no_shadows(Forms, State0),
    IntroVars = intro_variables(FormsNoShadows, State0),
    State = State0#state{intro_vars = IntroVars},
    {Forms, FormsNoShadows, State}.

%% Make sure restore_locations() does not confuse integers with (the
%% unique) line numbers.
exclude_integers_from_unique_line_numbers(Forms, NodeInfo) ->
    Integers = find_integers(Forms),
    lists:foreach(fun(I) -> ets:insert(NodeInfo, {I}) end, Integers).

find_integers(Forms) ->
    F = fun(A) ->
                Fs1 = map_anno(fun(_) -> A end, Forms),
                ordsets:from_list(integers(Fs1, []))
        end,
    ordsets:to_list(ordsets:intersection(F(anno0()), F(anno1()))).

integers([E | Es], L) ->
    integers(Es, integers(E, L));
integers(T, L) when is_tuple(T) ->
    integers(tuple_to_list(T), L);
integers(I, L) when is_integer(I), I > ?ILIM ->
    [I | L];
integers(_, L) ->
    L.

-define(I(I), {integer, L, I}).
-define(A(A), {atom, L, A}).
-define(V(V), {var, L, V}).
-define(ABST_NO_MORE, {nil, L}).
-define(ABST_MORE(Obj, Cont), {cons, L, Obj, Cont}).

  Qualifier identifier .
  The first one encountered in a QLC has no=1 .
-record(qid, {lcid,no}).

mforms(Tag, L) ->
    lists:sort([{Tag,M} || {_File,Ms} <- L, M <- Ms]).

%% Avoid duplicated lint warnings and lint errors. Care has been taken
%% not to introduce unused variables in the transformed code.
%%
no_duplicates(Forms, Errors, Warnings0, ExtraWarnings0, Options) ->
    %% Some mistakes such as "{X} =:= {}" are found by strong
  validation as well as by qlc . Prefer the warnings from  :
   The Compiler and  do not agree on the location of errors .
   For now ,  's messages about failing patterns and filters
    %%  are ignored.
    ExtraWarnings = [W || W={_File,[{_,qlc,Tag}]} <-
                              ExtraWarnings0,
                    not lists:member(Tag, [nomatch_pattern,nomatch_filter])],
    Warnings1 = mforms(Warnings0) --
        ([{File,[{L,v3_core,nomatch}]} ||
             {File,[{L,qlc,M}]} <- mforms(ExtraWarnings),
             lists:member(M, [nomatch_pattern,nomatch_filter])]
         ++ 
         [{File,[{L,sys_core_fold,nomatch_guard}]} ||
             {File,[{L,qlc,M}]} <- mforms(ExtraWarnings),
             M =:= nomatch_filter]),
    Warnings = Warnings1 ++ ExtraWarnings,
    {Es1,Ws1} = compile_forms(Forms, Options),
    Es = mforms(Errors) -- mforms(Es1),
    Ws = mforms(Warnings) -- mforms(Ws1),
    {mforms2(error, Es),mforms2(warning, Ws)}.

mforms(L) ->
    lists:sort([{File,[M]} || {File,Ms} <- L, M <- Ms]).

mforms2(Tag, L) ->
    Line = anno0(),
    ML = lists:flatmap(fun({File,Ms}) ->
                               [[{attribute,Line,file,{File,0}}, {Tag,M}] ||
                                   M <- Ms]
                       end, lists:sort(L)),
    lists:flatten(lists:sort(ML)).

restore_locations([T | Ts], State) ->
    [restore_locations(T, State) | restore_locations(Ts, State)];
restore_locations(T, State) when is_tuple(T) ->
    list_to_tuple(restore_locations(tuple_to_list(T), State));
restore_locations(I, State) when I > ?ILIM ->
    restore_loc(I, State);
restore_locations(T, _State) ->
    T.

is_qlc_q_imported(Forms) ->
    [[] || {attribute,_,import,{?APIMOD,FAs}} <- Forms, {?Q,1} <- FAs] =/= [].

record_attributes(Forms) ->
    [A || A = {attribute, _, record, _D} <- Forms].

  Get the compile errors and warnings for the  as well as messages
%% for introduced variables used in list expressions and messages for
%% badargs. Since the QLCs will be replaced by some terms, the
%% compiler cannot find the errors and warnings after the parse
%% transformation.
%%
compile_messages(Forms, FormsNoShadows, Options, State) ->
    %% The qlc module cannot handle binary generators.
    BGenF = fun(_QId,{b_generate,Line,_P,_LE}=BGen, GA, A) ->
                    M = {loc(Line),?APIMOD,binary_generator},
                    {BGen,[{get(?QLC_FILE),[M]}|GA],A};
               (_QId, Q, GA, A) ->
                    {Q,GA,A}
            end,
    {_,BGens} = qual_fold(BGenF, [], [], Forms, State),
    GenForm = used_genvar_check(FormsNoShadows, State),
    ?DEBUG("GenForm = ~ts~n", [catch erl_pp:form(GenForm)]),
    {GEs,_} = compile_forms([GenForm], Options),
    UsedGenVarMsgs = used_genvar_messages(GEs, State),
    NodeInfo = State#state.node_info,
    WarnFun = fun(_Id, LC, A) -> {lc_nodes(LC, NodeInfo), A} end,
    {WForms,ok} = qlc_mapfold(WarnFun, ok, Forms, State),
    {Es,Ws} = compile_forms(WForms, Options),
    LcEs = lc_messages(Es, NodeInfo),
    LcWs = lc_messages(Ws, NodeInfo),
    Errors = badarg(Forms, State) ++ UsedGenVarMsgs++LcEs++BGens,
    Warnings = LcWs,
    {Errors,Warnings}.

badarg(Forms, State) ->
    F = fun(_Id, {lc,_L,_E,_Qs}=LC, Es) -> 
                {LC,Es};
           (Id, A, Es) -> 
                E = {get_lcid_line(Id),?APIMOD,not_a_query_list_comprehension},
                {A,[{get(?QLC_FILE), [E]} | Es]}
        end,
    {_,E0} = qlc_mapfold(F, [], Forms, State),
    E0.

lc_nodes(E, NodeInfo) ->
    map_anno(fun(Anno) ->
                     N = erl_anno:line(Anno),
                     [{N, Data}] = ets:lookup(NodeInfo, N),
                     NData = Data#{inside_lc => true},
                     true = ets:insert(NodeInfo, {N, NData}),
                     Anno
             end, E).

used_genvar_messages(MsL, S) ->
    [{File,[{Loc,?APIMOD,{used_generator_variable,V}}]}
       || {_, Ms} <- MsL,
           {XLoc,erl_lint,{unbound_var,_}} <- Ms,
           {Loc,File,V} <- [genvar_pos(XLoc, S)]].

lc_messages(MsL, NodeInfo) ->
    [{File,[{Loc,Mod,T} || {Loc,Mod,T} <- Ms, lc_loc(Loc, NodeInfo)]} ||
        {File,Ms} <- MsL].

lc_loc(N, NodeInfo) ->
    case ets:lookup(NodeInfo, N) of
        [{N, #{inside_lc := true}}] ->
            true;
        [{N, _}] ->
            false
    end.

genvar_pos(Location, S) ->
    case ets:lookup(S#state.node_info, Location) of
        [{Location, #{genvar_pos := Pos}}] ->
            Pos;
        [] ->
            Location
    end.

%% -> [{Qid,[variable()]}].
%%
%% For each qualifier the introduced variables are found. The
%% variables introduced in filters are very much like the variables
%% introduced in generator patterns. If no variables are introduced in
%% a qualifier, [variable()] is empty.
%%
%% Generator: all variables occurring in the pattern are introduced
%% variables.
%% Filter: all variables bound inside the filter are introduced
%% variables (unless they are unsafe).
%%
intro_variables(FormsNoShadows, State) ->
    NodeInfo = State#state.node_info,
    Fun = fun(QId, {T,_L,P0,_E0}=Q, {GVs,QIds}, Foo) when T =:= b_generate;
                                                          T =:= generate ->
                  PVs = qlc:var_ufold(fun({var,_,V}) -> {QId,V} end, P0),
                  {Q,{ordsets:to_list(PVs) ++ GVs,[{QId,[]} | QIds]},Foo};
             (QId, Filter0, {GVs,QIds}, Foo) ->
                  %% The filter F is replaced by begin E, F, E end,
                  %% where E is an LC expression consisting of a
  template mentioning all variables occurring in F.
                  Vs = ordsets:to_list(qlc:vars(Filter0)),
                  AnyLine = anno0(),
                  Vars = [{var,AnyLine,V} || V <- Vs],
                  LC = embed_vars(Vars, AnyLine),
                  LC1 = intro_anno(LC, before, QId, NodeInfo),
                  LC2 = intro_anno(LC, 'after', QId, NodeInfo),
                  Filter = {block,AnyLine,[LC1,Filter0,LC2]},
                  {Filter,{GVs,[{QId,[]} | QIds]},Foo}
          end,
    Acc0 = {[],[]},
    {FForms,{GenVars,QIds}} = 
        qual_fold(Fun, Acc0, [], FormsNoShadows, State),
    %% Note: the linter messages are the ones we are looking for.
    %% If there are no linter messages, the compiler will crash (ignored).
    Es0 = compile_errors(FForms),
    %% A variable is bound inside the filter if it is not bound before
    %% the filter, but it is bound after the filter (obviously).
    Before = [{QId,V} ||
                 {L,erl_lint,{unbound_var,V}} <- Es0,
                 {_L,{QId,before}} <- ets:lookup(NodeInfo, L)],
    After = [{QId,V} ||
                {L,erl_lint,{unbound_var,V}} <- Es0,
                {_L,{QId,'after'}} <- ets:lookup(NodeInfo, L)],
    Unsafe = [{QId,V} ||
                 {L,erl_lint,{unsafe_var,V,_Where}} <- Es0,
                 {_L,{QId,'after'}} <- ets:lookup(NodeInfo, L)],
    ?DEBUG("Before = ~p~n", [Before]),
    ?DEBUG("After = ~p~n", [After]),
    ?DEBUG("Unsafe = ~p~n", [Unsafe]),
    ?DEBUG("Filter ~p~n", [(Before -- After) -- Unsafe]),
    IV = (Before -- After) -- Unsafe,
    I1 = family(IV ++ GenVars),
    sofs:to_external(sofs:family_union(sofs:family(QIds), I1)).

intro_anno(LC, Where, QId, NodeInfo) ->
    Data = {QId,Where},
    Fun = fun(Anno) ->
                  Location = erl_anno:location(Anno),
                  true = ets:insert(NodeInfo, {Location,Data}),
                  Anno
          end,
    map_anno(Fun, save_anno(LC, NodeInfo)).

compile_errors(FormsNoShadows) ->
    case compile_forms(FormsNoShadows, []) of
        {[], _Warnings} ->
            [];
        {Errors, _Warnings} ->
            ?DEBUG("got errors ~tp~n", [Errors]),
            lists:flatmap(fun({_File,Es}) -> Es end, Errors)
    end.

compile_forms(Forms0, Options) ->
    Exclude = fun(eof) -> true;
                 (warning) -> true;
                 (error) -> true;
                 (_) -> false
              end,
    Forms = ([F || F <- Forms0, not Exclude(element(1, F))]
             ++ [{eof,0}]),
    try 
        case compile:noenv_forms(Forms, compile_options(Options)) of
            {ok, _ModName, Ws0} ->
                {[], Ws0};
            {error, Es0, Ws0} -> 
                {Es0, Ws0}
        end
    catch _:_ ->
        %% The compiler is not available. Use the linter instead.
        case erl_lint:module(Forms, lint_options(Options)) of
            {ok, Warnings} ->
                {[], Warnings};
            {error, Errors, Warnings} ->
                {Errors, Warnings}
        end
    end.

compile_options(Options) ->
    No = [report,report_errors,report_warnings,'P','E' | bitstr_options()],
    [strong_validation,return | skip_options(No, Options)].

lint_options(Options) ->
    skip_options(bitstr_options(), Options).

skip_options(Skip, Options) ->
    [O || O <- Options, not lists:member(O, Skip)].

bitstr_options() ->
    [binary_comprehension,bitlevel_binaries].    

  In LCs it is possible to use variables introduced in filters and
%% generator patterns in the right hand side of generators (ListExpr),
  but in QLCs this is not allowed .
%%
  A brand new function is returned such that there is one expression
  for each ListExpr . The expression mentions all introduced variables
  occurring in ListExpr . Running the function through the compiler
%% yields error messages for erroneous use of introduced variables.
%%
used_genvar_check(FormsNoShadows, State) ->
    NodeInfo = State#state.node_info,
    F = fun(QId, {T, Ln, _P, LE}=Q, {QsIVs0, Exprs0}, IVsSoFar0)
                                   when T =:= b_generate; T =:= generate ->
                F = fun(Var) ->
                            {var, Anno0, OrigVar} =
                                undo_no_shadows(Var, State),
                            {var, Anno, _} = NewVar = save_anno(Var, NodeInfo),
                            Location0 = erl_anno:location(Anno0),
                            Location = erl_anno:location(Anno),
                            [{Location, Data}] =
                                ets:lookup(NodeInfo, Location),
                            Pos = {Location0,get(?QLC_FILE),OrigVar},
                            NData = Data#{genvar_pos => Pos},
                            true = ets:insert(NodeInfo, {Location, NData}),
                            NewVar
                    end,
                Vs = [Var || {var, _, V}=Var <- qlc:var_fold(F, [], LE),
                             lists:member(V, IVsSoFar0)],
                Exprs = case Vs of
                            [] -> Exprs0;
                            _ -> [embed_vars(Vs, Ln) | Exprs0]
                        end,
                {QsIVs,IVsSoFar} = q_intro_vars(QId, QsIVs0, IVsSoFar0),
                {Q, {QsIVs, Exprs}, IVsSoFar};
           (QId, Filter, {QsIVs0, Exprs}, IVsSoFar0) ->
                {QsIVs, IVsSoFar} = q_intro_vars(QId, QsIVs0, IVsSoFar0),
                {Filter, {QsIVs, Exprs}, IVsSoFar}
        end,
    Acc0 = {State#state.intro_vars, [{atom, anno0(), true}]},
    {_, {[], Exprs}} = qual_fold(F, Acc0, [], FormsNoShadows, State),
    FunctionNames = [Name || {function, _, Name, _, _} <- FormsNoShadows],
    UniqueFName = qlc:aux_name(used_genvar, 1, sets:from_list(FunctionNames)),
    A = anno0(),
    {function,A,UniqueFName,0,[{clause,A,[],[],lists:reverse(Exprs)}]}.
    
q_intro_vars(QId, [{QId, IVs} | QsIVs], IVsSoFar) -> {QsIVs, IVs ++ IVsSoFar}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  The transformed code has two major parts : a fun where each
  qualifier is represented by one or more clauses , and a table where
%% list expressions (the right hand side of generators, LE) are
%% represented by funs (the table is further processed at runtime).
%% The separation into a fun and a table makes it possible to
%% rearrange qualifiers while keeping the speed offered by compiled
  code , and to run the LEs before evaluation of the  ( and possibly
  modify the LEs should that be necessary ) . Only when doing a fast
%% join are qualifiers rearranged.
%%
%% Extra generators (and clauses) are inserted for possible fast join
%% operations. The list expression for such a generator has the form
  { join ,  , QualifierNumber1 , QualifierNumber2 ,  ,
%% PatternFilter2, PatternConstants1, PatternConstants2} (it is not a
%% fun). Join generators are ignored at runtime unless a fast join is
%% possible, in which case they replace other generators. See also
%% qlc.erl.
%% 
  For each QLC , every filter is given a state number and every
  generator two state numbers ( one for initialization , one for
%% looping over values). State 1 is reserved for the template and
%% state 0 is entered when there are no more values to try, so
%% assuming no rearrangement of the qualifiers has taken place, the
  first qualifier is given state number 2 . For every state except 0 ,
%% the table tells which state to go to next. By modifying the table,
%% the order of the qualifiers can be altered at runtime.
%%
  The syntax of the value  returned from the fun is :
  Val = [ ] | [ term ( ) | Val ] | fun ( ) - > 
%% Note: the fun must not return a fun if it is to be called by
%% the function outlined below.
%%
%% An outline of the generated fun:
%%
  fun(0 , RL , ... ) when is_list(RL ) - > % the final state
%%       lists:reverse(RL);   % eval, all answers collected in a list
%%    (0, ...) -> [];    % cursor (or fold)
     ( 1 , RL , ... ) when is_list(RL ) - > % the template state
%%       Fun(<last generator loop state>, [Template | RL], ...);
     ( 1 , .... ) - >             % return the object and a continuation
%%       [Template | fun() -> Fun(<last generator loop state>, ...)];
     ( 2 , ... ) - > % an sample generator , initialization state
%%       Fun(3, ..., <initial value>, ...);
     ( 3 , ... , [ Pattern | Val ] , ... ) - > % looping over values ( a list )
        Fun(<next qualifier state > , ... ,  , ... ) ; % arguments are bound
     ( 3 , ... , [ _ | Val ] , ... ) - > % pattern does not match
        Fun(3 , ... ,  , ... ) ;
     ( 3 , ... , [ ] , ... ) - >
%%       Fun(<last generator loop state>, ...);
     ( 3 , .... , F , ... ) - > % looping over values ( using continuations )
%%       case F() of % get the next value by calling a continuation
%%           [Pattern | Val] -> 
                Fun(<next qualifier state > ... ,  , ... ) ;
%%           [_ | Val] -> 
                Fun(3 , ... ,  , ... ) ;
%%           [] ->
               Fun(<last generator loop state > , ... ) ;
%%           T -> % returned immediately, typically an error tuple
%%              T
%%       end;
     ( 4 , ... ) - > % a sample filter
%%       case Filter of
%%           true -> Fun(<next qualifier state>, ...);
%%           false -> Fun(<last generator loop state>, ...)
%%       end;
     ( 5 , ... ) - > % a filter so simple that it could be used as a guard
%%       if 
%%          Guard -> Fun(<next qualifier state>, ...);
%%          true -> Fun(<last generator loop state>, ...)
%%       end
%% 
%% <last generator loop state> means state 0 if there is no last
%% generator. <initial value> is the evaluated list expression
%% (evaluated once only). Among the arguments indicated by ellipses
%% are all variables introduced in patterns and filters.
%%
  transform/2 replaces each  ( call to  : q/1 ) with a qlc_lc
%% record. The general case is that calling the fun stored in the 'lc'
  field returns { qlc_v1 , QFun , CodeF , Qdata , QOpt } such that :  is
  the above mentioned fun ; CodeF is a fun returning the original code
  for the template , every pattern , and every filter ; Qdata is the
%% above mentioned table; QOpt is a property list implemented as a fun
  of one argument - an atom - which returns information about such
%% things as constant columns, match specifications, &c.
%% There is one special case when calling the fun stored in the 'lc'
%% field returns something else:
  - If the QLC has the form [ Var || Var < - LE ] and there are no
    options to qlc : q/2 , a tuple { simple_v1 , P , LEf , Line } is returned .
%%   The objects returned are the objects returned by the generator
%%   (calling LEf returns the objects generated by LE).

transform(FormsNoShadows, State) ->
    _ = erlang:system_flag(backtrace_depth, 500),
    IntroVars = State#state.intro_vars,
    AllVars = sets:from_list(ordsets:to_list(qlc:vars(FormsNoShadows))),
    ?DEBUG("AllVars = ~p~n", [sets:to_list(AllVars)]),
    F1 = fun(QId, {generate,_,P,LE}, Foo, {GoI,SI}) ->
                 {{QId,GoI,SI,{gen,P,LE}},Foo,{GoI + 3, SI + 2}};
            (QId, F, Foo, {GoI,SI}) ->
                 {{QId,GoI,SI,{fil,F}},Foo,{GoI + 2,SI + 1}}
         end,
    TemplS = qlc:template_state(),
    GoState = {TemplS + 1, TemplS + 1},
    {ModifiedForms1,_} = 
        qual_fold(F1, [], GoState, FormsNoShadows, State),

  This is for info/2 .  in filters and the template are
    %% translated before the expression itself is translated. info/2
    %% must not display the result of the translation, but the source
    %% code.
    {_,Source0} = qual_fold(fun(_QId, {generate,_,_P,_E}=Q, Dict, Foo) -> 
                                    {Q,Dict,Foo};
                               (QId, F, Dict, Foo) ->
                                    {F,dict:store(QId, F, Dict),Foo}
                            end, dict:new(), [], FormsNoShadows, State),
    {_,Source} = qlc_mapfold(fun(Id, {lc,_L,E,_Qs}=LC, Dict) ->
                                     {LC,dict:store(Id, E, Dict)}
                             end, Source0, FormsNoShadows, State),


    %% Unused variables introduced in filters are not optimized away.
    F2 = fun(Id, {lc,_L,E,Qs}, {IntroVs0,XWarn0}) ->
                 LcNo = get_lcid_no(Id),
                 LcL = get_lcid_line(Id),
                 [RL,Fun,Go,NGV,S0,RL0,Go0,AT,Err] = 
                     aux_vars(['RL','Fun','Go','C','S0','RL0','Go0','AT','E'],
                              LcNo, AllVars),
                 ?DEBUG("RL = ~p, Fun = ~p, Go = ~p~n", [RL, Fun, Go]),
                 {IntroVs, RestIntroVs} = lists:split(length(Qs), IntroVs0),
                 IntroVs_Qs = lists:zip(IntroVs, Qs),
                 F = fun({{QId,IVs}, {QId,GoI,SI,{gen,P,LE}}}, AllIVs0) ->
                             GV = aux_var('C', LcNo, QId#qid.no, 1, AllVars),
                             GenIVs = [GV | IVs],
                             {{QId,{GenIVs,{{gen,P,LE,GV},GoI,SI}}},
                              GenIVs ++ AllIVs0};
                        ({{QId,IVs}, {QId,GoI,SI,{fil,F}}}, AllIVs0) ->
                             {{QId,{IVs,{{fil,F},GoI,SI}}},
                              IVs++AllIVs0}
                     end,
                 {QCs, AllIVs} = lists:mapfoldl(F, [], IntroVs_Qs),

                 Dependencies = qualifier_dependencies(Qs, IntroVs),
                 L = no_compiler_warning(LcL),
                 {EqColumnConstants, EqualColumnConstants,
                  ExtraConsts, SizeInfo} =
                     constants_and_sizes(Qs, E, Dependencies, AllIVs, State),
                 {JoinInfo, XWarn} = 
                     join_kind(Qs, LcL, AllIVs, Dependencies, State),
                 %% Not at all sure it is a good idea to try and find 
  failing qualifiers ;  does it so much better .
                 %% But there are a few cases where qlc finds more... (r12b).
                 FWarn = warn_failing_qualifiers(Qs, AllIVs, Dependencies, 
                                                 State),
                 JQs = join_quals(JoinInfo, QCs, L, LcNo, ExtraConsts, AllVars),
                 XQCs = QCs ++ JQs,
                 Cs0 = clauses(XQCs, RL, Fun, Go, NGV, Err, AllIVs, State),
                 Template = template(E, RL, Fun, Go, AT, L, AllIVs, State),
                 Fin = final(RL, AllIVs, L, State),
                 FunC = {'fun',L,{clauses,Fin ++ Template ++ Cs0}},
                 As0 = pack_args(abst_vars([S0, RL0, Fun, Go0 
                                            | replace(AllIVs, AllIVs, nil)], 
                                           L), L, State),
                 AsW = abst_vars([S0, RL0, Go0], L),
                 FunW = {'fun',L,{clauses,[{clause,L,AsW,[],
                                            [{match,L,{var,L,Fun},FunC},
                                             {call,L,{var,L,Fun},As0}]}]}},
                 {ok, OrigE0} = dict:find(Id, Source),
                 OrigE = undo_no_shadows(OrigE0, State),
                 QCode = qcode(OrigE, XQCs, Source, L, State),
                 Qdata = qdata(XQCs, L),
                 TemplateInfo = 
                     template_columns(Qs, E, AllIVs, Dependencies, State),
  ExtraConsts should be used by match_spec_quals .
                 MSQs = match_spec_quals(E, Dependencies, Qs, State),
                 Opt = opt_info(TemplateInfo, SizeInfo, JoinInfo, MSQs, L,
                                EqColumnConstants, EqualColumnConstants),
                 LCTuple = 
                     case qlc_kind(OrigE, Qs, State) of
                         qlc ->
                             {tuple,L,[?A(qlc_v1),FunW,QCode,Qdata,Opt]};
                         {simple, PL, LE, V} ->
                             Init = closure(LE, L),
                             simple(L, V, Init, PL)
                     end,
                 LCFun = {'fun',L,{clauses,[{clause,L,[],[],[LCTuple]}]}},
                 {tuple,_,Fs0} = abstr(#qlc_lc{}, L),
                 Fs = set_field(#qlc_lc.lc, Fs0, LCFun),
                 {{tuple,L,Fs},{RestIntroVs,FWarn++XWarn++XWarn0}}
         end,
    {NForms,{[],XW}} = qlc_mapfold(F2, {IntroVars,[]}, ModifiedForms1, State),
    display_forms(NForms),
    {NForms, State#state{xwarnings = XW}}.

join_kind(Qs, LcL, AllIVs, Dependencies, State) ->
    {EqualCols2, EqualColsN} = equal_columns(Qs, AllIVs, Dependencies, State),
    {MatchCols2, MatchColsN} = eq_columns(Qs, AllIVs, Dependencies, State),
    Tables = lists:usort
               ([T || {C,_Skip} <- EqualCols2, {T,_} <- C]
             ++ [T || {C,_Skip} <- EqualCols2, T <- C, is_integer(T)]),
    if 
        EqualColsN =/= []; MatchColsN =/= [] -> 
            {[], 
             [{get(?QLC_FILE),[{LcL,?APIMOD,too_complex_join}]}]};
        EqualCols2 =:= [], MatchCols2 =:= [] ->
            {[], []};
        length(Tables) > 2 -> 
            {[], 
             [{get(?QLC_FILE),[{LcL,?APIMOD,too_many_joins}]}]};
        EqualCols2 =:= MatchCols2 ->
            {EqualCols2, []};
        true -> 
            {{EqualCols2, MatchCols2}, []}
    end.

qlc_kind(OrigE, Qs, State) ->
    {OrigFilterData, OrigGeneratorData} =
        qual_data(undo_no_shadows(Qs, State)),
    OrigAllFilters = filters_as_one(OrigFilterData),
    {_FilterData, GeneratorData} = qual_data(Qs),
    case {OrigE, OrigAllFilters, OrigGeneratorData} of
        {{var,_,V}, {atom,_,true}, [{_,{gen,{var,PatternL,V},_LE}}]} ->
            [{_,{gen,_,LE}}] = GeneratorData,
            {simple, PatternL, LE, V}; % V is for info()
        _ ->
            qlc
    end.

%% Finds filters and patterns that cannot match any values at all. 
%% Nothing but the patterns and the filters themselves is analyzed.
  A much weaker analysis than the one of  's .
warn_failing_qualifiers(Qualifiers, AllIVs, Dependencies, State) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),    
    Anon = 1,
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    {PFrame, _PatternVars} = 
        pattern_frame(GeneratorData, BindFun, Anon, State),
    {_, _, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    PFrames = frame2frames(PFrame),
    {_, Warnings} = 
        lists:foldl(fun({_QId,{fil,_Filter}}, {[]=Frames,Warnings}) ->
                            {Frames,Warnings};
                       ({_QId,{fil,Filter}}, {Frames,Warnings}) ->
                        case filter(reset_anno(Filter), Frames, BindFun,
                                    State, Imported) of
                            [] ->
                                {[],
                                 [{get(?QLC_FILE),
                                   [{loc(element(2, Filter)),?APIMOD,
                                     nomatch_filter}]} | Warnings]};
                            Frames1 -> 
                                {Frames1,Warnings}
                        end;
                   ({_QId,{gen,Pattern,_}}, {Frames,Warnings}) ->
                        case pattern(Pattern, Anon, [], BindFun, State) of
                            {failed, _, _} -> 
                                {Frames,
                                 [{get(?QLC_FILE),
                                   [{loc(element(2, Pattern)),?APIMOD,
                                     nomatch_pattern}]} | Warnings]};
                            _ ->
                                {Frames,Warnings}
                        end
                end, {PFrames,[]}, FilterData++GeneratorData),
    Warnings.

-define(TNO, 0).
-define(TID, #qid{lcid = template, no = ?TNO}).

opt_info(TemplateInfo, Sizes, JoinInfo, MSQs, L, 
         EqColumnConstants0, EqualColumnConstants0) ->
    SzCls = [{clause,L,[?I(C)],[],[?I(Sz)]} || {C,Sz} <- lists:sort(Sizes)]
            ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    S = [{size, {'fun', L, {clauses, SzCls}}}],
    J = case JoinInfo of [] -> []; _ -> [{join, abstr(JoinInfo, L)}] end,
  Superfluous clauses may be emitted :
    TCls0 = lists:append(
              [[{clause,L,[abstr(Col, L),EqType],[],
                 [abstr(TemplCols, L)]} ||
                   {Col,TemplCols} <- TemplateColumns]
               || {EqType, TemplateColumns} <- TemplateInfo]),
    TCls = lists:sort(TCls0) ++ [{clause,L,[?V('_'),?V('_')],[],[{nil,L}]}],
    T = [{template, {'fun', L, {clauses, TCls}}}],

    %% The template may also have a constant function (IdNo = 0).
    %% Only constant template columns are interesting.
    EqColumnConstants = opt_column_constants(EqColumnConstants0),
    CCs = opt_constants(L, EqColumnConstants),
    EqC = {constants,{'fun',L,{clauses,CCs}}},

    EqualColumnConstants = opt_column_constants(EqualColumnConstants0),
    ECCs = opt_constants(L, EqualColumnConstants),
    EqualC = {equal_constants,{'fun',L,{clauses,ECCs}}},
    C = [EqC | [EqualC || true <- [CCs =/= ECCs]]],

    %% Comparisons yield more constant columns than matchings.
    ConstCols = [{IdNo,Col} || 
                    {{IdNo,Col},[_],_FilNs} <- EqualColumnConstants],
    ConstColsFamily = family_list(ConstCols),
    NSortedCols0 = [{IdNo,hd(lists:seq(1, length(Cols)+1)--Cols)} ||
                       {IdNo,Cols} <- ConstColsFamily],
    NCls = [{clause,L,[?I(IdNo)],[],[?I(N-1)]} ||
               {IdNo,N} <- NSortedCols0, N > 0]
           ++ [{clause,L,[?V('_')],[],[?I(0)]}],
    N = [{n_leading_constant_columns,{'fun',L,{clauses,NCls}}}],

    ConstCls = [{clause,L,[?I(IdNo)],[],[abstr(Cols,L)]} ||
                   {IdNo,Cols} <- ConstColsFamily] 
               ++ [{clause,L,[?V('_')],[],[{nil,L}]}],
    CC = [{constant_columns,{'fun',L,{clauses,ConstCls}}}],

    MSCls = [{clause,L,[?I(G)],[],[{tuple,L,[MS,abstr(Fs,L)]}]} ||
                {G,MS,Fs} <- MSQs]
          ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    MS = [{match_specs, {'fun',L,{clauses,MSCls}}}],

    Cls = [{clause,L,[?A(Tag)],[],[V]} || 
              {Tag,V} <- lists:append([J, S, T, C, N, CC, MS])]
          ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    {'fun', L, {clauses, Cls}}.

opt_column_constants(ColumnConstants0) ->
    [CC || {{IdNo,_Col},Const,_FilNs}=CC <- ColumnConstants0,
           (IdNo =/= ?TNO) or (length(Const) =:= 1)].

opt_constants(L, ColumnConstants) ->
    Ns = lists:usort([IdNo || {{IdNo,_Col},_Const,_FilNs} <- ColumnConstants]),
    [{clause,L,[?I(IdNo)],[],[column_fun(ColumnConstants, IdNo, L)]}
     || IdNo <- Ns]
     ++ [{clause,L,[?V('_')],[],[?A(no_column_fun)]}].

abstr(Term, Anno) ->
    erl_parse:abstract(Term, loc(Anno)).

%% Extra generators are introduced for join.
join_quals(JoinInfo, QCs, L, LcNo, ExtraConstants, AllVars) ->
    {LastGoI, LastSI} =
        lists:foldl(fun({_QId,{_QIVs,{{fil,_},GoI,SI}}}, 
                        {GoI0, _SI0}) when GoI >= GoI0 ->
                            {GoI + 2, SI + 1};
                       ({_QId,{_QIVs,{{gen,_,_,_},GoI,SI}}}, 
                        {GoI0, _SI0}) when GoI >= GoI0 ->
                            {GoI + 3, SI + 2};
                       (_, A) ->
                            A
                    end, {0, 0}, QCs),
    LastQId = lists:max([QId || {QId,{_QIVs,{_Q,_GoI,_SI}}} <- QCs]),
  Only two tables for the time being .
    %% The join generator re-uses the generator variable assigned to
  the first of the two joined generators . Its introduced variables
  are the variables introduced by any of the two joined generators .
    %% Its abstract code is a pair of the joined generators' patterns.
    QNums = case JoinInfo of
                {EqualCols, MatchCols} ->
                    EQs = join_qnums(EqualCols),
                    MQs = join_qnums(MatchCols),
                    [{Q1,Q2,'=:='} || {Q1,Q2} <- MQs] ++
                        [{Q1,Q2,'=='} || {Q1,Q2} <- EQs -- MQs];
                EqualCols ->
                    [{Q1,Q2,'=='} || {Q1,Q2} <- join_qnums(EqualCols)]
            end,
    LD = [begin 
              [{QId1,P1,GV1,QIVs1}] = 
                  [{QId,P,GV,QIVs} || 
                      {QId,{QIVs,{{gen,P,_,GV},_GoI,_SI}}} <- QCs, 
                      QId#qid.no =:= Q1],
              [{QId2,P2,QIVs2}] = 
                  [{QId,P,QIVs--[GV]} || 
                      {QId,{QIVs,{{gen,P,_,GV},_,_}}} <- QCs,
                      QId#qid.no =:= Q2],
              {QId1,Op,P1,GV1,QIVs1++QIVs2,QId2,P2}
          end || {Q1, Q2, Op} <- lists:usort(QNums)],
    Aux = abst_vars(aux_vars(['F','H','O','C'], LcNo, AllVars), L),
    F = fun({QId1,Op,P1,GV1,QIVs,QId2,P2}, {QId,GoI,SI}) ->
                AP1 = anon_pattern(P1),
                AP2 = anon_pattern(P2),
                Cs1 = join_handle_constants(QId1, ExtraConstants),
                Cs2 = join_handle_constants(QId2, ExtraConstants),
                H1 = join_handle(AP1, L, Aux, Cs1),
                H2 = join_handle(AP2, L, Aux, Cs2),
                %% Op is not used.
                Join = {join,Op,QId1#qid.no,QId2#qid.no,H1,H2,Cs1,Cs2},
                G = {NQId=QId#qid{no = QId#qid.no + 1},
                     {QIVs,{{gen,{cons,L,P1,P2},Join,GV1},GoI,SI}}},
                A = {NQId, GoI + 3, SI + 2},
                {G, A}
        end,
    {Qs, _} = lists:mapfoldl(F, {LastQId, LastGoI, LastSI}, LD),
    Qs.

join_qnums(Cols) ->
    lists:usort([{Q1, Q2} || {[{Q1,_C1}, {Q2,_C2}], _Skip} <- Cols]).

%% Variables occurring only once are replaced by '_'.
anon_pattern(P) ->
    MoreThanOnce = lists:usort(occ_vars(P) -- qlc:vars(P)),
    {AP, foo} = var_mapfold(fun({var, L, V}, A) ->
                                    case lists:member(V, MoreThanOnce) of
                                        true -> 
                                            {{var, L, V}, A};
                                        false ->
                                            {{var, L, '_'}, A}
                                    end
                            end, foo, P),
    AP.

%% Creates a handle that filters the operands of merge join using the
%% pattern. It is important that objects that do not pass the pattern
%% are filtered out because the columns of the pattern are inspected
%% in order to determine if key-sorting the operands can be avoided.
%% 
%% No objects will be filtered out if the pattern is just a variable.
join_handle(AP, L, [F, H, O, C], Constants) ->
    case {AP, Constants} of
        {{var, _, _}, []} ->
            {'fun',L,{clauses,[{clause,L,[H],[],[H]}]}};
        _ ->
            A = anno0(),
            G0 = [begin
                      Call = {call,A,{atom,A,element},[{integer,A,Col},O]},
                      list2op([{op,A,Op,Con,Call} || {Con,Op} <- Cs], 'or')
                  end || {Col,Cs} <- Constants],
            G = if G0 =:= [] -> G0; true -> [G0] end,
            CC1 = {clause,L,[AP],G,[{cons,L,O,closure({call,L,F,[F,C]},L)}]},
            CC2 = {clause,L,[?V('_')],[],[{call,L,F,[F,C]}]},
            Case = {'case',L,O,[CC1,CC2]},
            Cls = [{clause,L,[?V('_'),{nil,L}],[],[{nil,L}]},
                   {clause,L,[F,{cons,L,O,C}],[],[Case]},
                   {clause,L,[F,C],[[{call,L,?A(is_function),[C]}]],
                    [{call,L,F,[F,{call,L,C,[]}]}]},
                   {clause,L,[?V('_'),C],[],[C]}],
            Fun = {'fun', L, {clauses, Cls}},
            {'fun',L,{clauses,[{clause,L,[H],[],[{match,L,F,Fun}, 
                                                 closure({call,L,F,[F,H]}, 
                                                         L)]}]}}
    end.

join_handle_constants(QId, ExtraConstants) ->
    IdNo = QId#qid.no,
    case lists:keyfind(IdNo, 1, ExtraConstants) of
        {IdNo, ConstOps} ->
            ConstOps;
        false ->
            []
    end.

%%% By the term "imported variable" is meant a variable that is bound
  outside ( before ) the QLC . Perhaps " parameter " would be a more
%%% suitable name.

%% The column fun is to be used when there is a known key column or
%% indices. The argument is a column number and the return value is a
%% list of the values to look up to get all objects needed to evaluate
%% the filter. The order of the objects need not be the same as the
%% order the traverse fun would return them.

column_fun(Columns, QualifierNumber, LcL) ->
    A = anno0(),
    ColCls0 = 
        [begin
  at least one value to look up
             Vs1 = list2cons(Vs0),
             Fils1 = {tuple,A,[{atom,A,FTag},
                               lists:foldr
                                   (fun(F, Ac) -> {cons,A,{integer,A,F},Ac}
                                    end, {nil,A}, Fils)]},
             Tag = case ordsets:to_list(qlc:vars(Vs1)) of
                       Imp when length(Imp) > 0, % imported vars
                                length(Vs0) > 1 ->
                           usort_needed;
                       _ ->
                           values
                   end,
             Vs = {tuple,A,[{atom,A,Tag},Vs1,Fils1]},
             {clause,A,[erl_parse:abstract(Col)],[],[Vs]}
         end ||
            {{CIdNo,Col}, Vs0, {FTag,Fils}} <- Columns,
            CIdNo =:= QualifierNumber]
        ++ [{clause,A,[{var,A,'_'}],[],[{atom,A,false}]}],
    ColCls = set_anno(ColCls0, LcL),
    {'fun', LcL, {clauses, ColCls}}.

  Tries to find columns of the template that ( 1 ) are equal to ( or
  match ) or ( 2 ) match columns of the patterns of the generators . The
%% results are to be used only for determining which columns are
%% sorted. The template can be handled very much like a generator
%% pattern (the variables are not fresh, though). As in filters calls
%% like element(I, T) are recognized.
  - > [   , Equal | Match } ]
%% Equal = Match = TemplateColumns
  EqType = abstract code for { _ | ' = = ' | ' = : = ' }
  TemplateColumns = [ { Column , Integers } ]     % integer is position in template
  Column = { QualifierNumber , ColumnNumber } } % column is position in pattern

template_columns(Qs0, E0, AllIVs, Dependencies, State) ->
    E = expand_expr_records(pre_expand(E0), State),
    TemplateAsPattern = template_as_pattern(E),
    Qs = [TemplateAsPattern | Qs0],
    EqualColumns = equal_columns2(Qs, AllIVs, Dependencies, State),
    MatchColumns = eq_columns2(Qs, AllIVs, Dependencies, State),
    Equal = template_cols(EqualColumns), 
    Match = template_cols(MatchColumns),
    L = anno0(),
    if 
        Match =:= Equal -> 
            [{?V('_'), Match}];
        true -> 
            [{?A('=='), Equal}, {?A('=:='), Match}]
    end.

equal_columns2(Qualifiers, AllIVs, Dependencies, State) ->
    {JI, _Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State,_JoinOp = '=='),
    JI.

eq_columns2(Qualifiers, AllIVs, Dependencies, State) ->
    {JI, _SKip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=:='),
    JI.

template_cols(ColumnClasses) ->
    lists:sort([{{IdNo,Col}, lists:usort(Cs)} ||
                   Class <- ColumnClasses,
                   {IdNo,Col} <- Class,
                   IdNo =/= ?TNO,
                   [] =/= (Cs = [C || {?TNO,C} <- Class])]).

template_as_pattern(E) ->
    P = simple_template(E),
    {?TID,foo,foo,{gen,P,{nil,anno0()}}}.

simple_template({call,L,{remote,_,{atom,_,erlang},{atom,_,element}}=Call,
                 [{integer,_,I}=A1,A2]}) when I > 0 ->
    %% This kludge is known by pattern/5 below.
    {call, L, Call, [A1, simple_template(A2)]};
simple_template({var, _, _}=E) ->
    E;
simple_template({tuple, L, Es}) ->
    {tuple, L, [simple_template(E) || E <- Es]};
simple_template({cons, L, H, T}) ->
    {cons, L, simple_template(H), simple_template(T)};
simple_template(E) ->
    case catch erl_parse:normalise(E) of
        {'EXIT', _} -> unique_var();
        _ -> E
    end.

%% -> [{QId,[QId']}].
  Qualifier QId ( a filter ) uses variables introduced in QId ' .
qualifier_dependencies(Qualifiers, IntroVs) ->
    Intro = sofs:relation([{IV,QId} || {QId,IVs} <- IntroVs, IV <- IVs]),
    {FilterData, _} = qual_data(Qualifiers),
    Used = sofs:relation([{QId,UV} ||
                             {QId,{fil,F}} <- FilterData,
                             UV <- qlc:vars(F)]),
    Depend = sofs:strict_relation(sofs:relative_product(Used, Intro)),
    G = sofs:family_to_digraph(sofs:relation_to_family(Depend)),
    Dep0 = [{V,digraph_utils:reachable_neighbours([V], G)} || 
               V <- digraph:vertices(G)],
    true = digraph:delete(G),
    FilterIds = sofs:set(filter_ids(Qualifiers)),
    Dep1 = sofs:restriction(sofs:family(Dep0), FilterIds),
    NoDep = sofs:constant_function(FilterIds, sofs:empty_set()),
    sofs:to_external(sofs:family_union(Dep1, NoDep)).

filter_ids(Qualifiers) ->
    {FilterData, _} = qual_data(Qualifiers),
    [QId || {QId,_} <- FilterData].

  - > [ { QualifierNumber , MatchSpec,[QualifierNumber ' ] }
%% The qualifiers [QualifierNumber'] are filters (F1, ..., Fn) that
  depend on QualifierNumber ( a generator Pattern < - LE ) only .
  MatchSpec is the match specification for [ Pattern ' || Pattern < - LE ,
%% F1, ..., Fn], where Pattern' is Template if all qualifiers can be 
  replaced by one match specification , otherwise a modified Pattern .
match_spec_quals(Template, Dependencies, Qualifiers, State) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    NoFilterGIds = [GId || {GId,_} <- GeneratorData] 
                   -- lists:flatmap(fun({_,GIds}) -> GIds end, Dependencies),
    Filters = filter_list(FilterData, Dependencies, State),
    Candidates = [{QId2#qid.no,Pattern,[Filter],F} || 
                     {QId,[QId2]} <- Dependencies,
                     {GQId,{gen,Pattern,_}} <- GeneratorData,
                     GQId =:= QId2,
                     {FQId,{fil,F}}=Filter <- Filters, % guard filters only
                     FQId =:= QId] 
               ++ [{GId#qid.no,Pattern,[],{atom,anno0(),true}} ||
                      {GId,{gen,Pattern,_}} <- GeneratorData,
                      lists:member(GId, NoFilterGIds)],
    E = {nil, anno0()},
    GF = [{{GNum,Pattern},Filter} || 
             {GNum,Pattern,Filter,F} <- Candidates,
             no =/= try_ms(E, Pattern, F, State)],
    GFF = sofs:relation_to_family(sofs:relation(GF, 
                                                [{gnum_pattern,[filter]}])),
    GFFL = sofs:to_external(sofs:family_union(GFF)),
    try
        [{{GNum,Pattern}, GFilterData}] = GFFL,
        true = length(GFilterData) =:= length(FilterData),
        [_] = GeneratorData,
        AbstrMS = gen_ms(Template, Pattern, GFilterData, State),
  There is one generator and every filter uses some of the
        %% variables introduced by the generator. The whole qlc
        %% expressione can be replaced by a match specification.
        [{GNum, AbstrMS, all}]
    catch _:_ ->
        {TemplVar, _} = anon_var({var,anno0(),'_'}, 0),
        [one_gen_match_spec(GNum, Pattern, GFilterData, State, TemplVar) ||
            {{GNum,Pattern},GFilterData} <- GFFL]
    end.

one_gen_match_spec(GNum, Pattern0, GFilterData, State, TemplVar) ->
    {E, Pattern} = pattern_as_template(Pattern0, TemplVar),
    AbstrMS = gen_ms(E, Pattern, GFilterData, State),
    {GNum, AbstrMS, [FId#qid.no || {FId,_} <- GFilterData]}.

gen_ms(E, Pattern, GFilterData, State) ->
    {ok, MS, AMS} = try_ms(E, Pattern, filters_as_one(GFilterData), State),
    case MS of
        [{'$1',[true],['$1']}] ->
            {atom, anno0(), no_match_spec};
        _ ->
            AMS
    end.

%% -> {Template, Pattern'}
  The pattern is accepted by ets : fun2ms/1 , that is , = /2 can only
%% occur at top level. Introduce or reuse a top-level variable as
%% template
pattern_as_template({var,_,'_'}, TemplVar) ->
    {TemplVar, TemplVar};
pattern_as_template({var,_,_}=V, _TemplVar) ->
    {V, V};
pattern_as_template({match,L,E,{var,_,'_'}}, TemplVar) ->
    {TemplVar, {match,L,E,TemplVar}};
pattern_as_template({match,L,{var,_,'_'},E}, TemplVar) ->
    {TemplVar, {match,L,E,TemplVar}};
pattern_as_template({match,_,_E,{var,_,_}=V}=P, _TemplVar) ->
    {V, P};
pattern_as_template({match,_,{var,_,_}=V,_E}=P, _TemplVar) ->
    {V, P};
pattern_as_template(E, TemplVar) ->
    L = anno0(),
    {TemplVar, {match, L, E, TemplVar}}.

%% Tries to find columns which are compared or matched against
%% constant values or other columns. To that end unification is used.
%% A frame is a list of bindings created by unification.
%% Also tries to find the number of columns of patterns.
%% Note that the template is handled more or less as a pattern.
  - > { ColumnConstants ,  , ExtraConstants }
%% ColumnConstants = [{Column,[Constant],[FilterNo]}]
  SizeInfo = [ { QualifierNumber , NumberOfColumns } ]
  Column = { QualifierNumber , ColumnNumber } }
  FilterNo is a filter that can be skipped at runtime provided constants
%% are looked up.
  ExtraConstants =
%%     [{GeneratorNumber,[{ColumnNumber,
                          [ { AbstractConstant , AbstractOperator } ] } ] } ]
%% For every generator such that the unification binds value(s) to
%% some column(s), extra constants are returned. These constants are
%% the results of the unification, and do not occur in the pattern of
%% the generator.
constants_and_sizes(Qualifiers0, E, Dependencies, AllIVs, State) ->
    TemplateAsPattern = template_as_pattern(E),
    Qualifiers = [TemplateAsPattern | Qualifiers0],
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    {Filter, Anon1, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    PatBindFun = fun(_Op, Value) -> is_bindable(Value) end,
    {PatternFrame, PatternVars} = 
        pattern_frame(GeneratorData, PatBindFun, Anon1, State),
    PatternFrames = frame2frames(PatternFrame),
    FilterFun = 
        fun(BindFun) -> 
              filter(Filter, PatternFrames, BindFun, State, Imported)
        end,
    SzFs = FilterFun(PatBindFun),

    SizeInfo = pattern_sizes(PatternVars, SzFs),
    SelectorFun = const_selector(Imported),
    PatternConstants = 
        lists:flatten(frames_to_columns(PatternFrames, PatternVars,
                                        deref_pattern(Imported),
                                        SelectorFun, Imported,
                                        '=:=')),

    {EqColumnConstants, _EqExtraConsts} = 
        constants(FilterFun, PatternVars, PatternConstants, PatternFrame,
                  FilterData, Dependencies, _LookupOp1 = '=:=', 
                  Imported, State),
    {EqualColumnConstants, EqualExtraConsts} = 
        constants(FilterFun, PatternVars, PatternConstants, PatternFrame,
                  FilterData, Dependencies, _LookupOp2 = '==', 
                  Imported, State),

    %% Use compared extra constants only because:
    %% - merge join compares terms;
    %% - the constants from the matching unification is a subset of the
    %%   constants from the comparing unification.
    %% Using constants from the matching unification would make it
    %% possible to skip some (more) objects when joining.
    ExtraCon1 = 
        [{{GId,Col},{Val,Op}} ||
            {Consts,Op} <- [{EqualExtraConsts,'=='}],
            {{GId,Col},Val} <- Consts],
    ExtraConstants = 
      family_list([{GId, {Col,ValOps}} ||
                      {{GId,Col},ValOps} <- family_list(ExtraCon1)]),
    {EqColumnConstants, EqualColumnConstants, ExtraConstants, SizeInfo}.

constants(FilterFun, PatternVars, PatternConstants, PatternFrame, 
          FilterData, Dependencies, LookupOp, Imported, State) ->
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    Fs = FilterFun(BindFun),
    SelectorFun = const_selector(Imported),
    ColumnConstants0 = frames_to_columns(Fs, PatternVars, 
                                         deref_lookup(Imported, LookupOp),
                                         SelectorFun, Imported, LookupOp),
    ColumnConstants1 = lists:flatten(ColumnConstants0),
    ExtraConstants = 
       [{{GId,Col},Val} ||
           {{GId,Col},Vals} <- ColumnConstants1 -- PatternConstants,
           GId =/= ?TNO,
           Val <- Vals],
    ColumnConstants = lu_skip(ColumnConstants1, FilterData, PatternFrame,
                              PatternVars, Dependencies, State,
                              Imported, LookupOp),
    {ColumnConstants, ExtraConstants}.

%%% ** Comparing Terms **
%%%  When comparing the key against a term where some integer (or float
%%% comparing equal to an integer) occurs, one has to be careful if the
  table matches keys . One way would be to look up the term both with
%%% the integer and with the float comparing equal to the integer--then
%%% all objects that could possibly be answers are filtered (with
%%% reasonable assumptions). But if integers occur several times in the
%%% term all combinations have to be looked up, and that could be just
%%% too many.
%%%  If imported variables occur in the term one could assume at compile
%%% time that they are not integers and check that assumption at
%%% runtime. However, this would probably be bad design since some keys
%%% can be looked up, but others cannot.
%%%  However, the current implementation is simple: do not bind a
%%% variable to a term if imported variables or integers occur in the
%%% term.

deref_lookup(Imported, '==') ->
    %% Comparing table. Every value can be looked up.
    fun(PV, F) -> deref_values(PV, F, Imported) end;
deref_lookup(Imported, '=:=') ->
    %% Matching table. Ignore comparisons unless the value is free of
    %% integers. See also Comparing Terms.
    BFun = fun(DV, Op) ->
                   Op =:= '=:=' orelse free_of_integers(DV, Imported)
           end,
    fun(PV, F) -> deref_values(PV, F, BFun, Imported) end.

%% Augment ColConstants with filters that do not need to be run
%% provided that constants are looked up.
%% Does not find all filters that can be removed.
lu_skip(ColConstants, FilterData, PatternFrame, PatternVars, 
        Dependencies, State, Imported, LookupOp) ->
    %% If there is a test that does not compare or match, then the
    %% filter cannot be skipped.
    FailSelector = fun(_Frame) -> fun(Value) -> {yes, Value} end end,
    %% In runtime, constants are looked up and matched against a pattern 
    %% (the pattern acts like a filter), then the filters are run.
    PatternFrames = frame2frames(PatternFrame),
    PatternColumns = 
        lists:flatten(frames_to_columns(PatternFrames, PatternVars,
                                        deref_pattern(Imported), FailSelector,
                                        Imported, LookupOp)),

  Note : ColFil can contain filters for columns that can not be
    %% looked up. Such (possibly bogus) elements are however not used.
  Note : one filter at a time is tested ; only the pattern is
    %% assumed to have been run when the filter is run. Sometimes it
    %% would be advantageously to assume some filter(s) occurring
    %% before the filter had been run as well 
  ( an example : { { X , Y } } < - LE , X = : = 1 , Y = : = a ) .
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    ColFil = [{Column, FId#qid.no} ||
                 {FId,{fil,Fil}} <- 
                     filter_list(FilterData, Dependencies, State),
                 [] =/= (SFs = safe_filter(reset_anno(Fil), PatternFrames,
                                           BindFun, State, Imported)),
                 {GId,PV} <- PatternVars,
                 [] =/= 
                    (Cols = hd(frames_to_columns(SFs, [{GId, PV}],
                                                 deref_lu_skip(LookupOp,
                                                               Imported),
                                                 const_selector(Imported),
                                                 Imported, LookupOp))),
  The filter must not test more than one column ( unless the
                 %% pattern has already done the test):
                 %% Note: if the pattern and the filter test the same
                 %% column, the filter will not be skipped.
  ( an example : { X=1 } < - ... , X = : = 1 ) .
                 length(D = Cols -- PatternColumns) =:= 1,
                 {{_,Col} = Column, Constants} <- D,
                 %% Check that the following holds for all frames.
                 lists:all(
                   fun(Frame) ->
                     %% The column is compared/matched against a constant.
                     %% If there are no more comparisons/matches then
                     %% the filter can be replaced by the lookup of
                     %% the constant.
                     {VarI, FrameI} = unify_column(Frame, PV, Col, BindFun,
                                                   Imported),
                     VarValues = deref_skip(VarI, FrameI, LookupOp, Imported),

                     {NV, F1} = unify_column(PatternFrame, PV, Col, BindFun,
                                             Imported),
                     F2 = unify_var_bindings(VarValues, '=:=', NV, F1, 
                                             BindFun, Imported, false),
                     %% F2: the pattern has been matched and the
                     %% constant has been looked up. If Frame has no
                     %% more bindings than F2 (modulo unique
                     %% variables), then the filter can be skipped. 
                     %% 
                     %% Under rare circumstances (for instance: 
  " X = : = 1 , X = : = U " , U imported ; only 1 is looked up ) ,
                     %% not all constants mentioned in a filter are looked up.
                     %% The filter can only be skipped if all constants
                     %% are looked up.
                     LookedUpConstants = 
                         case lists:keyfind(Column, 1, ColConstants) of
                             false -> [];
                             {Column, LUCs} -> LUCs
                         end,
                     %% Don't try to handle filters that compare several
  values equal . See also frames_to_columns ( ) .
                     length(VarValues) =< 1 andalso
                     (Constants -- LookedUpConstants =:= []) andalso
                     bindings_is_subset(Frame, F2, Imported)
                   end, SFs)],
    ColFils = family_list(ColFil),
    %% The skip tag 'all' means that all filters are covered by the lookup.
  It does not imply that there is only one generator as is the case
    %% for match specifications (see match_spec_quals above).
    [{Col, Constants, skip_tag(Col, ColFils, FilterData)} ||
        {Col,Constants} <- ColConstants].

deref_skip(E, F, _LookupOp, Imported) ->
    deref(E, F, Imported).

deref_lu_skip('==', Imported) ->
    %% Comparing table. Cannot skip filters that match integers.
    BFun = fun(DV, Op) ->
                   Op =:= '==' orelse free_of_integers(DV, Imported)
           end,
    fun(PV, F) -> deref_values(PV, F, BFun, Imported) end;
deref_lu_skip('=:=', Imported) ->
    %% Matching table. Skip filters regardless of operator.
    fun(PV, F) -> deref_values(PV, F, Imported) end.

equal_columns(Qualifiers, AllIVs, Dependencies, State) ->
    {Cs, Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=='),
    join_gens(Cs, Qualifiers, Skip).

eq_columns(Qualifiers, AllIVs, Dependencies, State) ->
    {Cs, Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=:='),
    join_gens(Cs, Qualifiers, Skip).

%% -> {TwoGens, ManyGens}
join_gens(Cs0, Qs, Skip) ->
    Cs = [family_list(C) || C <- Cs0],
    {FD, _GeneratorData} = qual_data(Qs),
    {join_gens2(lists:filter(fun(C) -> length(C) =:= 2 end, Cs), FD, Skip),
     join_gens2(lists:filter(fun(C) -> length(C) > 2 end, Cs), FD, Skip)}.

join_gens2(Cs0, FilterData, Skip) ->
    [{J, skip_tag(case lists:keyfind(J, 1, Skip) of
                      {J, FilL} ->
                          FilL;
                      false ->
                          []
                  end, FilterData)} ||
        J <- lists:append([qlc:all_selections(C) || C <- Cs0])].

skip_tag(FilList, FilterData) ->
    {if
         length(FilterData) =:= length(FilList) ->
             all;
         true ->
             some
     end, FilList}.

skip_tag(Col, ColFils, FilterData) ->
    case lists:keyfind(Col, 1, ColFils) of
        {Col, FilL} ->
            Tag = if
                      length(FilterData) =:= length(FilL) ->
                          all;
                      true ->
                          some
                  end,
            {Tag, FilL};
        false -> 
            {some,[]}
    end.

%% Tries to find columns (possibly in the same table) that are equal.
  If LookupOp is ' = : = ' then " equal " means that the columns are matched ;
  if LookupOp is ' = = ' then " equal " means that the columns are matched or
%% compared.
  - > [ [ { QualifierNumber , ColumnNumber } ] ] % Eq.classes .
join_info(Qualifiers, AllIVs, Dependencies, State, JoinOp) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    {Filter, Anon1, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    BindFun = fun(_Op, V) -> bind_no_const(V, Imported) end,
    {PatternFrame, PatternVars} = 
        pattern_frame(GeneratorData, BindFun, Anon1, State),
    PatternFrames = frame2frames(PatternFrame),
    Fs = filter(Filter, PatternFrames, BindFun, State, Imported),
    SelectorFun = no_const_selector(Imported),
    Cols = frames_to_columns(Fs, PatternVars,
                             fun(PV1, F) -> deref_join(PV1, F, JoinOp) end,
                             SelectorFun, Imported, '=:='),
    JC = join_classes(Cols),
    Skip = join_skip(JC, FilterData, PatternFrame,
                     PatternVars, Dependencies, State, Imported, JoinOp),
    {JC, Skip}.

deref_join(E, Frame, '==') ->
    deref_values(E, Frame, _Imp = []);
deref_join(E, Frame, '=:=') ->
    %% Matching table. It is possible that some objects read from the
    %% other table (the one with the objects to look up) contain
    %% integers. By making all variables imported it is ensured that
    %% comparisons are kept. See also Comparing Terms.
    deref_values(E, Frame, fun(_DV, Op) -> Op =:= '=:=' end, all).

join_classes(Cols0) ->
    ColVar = sofs:relation(lists:append(Cols0)),
    Cols = sofs:partition(2, ColVar),
    [[C || {C,_} <- Cs] || Cs <- sofs:to_external(Cols), length(Cs) > 1].

join_skip(JoinClasses, FilterData, PatternFrame, PatternVars, Dependencies,
          State, Imported, JoinOp) ->
    PatternFrames = frame2frames(PatternFrame),
    ColFil = [{JoinClass,FId#qid.no} ||
                 [{Q1,C1}, {Q2,C2}]=JoinClass <- JoinClasses,
                 {GId1, PV1} <- PatternVars,
                 GId1#qid.no =:= Q1,
                 {GId2, PV2} <- PatternVars,
                 GId2#qid.no =:= Q2,

  Select a filter that depends on the two generators :
                 {FId,{fil,Fil}} <- 
                     filter_list(FilterData, Dependencies, State),
                 {value,{_,GIds}} <- 
                     [lists:keysearch(FId, 1, Dependencies)],
                 GIds =:= lists:sort([GId1,GId2]),

                 begin
                     %% Do what the join does: 
  element(C1 , G1 ) JoinOp element(C2 , G2 ) .
                     %% As for lu_skip: sometimes it would be
                     %% advantageously to assume some filter(s)
                     %% occurring before the join filter had been run
                     %% as well.
                     BindFun = fun(_Op, V) -> is_bindable(V) end,
                     {V1, JF1} = 
                       unify_column(PatternFrame, PV1, C1, BindFun, Imported),
                     {V2, JF2} = 
                         unify_column(JF1, PV2, C2, BindFun, Imported),
                     JF = unify(JoinOp, V1, V2, JF2, BindFun, Imported),

                     %% "Run" the filter:
                     SFs = safe_filter(reset_anno(Fil), PatternFrames,
                                       BindFun, State, Imported),
                     JImp = qlc:vars([SFs, JF]), % kludge
                     lists:all(fun(Frame) -> 
                                       bindings_is_subset(Frame, JF, JImp)
                               end, SFs) andalso SFs =/= []
                 end],
    family_list(ColFil).

filter_info(FilterData, AllIVs, Dependencies, State) ->
    FilterList = filter_list(FilterData, Dependencies, State),
    Filter0 = reset_anno(filters_as_one(FilterList)),
    Anon0 = 0,
    {Filter, Anon1} = anon_var(Filter0, Anon0),
    Imported = ordsets:subtract(qlc:vars(Filter), % anonymous too
                                ordsets:from_list(AllIVs)), 
    {Filter, Anon1, Imported}.

%% Selects the guard filters. Other filters than guard filters are
%% ignored when trying to find constants and join columns. Note: there
%% must not occur any non-guard filter between a guard filter and the
%% generator(s) the guard filter depends on. The reason is that such a
%% filter could fail for some object(s) excluded by lookup or join. If
%% the failing filter is placed _after_ the guard filter, the failing
%% objects have already been filtered out by the guard filter.
  Note : guard filters using variables from one generator are allowed
%% to be placed after further generators (the docs states otherwise, but 
%% this seems to be common practice).
filter_list(FilterData, Dependencies, State) ->
    sel_gf(FilterData, 1, Dependencies, State, [], []).

sel_gf([], _N, _Deps, _RDs, _Gens, _Gens1) ->
    [];
sel_gf([{#qid{no = N}=Id,{fil,F}}=Fil | FData], N, Deps, State, Gens, Gens1) ->
    case is_guard_test(F, State) of
        true ->
            {Id,GIds} = lists:keyfind(Id, 1, Deps),
            case length(GIds) =< 1 of
                true ->
                    case generators_in_scope(GIds, Gens1) of
                        true ->
                            [Fil|sel_gf(FData, N+1, Deps, State, Gens, Gens1)];
                        false ->
                            sel_gf(FData, N + 1, Deps, State, [], [])
                    end;
                false ->
                    case generators_in_scope(GIds, Gens) of
                        true ->
                            [Fil | sel_gf(FData, N + 1, Deps, State, Gens, [])];
                        false ->
                            sel_gf(FData, N + 1, Deps, State, [], [])
                    end
            end;
        false ->
            sel_gf(FData, N + 1, Deps, State, [], [])
    end;
sel_gf(FData, N, Deps, State, Gens, Gens1) ->
    sel_gf(FData, N + 1, Deps, State, [N | Gens], [N | Gens1]).

generators_in_scope(GenIds, GenNumbers) ->
    lists:all(fun(#qid{no=N}) -> lists:member(N, GenNumbers) end, GenIds).

pattern_frame(GeneratorData, BindFun, Anon1, State) ->
    Frame0 = [],
    {PatternFrame, _Anon2, PatternVars} =
        lists:foldl(fun({QId,{gen,Pattern,_}}, {F0,An0,PVs}) ->
                            {F1, An1, PV} = 
                                pattern(Pattern, An0, F0, BindFun, State),
                            {F1, An1, [{QId,PV} | PVs]}
                    end, {Frame0, Anon1, []}, GeneratorData),
    {PatternFrame, PatternVars}.
              
const_selector(Imported) ->
    selector(Imported, fun is_const/2).

no_const_selector(Imported) ->
    selector(Imported, fun(V, I) -> not is_const(V, I) end).

selector(Imported, TestFun) ->
    fun(_Frame) ->
            fun(Value) -> 
                    case TestFun(Value, Imported) of
                        true ->
                            {yes, Value};
                        false ->
                            no
                    end
            end
    end.

bind_no_const(Value, Imported) ->
    case is_const(Value, Imported) of
        true ->
            false;
        false ->
            is_bindable(Value)
    end.

%% Tuple tails are variables, never constants.
is_const(Value, Imported) ->
    %% is_bindable() has checked that E is normalisable. 
    [] =:= ordsets:to_list(ordsets:subtract(qlc:vars(Value), Imported)).

is_bindable(Value) ->
    case normalise(Value) of
        {ok, _C} ->
            true;
        not_ok ->
            false
    end.

pattern(P0, AnonI, Frame0, BindFun, State) ->
    P1 = try 
             expand_pattern_records(P0, State)
         catch _:_ -> P0 % template, records already expanded
         end,
    %% Makes test for equality simple:
    P2 = reset_anno(P1),
    {P3, AnonN} = anon_var(P2, AnonI),
    {P4, F1} = match_in_pattern(tuple2cons(P3), Frame0, BindFun),
    {P, F2} = element_calls(P4, F1, BindFun, _Imp=[]), % kludge for templates
    {var, _, PatternVar} = UniqueVar = unique_var(),
    F = unify('=:=', UniqueVar, P, F2, BindFun, _Imported = []),
    {F, AnonN, PatternVar}.

frame2frames(failed) ->
    [];
frame2frames(F) ->
    [F].

match_in_pattern({match, _, E10, E20}, F0, BF) ->
    {E1, F1} = match_in_pattern(E10, F0, BF),
    {E2, F} = match_in_pattern(E20, F1, BF),
    %% This is for join: chosing a constant could "hide" a variable.
    E = case BF('=:=', E1) of
            true -> E1;
            false -> E2
        end,
    {E, unify('=:=', E1, E2, F, BF, _Imported = [])};
match_in_pattern(T, F0, BF) when is_tuple(T) ->
    {L, F} = match_in_pattern(tuple_to_list(T), F0, BF),
    {list_to_tuple(L), F};
match_in_pattern([E0 | Es0], F0, BF) ->
    {E, F1} = match_in_pattern(E0, F0, BF),
    {Es, F} = match_in_pattern(Es0, F1, BF),
    {[E | Es], F};
match_in_pattern(E, F, _BF) ->
    {E, F}.

-define(ANON_VAR(N), N).

anon_var(E, AnonI) ->
    var_mapfold(fun({var, L, '_'}, N) ->
                        {{var, L, ?ANON_VAR(N)}, N+1};
                   (Var, N) -> {Var, N}
                end, AnonI, E).

reset_anno(T) ->
    set_anno(T, anno0()).

set_anno(T, A) ->
    map_anno(fun(_L) -> A end, T).

-record(fstate, {state, bind_fun, imported}).

filter(_E, []=Frames0, _BF, _State, _Imported) ->
    Frames0;
filter(E0, Frames0, BF, State, Imported) ->
    E = pre_expand(E0),
    FState = #fstate{state = State, bind_fun = BF, imported = Imported},
    filter1(E, Frames0, FState).

  One frame for each path through the and/or expression .
%%
  " A xor B " is equal to " ( A and not B ) or ( not A and B ) " .
%% Ignoring "not B" and "not A" this is the same as "A or B"; 
  " xor " can be handled just as " or " .
%% 
%% One must handle filters with care, both when joining and when
%% looking up values. The reference is a nested loop: if the filter
%% fails for some combination of values, it must fail also when
%% looking up values or joining. In other words, the excluded
%% combinations of values must not evaluate to anything but 'false'.
%% Filters looking like guards are allowed to fail since for such
%% filter the so called guard semantics ensures that the value is
%% 'false' if it is not 'true'. This behavior was inherited from the
%% ordinary list comprehension, where it has been considered a bug
  kept for backward compatibility . Now it has become part of the 
%% semantics, and hard to change (at least in the qlc module).
%%
%% A special case is =/2. If there is a chance that the =/2 fails
%% (badmatch) for some combination of values, that combination cannot
%% be excluded. If the variable is bound only once, it is OK, but not
%% twice (or more). The current implementation does not handle =/2 at
%% all (except in generator patterns).

filter1({op, _, Op, L0, R0}, Fs, FS) when Op =:= '=:='; Op =:= '==' ->
    #fstate{state = S, bind_fun = BF, imported = Imported} = FS,
    %% In the transformed code there are no records in lookup values
    %% because records are expanded away in prep_expr.
    lists:flatmap(fun(F0) ->
                          {L, F1} = prep_expr(L0, F0, S, BF, Imported),
                          {R, F2} = prep_expr(R0, F1, S, BF, Imported),
                          case unify(Op, L, R, F2, BF, Imported) of
                              failed -> [];
                              F -> [F]
                          end
                  end, Fs);
filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'and'; Op =:= 'andalso' ->
    filter1(R, filter1(L, Fs, FS), FS);
filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'or'; 
                                        Op =:= 'orelse';
                                        Op =:= 'xor' ->
    filter1(L, Fs, FS) ++ filter1(R, Fs, FS);
filter1({atom,_,Atom}, _Fs, _FS) when Atom =/= true ->
    [];
filter1({call,L,{remote,_,{atom,_,erlang},{atom,_,is_record}},[T,R]},
        Fs, FS) ->
    filter1({op,L,'=:=',{call,L,{remote,L,{atom,L,erlang},{atom,L,element}},
                         [{integer,L,1},T]},R},
            Fs, FS);
  erlang : is_record/3 ( the size information is ignored ):
filter1({call,L,{remote,L1,{atom,_,erlang}=M,{atom,L2,is_record}},[T,R,_Sz]},
        Fs, FS) ->
    filter1({call,L,{remote,L1,M,{atom,L2,is_record}},[T,R]}, Fs, FS);
filter1(_E, Fs, _FS) ->
    Fs.

%% filter() tries to extract as much information about constant
%% columns as possible. It ignores those parts of the filter that are
%% uninteresting. safe_filter() on the other hand ensures that the
  bindings returned capture _ all _ aspects of the filter ( wrt BF ) .
safe_filter(_E, []=Frames0, _BF, _State, _Imported) ->
    Frames0;
safe_filter(E0, Frames0, BF, State, Imported) ->
    E = pre_expand(E0),
    FState = #fstate{state = State, bind_fun = BF, imported = Imported},
    safe_filter1(E, Frames0, FState).

safe_filter1({op, _, Op, L0, R0}, Fs, FS) when Op =:= '=:='; Op =:= '==' ->
    #fstate{state = S, bind_fun = BF, imported = Imported} = FS,
    lists:flatmap(fun(F0) ->
                          {L, F1} = prep_expr(L0, F0, S, BF, Imported),
                          {R, F2} = prep_expr(R0, F1, S, BF, Imported),
                          case safe_unify(Op, L, R, F2, BF, Imported) of
                              failed -> [];
                              F -> [F]
                          end
                  end, Fs);
safe_filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'and'; Op =:= 'andalso' ->
    safe_filter1(R, safe_filter1(L, Fs, FS), FS);
safe_filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'or'; Op =:= 'orelse' ->
    safe_filter1(L, Fs, FS) ++ safe_filter1(R, Fs, FS);
safe_filter1({atom,_,true}, Fs, _FS) ->
    Fs;
safe_filter1(_E, _Fs, _FS) ->
    [].

%% Substitutions: 
  M : F ( ) for { M , F } ( ) ;  : F ( ) for F ( ) ; is_record ( ) for record ( ) .
pre_expand({call,L1,{atom,L2,record},As}) ->
    pre_expand({call,L1,{atom,L2,is_record},As});
pre_expand({call,L,{atom,_,_}=F,As}) ->
    pre_expand({call,L,{remote,L,{atom,L,erlang},F},As});
pre_expand({call,L,{tuple,_,[M,F]},As}) ->
    pre_expand({call,L,{remote,L,M,F},As});
pre_expand(T) when is_tuple(T) ->
    list_to_tuple(pre_expand(tuple_to_list(T)));
pre_expand([E | Es]) ->
    [pre_expand(E) | pre_expand(Es)];
pre_expand(T) ->
    T.

  - > [ [ { { QualifierNumber , ColumnNumber } , [ Value ] } ] ]
frames_to_columns([], _PatternVars, _DerefFun, _SelectorFun, _Imp, _CompOp) ->
    [];
frames_to_columns(Fs, PatternVars, DerefFun, SelectorFun, Imp, CompOp) ->
    %% It is important that *the same* variables are introduced for
    %% columns in every frame. (When trying to find constant columns
    %% it doesn't matter, but when trying to find joined columns, the
    %% same variables have to be the representatives in every frame.)
    SizesVarsL =
        [begin 
             PatVar = {var,anno0(),PV},
             PatternSizes = [pattern_size([F], PatVar, false) || 
                                F <- Fs],
             MaxPZ = lists:max([0 | PatternSizes -- [undefined]]),
             Vars = pat_vars(MaxPZ),
             {PatternId#qid.no, PatVar, PatternSizes, Vars}
         end || {PatternId, PV} <- PatternVars],
    BF = fun(_Op, Value) -> is_bindable(Value) end,
    Fun = fun({_PatN, PatVar, PatSizes, Vars}, Frames) -> 
                  [unify('=:=', pat_tuple(Sz, Vars), PatVar, Frame, BF, Imp) ||
                      {Sz, Frame} <- lists:zip(PatSizes, Frames)]
          end,
    NFs = lists:foldl(Fun, Fs, SizesVarsL),
    [frames2cols(NFs, PatN, PatSizes, Vars, DerefFun, SelectorFun, CompOp) ||
        {PatN, _PatVar, PatSizes, Vars} <- SizesVarsL].

frames2cols(Fs, PatN, PatSizes, Vars, DerefFun, SelectorFun, CompOp) ->
    Rs = [ begin
               RL = [{{PatN,Col},cons2tuple(element(2, Const))} ||
                        {V, Col} <- lists:zip(lists:sublist(Vars, PatSz),
                                              lists:seq(1, PatSz)),
                        %% Do not handle the case where several
  values compare equal , e.g. " X = : = 1
  andalso X = = 1.0 " . Looking up both
  values or one of them wo n't always do
                        %% because it is more or less undefined
                        %% whether the table returns the given key
  or the one stored in the table . Or
                        %% rather, it would be strange if the table
                        %% did not return the stored key upon
                        %% request, but the 'lookup_fun' function
                        %% may have to add the given key (see also
  gb_table in qlc(3 ) ) . ( Not a very strong
  argument . " X = : = 1 " could ( should ? ) be
                        %% seen as a bug.) Note: matching tables
                        %% cannot skip the filter, but looking up
                        %% one of the values should be OK.
                        tl(Consts = DerefFun(V, F)) =:= [],
                        (Const = (SelectorFun(F))(hd(Consts))) =/= no],
               sofs:relation(RL) % possibly empty
            end || {F,PatSz} <- lists:zip(Fs, PatSizes)],
    Ss = sofs:from_sets(Rs),
    %% D: columns occurring in every frame (path).
    D = sofs:intersection(sofs:projection(fun(S) -> sofs:projection(1, S) end,
                                          Ss)),
    Cs = sofs:restriction(sofs:relation_to_family(sofs:union(Ss)), D),
    [C || {_,Vs}=C <- sofs:to_external(Cs), not col_ignore(Vs, CompOp)].

pat_vars(N) ->
    [unique_var() || _ <- lists:seq(1, N)].

pat_tuple(Sz, Vars) when is_integer(Sz), Sz > 0 ->
    TupleTail = unique_var(),
    {cons_tuple, list2cons(lists:sublist(Vars, Sz) ++ TupleTail)};
pat_tuple(_, _Vars) ->
    unique_var().

  Do not handle tests as " X = : = 1.0 orelse X = = 1 " either .
%% Similar problems as described above.
col_ignore(_Vs, '=:=') ->
    false;
col_ignore(Vs, '==') ->
    length(Vs) =/= length(lists:usort([element(2, normalise(V)) || V <- Vs])).

pattern_sizes(PatternVars, Fs) ->
    [{QId#qid.no, Size} || 
        {QId,PV} <- PatternVars,
        undefined =/= (Size = pattern_size(Fs, {var,anno0(),PV}, true))].

pattern_size(Fs, PatternVar, Exact) ->
    Fun = fun(F) -> (deref_pattern(_Imported = []))(PatternVar, F) end,
    Derefs = lists:flatmap(Fun, Fs),
    Szs = [pattern_sz(Cs, 0, Exact) || {cons_tuple, Cs} <- Derefs],
    case lists:usort(Szs) of
        [Sz] when is_integer(Sz), Sz >= 0 -> Sz;
        [] when not Exact -> 0;
        _  -> undefined
    end.

pattern_sz({cons,_,_C,E}, Col, Exact) ->
    pattern_sz(E, Col+1, Exact);
pattern_sz({nil,_}, Sz, _Exact) ->
    Sz;
pattern_sz(_, _Sz, true) ->
    undefined;
pattern_sz(_, Sz, false) ->
    Sz.

deref_pattern(Imported) ->
    fun(PV, F) -> deref_values(PV, F, Imported) end.

prep_expr(E, F, S, BF, Imported) ->
    element_calls(tuple2cons(expand_expr_records(E, S)), F, BF, Imported).

unify_column(Frame, Var, Col, BindFun, Imported) ->
    A = anno0(),
    Call = {call,A,{remote,A,{atom,A,erlang},{atom,A,element}},
	    [{integer,A,Col}, {var,A,Var}]},
    element_calls(Call, Frame, BindFun, Imported).

%% cons_tuple is used for representing {V1, ..., Vi | TupleTail}.
%%
%% Tests like "element(2, X) =:= a" are represented by "tuple tails":
%% {_, a | _}. The tail may be unified later, when more information
%% about the size of the tuple is known.
element_calls({call,_,{remote,_,{atom,_,erlang},{atom,_,element}},
               [{integer,_,I},Term0]}, F0, BF, Imported) when I > 0 ->
    %% Note: erl_expand_records ensures that all calls to element/2
  have an explicit " erlang : " prefix .
    TupleTail = unique_var(),
    VarsL = [unique_var() || _ <- lists:seq(1, I)],
    Vars = VarsL ++ TupleTail,
    Tuple = {cons_tuple, list2cons(Vars)},
    VarI = lists:nth(I, VarsL),
    {Term, F} = element_calls(Term0, F0, BF, Imported),
    {VarI, unify('=:=', Tuple, Term, F, BF, Imported)};
element_calls(T, F0, BF, Imported) when is_tuple(T) ->
    {L, F} = element_calls(tuple_to_list(T), F0, BF, Imported),
    {list_to_tuple(L), F};
element_calls([E0 | Es0], F0, BF, Imported) ->
    {E, F1} = element_calls(E0, F0, BF, Imported),
    {Es, F} = element_calls(Es0, F1, BF, Imported),
    {[E | Es], F};
element_calls(E, F, _BF, _Imported) ->
    {E, F}.

unique_var() ->
    {var, anno0(), make_ref()}.

is_unique_var({var, _L, V}) ->
    is_reference(V).

expand_pattern_records(P, State) ->
    A = anno0(),
    E = {'case',A,{atom,A,true},[{clause,A,[P],[],[{atom,A,true}]}]},
    {'case',_,_,[{clause,A,[NP],_,_}]} = expand_expr_records(E, State),
    NP.

expand_expr_records(E, State) ->
    RecordDefs = State#state.records,
    A = anno1(),
    Forms0 = RecordDefs ++ [{function,A,foo,0,[{clause,A,[],[],[pe(E)]}]}],
    Forms = erl_expand_records:module(Forms0, [no_strict_record_tests]),
    {function,_,foo,0,[{clause,_,[],[],[NE]}]} = lists:last(Forms),
    NE.

%% Partial evaluation.
pe({op,Line,Op,A}) ->
    erl_eval:partial_eval({op,Line,Op,pe(A)});
pe({op,Line,Op,L,R}) ->
    erl_eval:partial_eval({op,Line,Op,pe(L),pe(R)});
pe(T) when is_tuple(T) ->
    list_to_tuple(pe(tuple_to_list(T)));
pe([E | Es]) ->
    [pe(E) | pe(Es)];
pe(E) ->
    E.

unify(Op, E1, E2, F, BF, Imported) ->
    unify(Op, E1, E2, F, BF, Imported, false).

safe_unify(Op, E1, E2, F, BF, Imported) ->
    unify(Op, E1, E2, F, BF, Imported, true).

unify(_Op, _E1, _E2, failed, _BF, _Imported, _Safe) -> % contradiction
    failed;
unify(_Op, E, E, F, _BF, _Imported, _Safe) ->
    F;
unify(Op, {var, _, _}=Var, E2, F, BF, Imported, Safe) ->
    extend_frame(Op, Var, E2, F, BF, Imported, Safe);
unify(Op, E1, {var, _, _}=Var, F, BF, Imported, Safe) ->
    extend_frame(Op, Var, E1, F, BF, Imported, Safe);
unify(Op, {cons_tuple, Es1}, {cons_tuple, Es2}, F, BF, Imported, Safe) ->
    unify(Op, Es1, Es2, F, BF, Imported, Safe);
unify(Op, {cons, _, L1, R1}, {cons, _, L2, R2}, F, BF, Imported, Safe) ->
    E = unify(Op, L1, L2, F, BF, Imported, Safe),
    unify(Op, R1, R2, E, BF, Imported, Safe);
unify(Op, E1, E2, F, _BF, _Imported, Safe) ->
    try
      {ok, C1} = normalise(E1),
      {ok, C2} = normalise(E2),
      if 
          Op =:= '=:=', C1 =:= C2 ->
              F;
          Op =:= '==', C1 == C2 ->
              F;
          true ->
              failed
      end 
    catch error:_ when Safe -> failed;
          error:_ when not Safe -> F   % ignored
    end.
%% Binaries are not handled at all (by unify).

%% Note that a variable can be bound to several values, for instance:
  X = : = 3 , X = = 3.0 . As a consequence , deref ( ) returns a list of
%% values.

%% Binding a variable to several values makes the unification and
%% dereferencing more complicated. An alternative would be not to try
%% to find lookup values for such QLCs at all. That might have been a
%% better design decision.

-record(bind, {var, value, op}). 

extend_frame(Op, Var, Value, F, BF, Imported, Safe) ->
    case var_values(Var, F) of
        [] ->
            case Value of
                {var, _, _} ->
                    case var_values(Value, F) of
                        [] ->
                            add_binding(Op, Value, Var, F, BF, Imported, Safe);
                        ValsOps ->
                            maybe_add_binding(ValsOps, Op, Value, Var, F, 
                                              BF, Imported, Safe)
                    end;
                _ ->
                    add_binding(Op, Var, Value, F, BF, Imported, Safe)
            end;
        ValsOps ->
            maybe_add_binding(ValsOps, Op, Var, Value, F, BF, Imported, Safe)
    end.

maybe_add_binding(ValsOps, Op, Var, Value, F0, BF, Imported, Safe) ->
    case unify_var_bindings(ValsOps, Op, Value, F0, BF, Imported, Safe) of
        failed ->
            failed;
        F ->
            case already_bound(Op, Var, Value, F) of
                true -> 
                    F;
                false ->
                    add_binding(Op, Var, Value, F, BF, Imported, Safe)
            end
    end.

already_bound(Op, Var, Value, F) ->
    %% Note: all variables are treated as imported. The dereferenced
    %% values must not depend on Imported.
    BFun = fun(_DV, BOp) ->  Op =:= BOp end,
    DerefValue = deref_value(Value, Op, F, BFun, all),
    DerefVar = deref_var(Var, F, BFun, all),
    DerefValue -- DerefVar =:= [].

unify_var_bindings([], _Op, _Value, F, _BF, _Imported, _Safe) ->
    F;
unify_var_bindings([{VarValue, Op2} | Bindings],
                   Op1, Value, F0, BF, Imported, Safe) ->
    Op = deref_op(Op1, Op2),
    case unify(Op, VarValue, Value, F0, BF, Imported, Safe) of
        failed ->
            failed;
        F ->
            unify_var_bindings(Bindings, Op1, Value, F, BF, Imported, Safe)
    end.

deref_op('=:=', '=:=') ->
    '=:=';
deref_op(_, _) ->
    '=='.

  Note : usort works ; { integer , L,3 } does not match { float , L,3.0 } .

var_values(Var, Frame) ->
    [{Value, Op} || 
        #bind{value = Value, op = Op} <- var_bindings(Var, Frame)].

deref_var(Var, Frame, Imported) ->
    deref_var(Var, Frame, fun(_DV, _Op) -> true end, Imported).

deref_var(Var, Frame, BFun, Imported) ->
    lists:usort([ValOp || 
                    #bind{value = Value, op = Op} <- var_bindings(Var, Frame),
                    ValOp <- deref_value(Value, Op, Frame, BFun, Imported)]).

deref_value(Value, Op, Frame, BFun, Imported) ->
    lists:usort([{Val,value_op(ValOp, Op, Imported)} || 
                    {Val,_Op}=ValOp <- deref(Value, Frame, BFun, Imported)]).

add_binding(Op, Var0, Value0, F, BF, Imported, Safe) ->
    {Var, Value} = maybe_swap_var_value(Var0, Value0, F, Imported),
    case BF(Op, Value) of
        true ->
            add_binding2(Var, Value, Op, F);
        false when Safe ->
            failed;
        false when not Safe ->
            F
    end.

add_binding2(Var, Value, Op, F) ->
    case occurs(Var, Value, F) of
        true ->
            failed;
        false ->
            [#bind{var = Var, value = Value, op = Op} | F]
    end.

%% Ensure that imported variables are visible in the dereferenced
%% value by pushing them to the end of the binding chain. Be careful
%% not to introduce loops.
maybe_swap_var_value(Var, Value, Frame, Imported) ->
    case do_swap_var_value(Var, Value, Frame, Imported) of
        true ->
            {Value, Var};
        false ->
            {Var, Value}
    end.

do_swap_var_value({var, _, V1}=Var1, {var, _, V2}=Var2, F, Imported) ->
    case swap_vv(Var1, Var2, F) of
        [] ->
            case swap_vv(Var2, Var1, F) of
                [] ->
                    ordsets:is_element(V1, Imported) andalso 
                        not ordsets:is_element(V2, Imported);
                _Bs ->
                    true
            end;                
        _Bs ->
           false
    end;
do_swap_var_value(_, _, _F, _Imp) ->
    false.

swap_vv(V1, V2, F) ->
    [V || #bind{value = V} <- var_bindings(V1, F), V =:= V2].

normalise(E) ->
    %% Tuple tails are OK.
    case catch erl_parse:normalise(var2const(cons2tuple(E))) of
        {'EXIT', _} ->
            not_ok;
        C ->
            {ok, C}
    end.

occurs(V, V, _F) ->
    true;
occurs(V, {var, _, _} = Var, F) ->
    lists:any(fun(B) -> occurs(V, B#bind.value, F) end, var_bindings(Var, F));
occurs(V, T, F) when is_tuple(T) ->
    lists:any(fun(E) -> occurs(V, E, F) end, tuple_to_list(T));
occurs(V, [E | Es], F) ->
    occurs(V, E, F) orelse occurs(V, Es, F);
occurs(_V, _E, _F) ->
    false.

deref_values(E, Frame, Imported) ->
    deref_values(E, Frame, fun(_DV, _Op) -> true end, Imported).

deref_values(E, Frame, BFun, Imported) ->
    lists:usort([V || 
                    {V, Op} <- deref(E, Frame, BFun, Imported),
                    BFun(V, Op)]).

deref(E, F, Imp) ->
    BFun = fun(_DV, _Op) -> true end,
    deref(E, F, BFun, Imp).

deref({var, _, _}=V, F, BFun, Imp) ->
    DBs = lists:flatmap(fun(B) -> deref_binding(B, F, BFun, Imp) 
                        end, var_bindings(V, F)),
    case DBs of
        [] ->
            [{V, '=:='}];
        _ ->
            lists:usort(DBs)
    end;
deref(T, F, BFun, Imp) when is_tuple(T) ->
    [{list_to_tuple(DL), Op} || 
        {DL, Op} <- deref(tuple_to_list(T), F, BFun, Imp)];
deref(Es, F, BFun, Imp) when is_list(Es) ->
    L = [deref(C, F, BFun, Imp) || C <- Es],
    lists:usort([deref_list(S) || S <- all_comb(L)]);
deref(E, _F, _BFun, _Imp) ->
    [{E, '=:='}].

var_bindings(Var, F) ->
    [B || #bind{var = V}=B <- F, V =:= Var].

deref_binding(Bind, Frame, BFun, Imp) ->
    #bind{value = Value, op = Op0} = Bind,
    [{Val, Op} ||
        {Val, _Op}=ValOp <- deref(Value, Frame, BFun, Imp),
        BFun(Val, Op = value_op(ValOp, Op0, Imp))].
    
deref_list(L) ->
    Op = case lists:usort([Op || {_Val, Op} <- L]) of
             ['=:='] ->
                 '=:=';
             _ ->
                 '=='
         end,
    {[V || {V, _Op} <- L], Op}.

value_op({_V, '=='}, _BindOp, _Imp) ->
    '==';
value_op({_V, '=:='}, _BindOp='=:=', _Imp) ->
    '=:=';
value_op({V, '=:='}, _BindOp='==', Imp) ->
    case free_of_integers(V, Imp) of
        true ->
            '=:=';
        false ->
            '=='
    end.

all_comb([]) ->
    [[]];
all_comb([Cs | ICs]) ->
    [[C | L] || C <- Cs, L <- all_comb(ICs)].

%% "Free of integers" here means that there are not imported variables
%% in V (which could take on integer values), but there may be other
%% variables in V.
free_of_integers(V, Imported) ->
    not has_integer(V) andalso not has_imported_vars(V, Imported).

%% Assumes that imported variables are representatives, if Value is a
%% dereferenced value.
has_imported_vars(Value, all) ->
    qlc:vars(Value) =/= [];
has_imported_vars(Value, Imported) ->
    [Var || Var <- qlc:vars(Value), lists:member(Var, Imported)] =/= [].

has_integer(Abstr) ->
    try
        has_int(Abstr)
    catch throw:true -> true
    end.

has_int({integer,_,I}) when float(I) == I ->
    throw(true);
has_int({float,_,F}) when round(F) == F ->
    throw(true);
has_int(T) when is_tuple(T) ->
    has_int(tuple_to_list(T));
has_int([E | Es]) ->
    has_int(E), 
    has_int(Es);
has_int(_) ->
    false.

tuple2cons({tuple, _, Es}) ->
    {cons_tuple, list2cons(tuple2cons(Es))};
tuple2cons(T) when is_tuple(T) ->
    list_to_tuple(tuple2cons(tuple_to_list(T)));
tuple2cons([E | Es]) ->
    [tuple2cons(E) | tuple2cons(Es)];
tuple2cons(E) ->
    E.

list2cons([E | Es]) ->
    {cons, anno0(), E, list2cons(Es)};
list2cons([]) ->
    {nil, anno0()};
list2cons(E) ->
    E.

%% Returns {..., Variable} if Variable is a tuple tail.
cons2tuple({cons_tuple, Es}) ->
    {tuple, anno0(), cons2list(Es)};
cons2tuple(T) when is_tuple(T) ->
    list_to_tuple(cons2tuple(tuple_to_list(T)));
cons2tuple([E | Es]) ->
    [cons2tuple(E) | cons2tuple(Es)];
cons2tuple(E) ->
    E.

cons2list({cons, _, L, R}) ->
    [cons2tuple(L) | cons2list(R)];
cons2list({nil, _}) ->
    [];
cons2list(E) -> % tuple tail (always a variable)
    [cons2tuple(E)].

  Returns true if all bindings in F1 also occur in F2 .
  Viewing F1 and F2 as sets , the fact that F1 is a subset of F2 iff
  F1 union F2 is equal to F2 is used . ( This should take care of
%% issues with anonymous variables.)
bindings_is_subset(F1, F2, Imported) ->
    BF = fun(_Op, _Value) -> true end, % don't need any test here
  Extend F2 with the bindings in F1 :
    F = lists:foldl(fun(#bind{var = V, value = Value, op = Op}, Frame) ->
                            unify(Op, V, Value, Frame, BF, Imported)
                    end, F2, F1),
    bindings_subset(F, F2, Imported) andalso bindings_subset(F2, F, Imported).

bindings_subset(F1, F2, Imp) ->
    Vars = lists:usort([V || #bind{var = V} <- F1, not is_unique_var(V)]),
    lists:all(fun(V) ->
                      deref_var(V, F1, Imp) =:= deref_var(V, F2, Imp)
              end, Vars).

%% Recognizes all QLCs on the form [T || P <- LE, F] such that
  ets : fun2ms(fun(P ) when F - > T end ) is a match spec . This is OK with
%% the guard semantics implemented in filter/_ below. If one chooses
%% not to have guard semantics, affected filters will have to be
%% recognized and excluded here as well.
try_ms(E, P, Fltr, State) ->
    L = anno1(),
    Fun =  {'fun',L,{clauses,[{clause,L,[P],[[Fltr]],[E]}]}},
    Expr = {call,L,{remote,L,{atom,L,ets},{atom,L,fun2ms}},[Fun]},
    Form = {function,L,foo,0,[{clause,L,[],[],[Expr]}]},
    X = ms_transform:parse_transform(State#state.records ++ [Form], []),
    case catch 
        begin
            {function,L,foo,0,[{clause,L,[],[],[MS0]}]} = lists:last(X),
            MS = erl_parse:normalise(var2const(MS0)),
            XMS = ets:match_spec_compile(MS),
            true = ets:is_compiled_ms(XMS),
            {ok, MS, MS0} 
        end of
        {'EXIT', _Reason} ->
            no;
        Reply ->
            Reply
    end.

filters_as_one([]) ->
    {atom, anno0(), true};
filters_as_one(FilterData) ->
    [{_,{fil,Filter1}} | Filters] = lists:reverse(FilterData),
    lists:foldr(fun({_QId,{fil,Filter}}, AbstF) ->
                        {op,anno0(),'andalso',Filter,AbstF}
                end, Filter1, Filters).

qual_data(Qualifiers) ->
    F = fun(T) -> 
                [{QId,Q} || {QId,_,_,Q} <- Qualifiers, element(1,Q) =:= T]
        end,
    {F(fil), F(gen)}.

set_field(Pos, Fs, Data) ->
    lists:sublist(Fs, Pos-1) ++ [Data] ++ lists:nthtail(Pos, Fs).

qdata([{#qid{no = QIdNo},{_QIVs,{{gen,_P,LE,_GV},GoI,SI}}} | QCs], L) ->
    Init = case LE of 
               {join, Op, Q1, Q2, H1, H2, Cs1_0, Cs2_0} ->
                   Cs1 = qcon(Cs1_0),
                   Cs2 = qcon(Cs2_0),
                   %% -- R12B-3: {nil,L}
                   %% R12B-4 --: {atom,L,v1}
                   Compat = {atom,L,v1}, % meant for redundant match spec
                   CF = closure({tuple,L,[Cs1,Cs2,Compat]}, L),
                   {tuple,L,[?A(join),?A(Op),?I(Q1),?I(Q2),H1,H2,CF]};
               _ ->
                   closure(LE, L)
           end,
    %% Create qual_data (see qlc.erl):
    {cons,L,{tuple,L,[?I(QIdNo),?I(GoI),?I(SI),{tuple,L,[?A(gen),Init]}]},
     qdata(QCs, L)};
qdata([{#qid{no = QIdNo},{_QIVs,{{fil,_F},GoI,SI}}} | QCs], L) ->
    %% Create qual_data (see qlc.erl):
    {cons,L,{tuple,L,[?I(QIdNo),?I(GoI),?I(SI),?A(fil)]},qdata(QCs, L)};
qdata([], L) ->
    {nil,L}.

qcon(Cs) ->
    A = anno0(),
    list2cons([{tuple,A,[{integer,A,Col},list2cons(qcon1(ConstOps))]} ||
                  {Col,ConstOps} <- Cs]).

qcon1(ConstOps) ->
    A = anno0(),
    [{tuple,A,[Const,abstr(Op, A)]} || {Const,Op} <- ConstOps].

%% The original code (in Source) is used for filters and the template
%% since the translated code can have QLCs and we don't want them to
%% be visible.
qcode(E, QCs, Source, L, State) ->
    CL = [begin
              Bin = term_to_binary(C, [compressed]),
              {bin, L, [{bin_element, L, 
                         {string, L, binary_to_list(Bin)},
                         default, default}]}
          end || {_,C} <- lists:keysort(1, [{qlc:template_state(),E} | 
                                            qcode(QCs, Source, State)])],
    {'fun', L, {clauses, [{clause, L, [], [], [{tuple, L, CL}]}]}}.

qcode([{_QId, {_QIvs, {{gen,P,_LE,_GV}, GoI, _SI}}} | QCs], Source, State) ->
    [{GoI,undo_no_shadows(P, State)} | qcode(QCs, Source, State)];
qcode([{QId, {_QIVs, {{fil,_F}, GoI, _SI}}} | QCs], Source, State) ->
    {ok,OrigF} = dict:find(QId, Source),
    [{GoI,undo_no_shadows(OrigF, State)} | qcode(QCs, Source, State)];
qcode([], _Source, _State) ->
    [].

closure(Code, L) ->
    {'fun',L,{clauses,[{clause,L,[],[],[Code]}]}}.

simple(L, Var, Init, Anno) ->
    {tuple,L,[?A(simple_v1),?A(Var),Init,abstr(loc(Anno), Anno)]}.

clauses([{QId,{QIVs,{QualData,GoI,S}}} | QCs], RL, Fun, Go, NGV, E, IVs,St) ->
    ?DEBUG("QIVs = ~p~n", [QIVs]),
    ?DEBUG("IVs = ~p~n", [IVs]),
    ?DEBUG("GoI = ~p, S = ~p~n", [GoI, S]),
    L = no_compiler_warning(get_lcid_line(QId#qid.lcid)),
    Cs = case QualData of
             {gen,P,_LE,GV} ->
                 generator(S, QIVs, P, GV, NGV, E, IVs, RL, Fun, Go,GoI,L,St);
             {fil,F} ->
                 filter(F, L, QIVs, S, RL, Fun, Go, GoI, IVs, St)
         end,
    Cs ++ clauses(QCs, RL, Fun, Go, NGV, E, IVs, St);
clauses([], _RL, _Fun, _Go, _NGV, _IVs, _E, _St) ->
    [].

final(RL, IVs, L, State) ->
    IAs = replace(IVs, IVs, '_'),
    AsL = pack_args([?I(0) | abst_vars([RL, '_', '_'] ++ IAs, L)], L, State),
    Grd = [is_list_c(RL, L)],
    Rev = {call,L,{remote,L,?A(lists),?A(reverse)},[?V(RL)]},
    CL = {clause,L,AsL,[Grd],[Rev]},
    AsF = pack_args([?I(0) | abst_vars(['_', '_', '_'] ++ IAs, L)], L, State),
    CF = {clause,L,AsF,[],[?ABST_NO_MORE]},
    [CL, CF].

template(E, RL, Fun, Go, AT, L, IVs, State) ->
    I = qlc:template_state(), GoI = qlc:template_state(),
    ARL = {cons,L,E,abst_vars(RL, L)},
    Next = next(Go, GoI, L),
    As0 = abst_vars([RL, Fun, Go] ++ IVs, L),
    As = pack_args([?I(I) | As0], L, State),
    NAs = pack_args([Next, ARL] ++ abst_vars([Fun, Go] ++ IVs, L), L, State),
    Grd = [is_list_c(RL, L)],
    CL = {clause,L,As,[Grd],[{call,L,?V(Fun),NAs}]},

    %% Extra careful here or arguments will be lifted into a wide fun.
    F = case split_args([Next | As0], L, State) of
            {ArgsL, ArgsT} -> 
                Call = {call,L,?V(Fun),ArgsL++[{var,L,AT}]},
                {block,L,
                 [{match,L,{var,L,AT},ArgsT},
                  {'fun',L,{clauses,[{clause,L,[],[],[Call]}]}}]};
            FNAs ->
                {'fun',L,{clauses,[{clause,L,[],[],[{call,L,?V(Fun),FNAs}]}]}}
        end,
    CF = {clause,L,As,[],[?ABST_MORE(E, F)]},
    [CL,CF].

generator(S, QIVs, P, GV, NGV, E, IVs, RL, Fun, Go, GoI, L, State) ->
    ComAs = abst_vars([RL, Fun, Go], L),
    InitC = generator_init(S, L, GV, RL, Fun, Go, GoI, IVs, State),
    As = [?I(S + 1)| ComAs ++ abst_vars(replace(QIVs -- [GV], IVs, '_'), L)],

    MatchS = next(Go, GoI + 1, L),
    AsM0 = [MatchS | ComAs ++ abst_vars(replace([GV], IVs, NGV), L)],
    AsM = pack_args(AsM0, L, State),

    ContS = ?I(S + 1),
    QIVs__GV = QIVs -- [GV],
    Tmp = replace([GV], replace(QIVs__GV, IVs, nil), NGV),
    AsC = pack_args([ContS | ComAs ++ abst_vars(Tmp, L)], L, State),

    DoneS = next(Go, GoI, L),
    AsD0 = [DoneS | ComAs ++ abst_vars(replace(QIVs, IVs, nil), L)],
    AsD = pack_args(AsD0, L, State),

    CsL = generator_list(P, GV, NGV, As, AsM, AsC, AsD, Fun, L, State),
    CsF = generator_cont(P, GV, NGV, E, As, AsM, AsC, AsD, Fun, L, State),
    [InitC | CsL ++ CsF].
    
generator_init(S, L, GV, RL, Fun, Go, GoI, IVs, State) ->
    As0 = abst_vars([RL, Fun, Go] ++ replace([GV], IVs, '_'), L),
    As = pack_args([?I(S) | As0], L, State),
    Next = next(Go, GoI + 2, L),
    NAs = pack_args([?I(S + 1) | replace([?V('_')], As0, Next)], L, State),
    {clause,L,As,[],[{call,L,?V(Fun),NAs}]}.

generator_list(P, GV, NGV, As, AsM, AsC, AsD, Fun, L, State) ->
    As1 = pack_args(replace([?V(GV)], As, {cons,L,P,?V(NGV)}), L, State),
    As2 = pack_args(replace([?V(GV)], As, {cons,L,?V('_'),?V(NGV)}), L,State),
    As3 = pack_args(replace([?V(GV)], As, {nil,L}), L, State),
    CM = {clause,L,As1,[],[{call,L,?V(Fun),AsM}]},
    CC = {clause,L,As2,[],[{call,L,?V(Fun),AsC}]},
    CD = {clause,L,As3,[],[{call,L,?V(Fun),AsD}]},
    [CM, CC, CD].

%% The clause 'CE' was added in R11B. The version of the generated was
%% however not incremented.
generator_cont(P, GV, NGV, E, As0, AsM, AsC, AsD, Fun, L, State) ->
    As = pack_args(As0, L, State),
    CF1 = ?ABST_MORE(P, ?V(NGV)),
    CF2 = ?ABST_MORE(?V('_'), ?V(NGV)),
    CF3 = ?ABST_NO_MORE,
    CF4 = ?V(E),
    CM = {clause,L,[CF1],[],[{call,L,?V(Fun),AsM}]},
    CC = {clause,L,[CF2],[],[{call,L,?V(Fun),AsC}]},
    CD = {clause,L,[CF3],[],[{call,L,?V(Fun),AsD}]},
    CE = {clause,L,[CF4],[],[CF4]},
    Cls = [CM, CC, CD, CE],
    B = {'case',L,{call,L,?V(GV),[]},Cls},
    [{clause,L,As,[],[B]}].
    
filter(E, L, QIVs, S, RL, Fun, Go, GoI, IVs, State) ->
    IAs = replace(QIVs, IVs, '_'),
    As = pack_args([?I(S) | abst_vars([RL, Fun, Go] ++ IAs, L)], L, State),
    NAs = abst_vars([RL, Fun, Go] ++ IVs, L),
    TNext = next(Go, GoI + 1, L),
    FNext = next(Go, GoI, L),
    NAsT = pack_args([TNext | NAs], L, State),
    NAsF = pack_args([FNext | NAs], L, State),
    %% This is the "guard semantics" used in ordinary list
    %% comprehension: if a filter looks like a guard test, it returns
    %% 'false' rather than fails.
    Body = case is_guard_test(E, State) of
               true -> 
                   CT = {clause,L,[],[[E]],[{call,L,?V(Fun),NAsT}]},
                   CF = {clause,L,[],[[?A(true)]],[{call,L,?V(Fun),NAsF}]},
                   [{'if',L,[CT,CF]}];
               false -> 
                   CT = {clause,L,[?A(true)],[],[{call,L,?V(Fun),NAsT}]},
                   CF = {clause,L,[?A(false)],[],[{call,L,?V(Fun),NAsF}]},
                   [{'case',L,E,[CT,CF]}]
           end,
    [{clause,L,As,[],Body}].
    
pack_args(Args, L, State) ->
    case split_args(Args, L, State) of
        {ArgsL, ArgsT} ->
            ArgsL ++ [ArgsT];
        _ ->
            Args
    end.

split_args(Args, L, State) when length(Args) > State#state.maxargs ->
    {lists:sublist(Args, State#state.maxargs-1), 
     {tuple,L,lists:nthtail(State#state.maxargs-1, Args)}};
split_args(Args, _L, _State) ->
    Args.
    
%% Replace every element in IEs that is a member of Es by R, keep all
%% other elements as they are.
replace(Es, IEs, R) ->
    [case lists:member(E, Es) of
         true -> R; 
         false -> E 
     end || E <- IEs].

is_list_c(V, L) ->
    {call,L,?A(is_list),[?V(V)]}.

next(Go, GoI, L) ->
    {call,L,?A(element),[?I(GoI),?V(Go)]}.

aux_vars(Vars, LcN, AllVars) ->
    [aux_var(Name, LcN, 0, 1, AllVars) || Name <- Vars].

aux_var(Name, LcN, QN, N, AllVars) ->
    qlc:aux_name(lists:concat([Name, LcN, '_', QN, '_']), N, AllVars).

no_compiler_warning(L) ->
    Anno = erl_anno:new(L),
    erl_anno:set_generated(true, Anno).

loc(A) ->
    erl_anno:location(A).

list2op([E], _Op) ->
    E;
list2op([E | Es], Op) ->
    {op,anno0(),Op,E,list2op(Es, Op)}.

anno0() ->
    erl_anno:new(0).

anno1() ->
    erl_anno:new(1).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

qual_fold(Fun, GlobAcc0, Acc0, Forms, State) ->
    F = fun(Id, {lc,L,E,Qs0}, GA0) ->
                {Qs,GA,_NA} = qual_fold(Qs0, Fun, GA0, Acc0, Id, 1, []),
                {{lc,L,E,Qs},GA};
           (_Id, Expr, GA) ->
                {Expr,GA}
        end,
    qlc_mapfold(F, GlobAcc0, Forms, State).

qual_fold([Q0 | Qs], F, GA0, A0, Id, No, NQs) ->
    QId = qid(Id, No),
    {Q,GA,A} = F(QId, Q0, GA0, A0),
    qual_fold(Qs, F, GA, A, Id, No + 1, [Q | NQs]);
qual_fold([], _F, GA, A, _Id, _No, NQs) ->
    {lists:reverse(NQs),GA,A}.

qlc_mapfold(Fun, Acc0, Forms0, State) ->
    {Forms, A, _NNo} = qlcmf(Forms0, Fun, State#state.imp, Acc0, 1),
    erase(?QLC_FILE),
    {Forms, A}.

qlcmf([E0 | Es0], F, Imp, A0, No0) ->
    {E, A1, No1} = qlcmf(E0, F, Imp, A0, No0),
    {Es, A, No} = qlcmf(Es0, F, Imp, A1, No1),
    {[E | Es], A, No};
qlcmf(?QLC_Q(L1, L2, L3, L4, LC0, Os0), F, Imp, A0, No0) when length(Os0) < 2 ->
    {Os, A1, No1} = qlcmf(Os0, F, Imp, A0, No0),
    {LC, A2, No} = qlcmf(LC0, F, Imp, A1, No1), % nested...
    NL = make_lcid(L1, No),
    {T, A} = F(NL, LC, A2),
    {?QLC_Q(L1, L2, L3, L4, T, Os), A, No + 1};
qlcmf(?IMP_Q(L1, L2, LC0, Os0), F, Imp=true, A0, No0) when length(Os0) < 2 ->
    {Os, A1, No1} = qlcmf(Os0, F, Imp, A0, No0),
    {LC, A2, No} = qlcmf(LC0, F, Imp, A1, No1), % nested...
    NL = make_lcid(L, No),
    {T, A} = F(NL, LC, A2),
    {?IMP_Q(L1, L2, T, Os), A, No + 1};
qlcmf({attribute,_L,file,{File,_Line}}=Attr, _F, _Imp, A, No) ->
    put(?QLC_FILE, File),
    {Attr, A, No};
qlcmf(T, F, Imp, A0, No0) when is_tuple(T) ->
    {TL, A, No} = qlcmf(tuple_to_list(T), F, Imp, A0, No0),
    {list_to_tuple(TL), A, No};
qlcmf(T, _F, _Imp, A, No) ->
    {T, A, No}.

occ_vars(E) ->
    qlc:var_fold(fun({var,_L,V}) -> V end, [], E).

%% Every Anno is replaced by a unique number. The number is used in a
%% table that holds data about the abstract node where Anno resides.
%% In particular, the original location is kept there, so that the
%% original abstract code can be re-created.
save_anno(Abstr, NodeInfo) ->
    F = fun(Anno) ->
                N = next_slot(NodeInfo),
                Location = erl_anno:location(Anno),
                Data = {N, #{location => Location}},
                true = ets:insert(NodeInfo, Data),
                erl_anno:new(N)
        end,
    map_anno(F, Abstr).

next_slot(T) ->
    I = ets:update_counter(T, var_n, 1),
    case ets:lookup(T, I) of
        [] ->
            I;
        _ ->
            next_slot(T)
    end.

restore_anno(Abstr, NodeInfo) ->
    F = fun(Anno) ->
                Location = erl_anno:location(Anno),
                case ets:lookup(NodeInfo, Location) of
                    [{Location, Data}] ->
                        OrigLocation = maps:get(location, Data),
                        erl_anno:set_location(OrigLocation, Anno);
                    [{Location}] -> % generated code
                        Anno;
                    [] ->
                        Anno
                end
        end,
    map_anno(F, Abstr).

restore_loc(Location, #state{node_info = NodeInfo}) ->
  case ets:lookup(NodeInfo, Location) of
      [{Location, #{location := OrigLocation}}] ->
          OrigLocation;
      [{Location}] ->
          Location;
      [] ->
          Location
  end.

no_shadows(Forms0, State) ->
    %% Variables that may shadow other variables are introduced in
  LCs and Funs . Such variables ( call them SV , Shadowing
    %% Variables) are now renamed. Each (new) occurrence in a pattern
    %% is assigned an index (integer), unique in the file. 
    %%
  The state { LastIndex , ActiveVars , UsedVars , AllVars , Singletons , State }
  holds the last index used for each SV ( LastIndex ) , the SVs in
  the current scope ( ActiveVars ) , used SVs ( UsedVars , the indexed
    %% name is the key), all variables occurring in the file
  (  ) , and all singletons . If an SV is not used ( that is ,
    %% is a member of Singletons), it is replaced by '_' (otherwise a
    %% warning for unused variable would erroneously be emitted). If
  the indexed name of an SV occurs in the file , next index is
    %% tried (to avoid mixing up introduced names with existing ones).
    %%
  The original names of variables are kept in a table in State .
    %% undo_no_shadows/2 re-creates the original code.
    AllVars = sets:from_list(ordsets:to_list(qlc:vars(Forms0))),
    ?DEBUG("nos AllVars = ~p~n", [sets:to_list(AllVars)]),
    VFun = fun(_Id, LC, Vs) -> nos(LC, Vs) end,
    LI = ets:new(?APIMOD,[]),
    UV = ets:new(?APIMOD,[]),
    D0 = dict:new(),
    S1 = {LI, D0, UV, AllVars, [], State},
    _ = qlc_mapfold(VFun, S1, Forms0, State),
    ?DEBUG("UsedIntroVars = ~p~n", [ets:match_object(UV, '_')]),
    Singletons = ets:select(UV, ets:fun2ms(fun({K,0}) -> K  end)),
    ?DEBUG("Singletons: ~p~n", [Singletons]),
    true = ets:delete_all_objects(LI),
    true = ets:delete_all_objects(UV),
    %% Do it again, this time we know which variables are singletons.
    S2 = {LI, D0, UV, AllVars, Singletons, State},
    {Forms,_} = qlc_mapfold(VFun, S2, Forms0, State),
    true = ets:delete(LI),
    true = ets:delete(UV),
    Forms.

nos([E0 | Es0], S0) ->
    {E, S1} = nos(E0, S0),
    {Es, S} = nos(Es0, S1),
    {[E | Es], S};
nos({'fun',L,{clauses,Cs}}, S) ->
    NCs = [begin
               {H, S1} = nos_pattern(H0, S),
               {[G, B], _} = nos([G0, B0], S1),
               {clause,Ln,H,G,B}
           end || {clause,Ln,H0,G0,B0} <- Cs],
    {{'fun',L,{clauses,NCs}}, S};
nos({named_fun,Loc,Name,Cs}, S) ->
    {{var,NLoc,NName}, S1} = case Name of
                                 '_' ->
                                     S;
                                 Name ->
                                     nos_pattern({var,Loc,Name}, S)
                               end,
    NCs = [begin
               {H, S2} = nos_pattern(H0, S1),
               {[G, B], _} = nos([G0, B0], S2),
               {clause,CLoc,H,G,B}
           end || {clause,CLoc,H0,G0,B0} <- Cs],
    {{named_fun,NLoc,NName,NCs}, S};
nos({lc,L,E0,Qs0}, S) ->
    %% QLCs as well as LCs. It is OK to modify LCs as long as they
    %% occur within QLCs--the warning messages have already been found
    %% by compile_errors.
    F = fun({T,Ln,P0,LE0}, QS0) when T =:= b_generate; T =:= generate -> 
                {LE, _} = nos(LE0, QS0),
                {P, QS} = nos_pattern(P0, QS0),
                {{T,Ln,P,LE}, QS};
           (Filter, QS) -> 
                nos(Filter, QS)
        end,
    {Qs, S1} = lists:mapfoldl(F, S, Qs0),
    {E, _} = nos(E0, S1),
    {{lc,L,E,Qs}, S};
nos({var,L,V}=Var, {_LI,Vs,UV,_A,_Sg,State}=S) when V =/= '_' ->
    case used_var(V, Vs, UV) of
        {true, VN} ->
            nos_var(L, V, State),
            {{var,L,VN}, S};
        false ->
            {Var, S}
    end;
nos(T, S0) when is_tuple(T) ->
    {TL, S} = nos(tuple_to_list(T), S0),
    {list_to_tuple(TL), S};
nos(T, S) ->
    {T, S}.

nos_pattern(P, S) ->
    {T, NS, _} = nos_pattern(P, S, []),
    {T, NS}.

nos_pattern([P0 | Ps0], S0, PVs0) ->
    {P, S1, PVs1} = nos_pattern(P0, S0, PVs0),
    {Ps, S, PVs} = nos_pattern(Ps0, S1, PVs1),
    {[P | Ps], S, PVs};
nos_pattern({var,L,V}, {LI,Vs0,UV,A,Sg,State}, PVs0) when V =/= '_' ->
    {Name, Vs, PVs} = 
        case lists:keyfind(V, 1, PVs0) of
            {V, VN} ->
                _ = used_var(V, Vs0, UV), 
                {VN, Vs0, PVs0};
            false -> 
                {VN, Vs1} = next_var(V, Vs0, A, LI, UV),
                N = case lists:member(VN, Sg) of
                        true -> '_';
                        false -> VN
                    end,
                {N, Vs1, [{V,VN} | PVs0]}
        end,
    nos_var(L, V, State),
    {{var,L,Name}, {LI,Vs,UV,A,Sg,State}, PVs};
nos_pattern(T, S0, PVs0) when is_tuple(T) ->
    {TL, S, PVs} = nos_pattern(tuple_to_list(T), S0, PVs0),
    {list_to_tuple(TL), S, PVs};
nos_pattern(T, S, PVs) ->
    {T, S, PVs}.

nos_var(Anno, Name, State) ->
    NodeInfo = State#state.node_info,
    Location = erl_anno:location(Anno),
    case ets:lookup(NodeInfo, Location) of
        [{Location, #{name := _}}] ->
            true;
        [{Location, Data}] ->
            true = ets:insert(NodeInfo, {Location, Data#{name => Name}});
        [] -> % cannot happen
            true
    end.

used_var(V, Vs, UV) ->
    case dict:find(V, Vs) of
        {ok,Value} ->
            VN = qlc:name_suffix(V, Value),
            _ = ets:update_counter(UV, VN, 1),
            {true, VN};
        error -> false
    end.

next_var(V, Vs, AllVars, LI, UV) ->
    NValue = case ets:lookup(LI, V) of
                 [{V, Value}] -> Value + 1;
                 [] -> 1
             end,
    true = ets:insert(LI, {V, NValue}),
    VN = qlc:name_suffix(V, NValue),
    case sets:is_element(VN, AllVars) of
        true -> next_var(V, Vs, AllVars, LI, UV);
        false -> true = ets:insert(UV, {VN, 0}),
                 NVs = dict:store(V, NValue, Vs),
                 {VN, NVs}
    end.

undo_no_shadows(E, State) ->
    var_map(fun(Anno) -> undo_no_shadows1(Anno, State) end, E).

undo_no_shadows1({var, Anno, _}=Var, State) ->
    Location = erl_anno:location(Anno),
    NodeInfo = State#state.node_info,
    case ets:lookup(NodeInfo, Location) of
        [{Location, #{name := Name}}] ->
            {var, Anno, Name};
        _ ->
            Var
    end.

  QLC identifier .
  The first one encountered in the file has No=1 .

make_lcid(Anno, No) when is_integer(No), No > 0 ->
    {No, erl_anno:line(Anno)}.

get_lcid_no({No, _Line}) ->
    No.

get_lcid_line({_No, Line}) ->
    Line.

qid(LCId, No) ->
    #qid{no = No, lcid = LCId}.

abst_vars([V | Vs], L) ->
    [abst_vars(V, L) | abst_vars(Vs, L)];
abst_vars([], _L) ->
    [];
abst_vars(nil, L) ->
    {nil,L};
abst_vars(V, L) ->
    {var,L,V}.

embed_vars(Vars, L) ->
    embed_expr({tuple,L,Vars}, L).

%% -> [Expr || _ <- []] on abstract format.
embed_expr(Expr, L) ->
    {lc,L,Expr,[{generate,L,{var,L,'_'},{nil,L}}]}.

%% Doesn't handle binaries very well, but don't bother for now.
var2const(E) ->
    var_map(fun({var, L, V}) -> {atom, L, V} end, E).

var_map(F, {var, _, _}=V) ->
    F(V);
var_map(F, {named_fun,NLoc,NName,Cs}) ->
    {var,Loc,Name} = F({var,NLoc,NName}),
    {named_fun,Loc,Name,var_map(F, Cs)};
var_map(F, T) when is_tuple(T) ->
    list_to_tuple(var_map(F, tuple_to_list(T)));
var_map(F, [E | Es]) ->
    [var_map(F, E) | var_map(F, Es)];
var_map(_F, E) ->
    E.

var_mapfold(F, A, {var, _, _}=V) ->
    F(V, A);
var_mapfold(F, A0, T) when is_tuple(T) ->
    {L, A} = var_mapfold(F, A0, tuple_to_list(T)),
    {list_to_tuple(L), A};
var_mapfold(F, A0, [E0 | Es0]) ->
    {E, A1} = var_mapfold(F, A0, E0),
    {Es, A} = var_mapfold(F, A1, Es0),
    {[E | Es], A};
var_mapfold(_F, A, E) ->
    {E, A}.

map_anno(F, AbstrList) when is_list(AbstrList) ->
    [map_anno1(F, Abstr) || Abstr <- AbstrList];
map_anno(F, Abstr) ->
    map_anno1(F, Abstr).

map_anno1(F, Abstr) ->
    erl_parse:map_anno(F, Abstr).

family_list(L) ->
    sofs:to_external(family(L)).

family(L) ->
    sofs:relation_to_family(sofs:relation(L)).

is_guard_test(E, #state{records = RDs, overridden = IsOverridden}) ->
    erl_lint:is_guard_test(E, RDs, IsOverridden).

%% In code that has been run through erl_expand_records, a guard
%% test will never contain calls without an explicit module
%% prefix.  Unfortunately, this module runs *some* of the code
%% through erl_expand_records, but not all of it.
%%
%% Therefore, we must set up our own list of local and imported functions
  that will override a BIF with the same name .

set_up_overridden(Forms) ->
    Locals = [{Name,Arity} || {function,_,Name,Arity,_} <- Forms],
    Imports0 = [Fs || {attribute,_,import,Fs} <- Forms],
    Imports1 = lists:flatten(Imports0),
    Imports2 = [Fs || {_,Fs} <- Imports1],
    Imports = lists:flatten(Imports2),
    Overridden = gb_sets:from_list(Imports ++ Locals),
    fun(FA) -> gb_sets:is_element(FA, Overridden) end.

-ifdef(debug).
display_forms(Forms) ->
    io:format("Forms ***~n"),
    lists:foreach(fun(Form) ->
                          io:format("~ts~n", [catch erl_pp:form(Form)])
                  end, Forms),
    io:format("End Forms ***~n").
-else.
display_forms(_) ->
    ok.
-endif.



 %CopyrightBegin%


 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at

     -2.0

 Unless required by applicable law or agreed to in writing, software
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.

 %CopyrightEnd%

 Purpose: Implements the qlc Parse Transform.
 Also in qlc.erl.
 Also in qlc.erl.
 #qlc_opt
-define(debug, true).

 Exported functions

 The returned value should conform to the types, but
 need not evaluate to anything meaningful.

 Local functions

 Make sure restore_locations() does not confuse integers with (the
 unique) line numbers.
 Avoid duplicated lint warnings and lint errors. Care has been taken
 not to introduce unused variables in the transformed code.

 Some mistakes such as "{X} =:= {}" are found by strong
  are ignored.
 for introduced variables used in list expressions and messages for
 badargs. Since the QLCs will be replaced by some terms, the
 compiler cannot find the errors and warnings after the parse
 transformation.

 The qlc module cannot handle binary generators.
 -> [{Qid,[variable()]}].

 For each qualifier the introduced variables are found. The
 variables introduced in filters are very much like the variables
 introduced in generator patterns. If no variables are introduced in
 a qualifier, [variable()] is empty.

 Generator: all variables occurring in the pattern are introduced
 variables.
 Filter: all variables bound inside the filter are introduced
 variables (unless they are unsafe).

 The filter F is replaced by begin E, F, E end,
 where E is an LC expression consisting of a
 Note: the linter messages are the ones we are looking for.
 If there are no linter messages, the compiler will crash (ignored).
 A variable is bound inside the filter if it is not bound before
 the filter, but it is bound after the filter (obviously).
 The compiler is not available. Use the linter instead.
 generator patterns in the right hand side of generators (ListExpr),

 yields error messages for erroneous use of introduced variables.


 list expressions (the right hand side of generators, LE) are
 represented by funs (the table is further processed at runtime).
 The separation into a fun and a table makes it possible to
 rearrange qualifiers while keeping the speed offered by compiled
 join are qualifiers rearranged.

 Extra generators (and clauses) are inserted for possible fast join
 operations. The list expression for such a generator has the form
 PatternFilter2, PatternConstants1, PatternConstants2} (it is not a
 fun). Join generators are ignored at runtime unless a fast join is
 possible, in which case they replace other generators. See also
 qlc.erl.
 
 looping over values). State 1 is reserved for the template and
 state 0 is entered when there are no more values to try, so
 assuming no rearrangement of the qualifiers has taken place, the
 the table tells which state to go to next. By modifying the table,
 the order of the qualifiers can be altered at runtime.

 Note: the fun must not return a fun if it is to be called by
 the function outlined below.

 An outline of the generated fun:

 the final state
       lists:reverse(RL);   % eval, all answers collected in a list
    (0, ...) -> [];    % cursor (or fold)
 the template state
       Fun(<last generator loop state>, [Template | RL], ...);
 return the object and a continuation
       [Template | fun() -> Fun(<last generator loop state>, ...)];
 an sample generator , initialization state
       Fun(3, ..., <initial value>, ...);
 looping over values ( a list )
 arguments are bound
 pattern does not match
       Fun(<last generator loop state>, ...);
 looping over values ( using continuations )
       case F() of % get the next value by calling a continuation
           [Pattern | Val] -> 
           [_ | Val] -> 
           [] ->
           T -> % returned immediately, typically an error tuple
              T
       end;
 a sample filter
       case Filter of
           true -> Fun(<next qualifier state>, ...);
           false -> Fun(<last generator loop state>, ...)
       end;
 a filter so simple that it could be used as a guard
       if 
          Guard -> Fun(<next qualifier state>, ...);
          true -> Fun(<last generator loop state>, ...)
       end
 
 <last generator loop state> means state 0 if there is no last
 generator. <initial value> is the evaluated list expression
 (evaluated once only). Among the arguments indicated by ellipses
 are all variables introduced in patterns and filters.

 record. The general case is that calling the fun stored in the 'lc'
 above mentioned table; QOpt is a property list implemented as a fun
 things as constant columns, match specifications, &c.
 There is one special case when calling the fun stored in the 'lc'
 field returns something else:
   The objects returned are the objects returned by the generator
   (calling LEf returns the objects generated by LE).
 translated before the expression itself is translated. info/2
 must not display the result of the translation, but the source
 code.
 Unused variables introduced in filters are not optimized away.
 Not at all sure it is a good idea to try and find 
 But there are a few cases where qlc finds more... (r12b).
 V is for info()
 Finds filters and patterns that cannot match any values at all. 
 Nothing but the patterns and the filters themselves is analyzed.
 The template may also have a constant function (IdNo = 0).
 Only constant template columns are interesting.
 Comparisons yield more constant columns than matchings.
 Extra generators are introduced for join.
 The join generator re-uses the generator variable assigned to
 Its abstract code is a pair of the joined generators' patterns.
 Op is not used.
 Variables occurring only once are replaced by '_'.
 Creates a handle that filters the operands of merge join using the
 pattern. It is important that objects that do not pass the pattern
 are filtered out because the columns of the pattern are inspected
 in order to determine if key-sorting the operands can be avoided.
 
 No objects will be filtered out if the pattern is just a variable.
 By the term "imported variable" is meant a variable that is bound
 suitable name.
 The column fun is to be used when there is a known key column or
 indices. The argument is a column number and the return value is a
 list of the values to look up to get all objects needed to evaluate
 the filter. The order of the objects need not be the same as the
 order the traverse fun would return them.
 imported vars
 results are to be used only for determining which columns are
 sorted. The template can be handled very much like a generator
 pattern (the variables are not fresh, though). As in filters calls
 like element(I, T) are recognized.
 Equal = Match = TemplateColumns
 integer is position in template
 column is position in pattern
 This kludge is known by pattern/5 below.
 -> [{QId,[QId']}].
 The qualifiers [QualifierNumber'] are filters (F1, ..., Fn) that
 F1, ..., Fn], where Pattern' is Template if all qualifiers can be 
 guard filters only
 variables introduced by the generator. The whole qlc
 expressione can be replaced by a match specification.
 -> {Template, Pattern'}
 occur at top level. Introduce or reuse a top-level variable as
 template
 Tries to find columns which are compared or matched against
 constant values or other columns. To that end unification is used.
 A frame is a list of bindings created by unification.
 Also tries to find the number of columns of patterns.
 Note that the template is handled more or less as a pattern.
 ColumnConstants = [{Column,[Constant],[FilterNo]}]
 are looked up.
     [{GeneratorNumber,[{ColumnNumber,
 For every generator such that the unification binds value(s) to
 some column(s), extra constants are returned. These constants are
 the results of the unification, and do not occur in the pattern of
 the generator.
 Use compared extra constants only because:
 - merge join compares terms;
 - the constants from the matching unification is a subset of the
   constants from the comparing unification.
 Using constants from the matching unification would make it
 possible to skip some (more) objects when joining.
 ** Comparing Terms **
  When comparing the key against a term where some integer (or float
 comparing equal to an integer) occurs, one has to be careful if the
 the integer and with the float comparing equal to the integer--then
 all objects that could possibly be answers are filtered (with
 reasonable assumptions). But if integers occur several times in the
 term all combinations have to be looked up, and that could be just
 too many.
  If imported variables occur in the term one could assume at compile
 time that they are not integers and check that assumption at
 runtime. However, this would probably be bad design since some keys
 can be looked up, but others cannot.
  However, the current implementation is simple: do not bind a
 variable to a term if imported variables or integers occur in the
 term.
 Comparing table. Every value can be looked up.
 Matching table. Ignore comparisons unless the value is free of
 integers. See also Comparing Terms.
 Augment ColConstants with filters that do not need to be run
 provided that constants are looked up.
 Does not find all filters that can be removed.
 If there is a test that does not compare or match, then the
 filter cannot be skipped.
 In runtime, constants are looked up and matched against a pattern 
 (the pattern acts like a filter), then the filters are run.
 looked up. Such (possibly bogus) elements are however not used.
 assumed to have been run when the filter is run. Sometimes it
 would be advantageously to assume some filter(s) occurring
 before the filter had been run as well 
 pattern has already done the test):
 Note: if the pattern and the filter test the same
 column, the filter will not be skipped.
 Check that the following holds for all frames.
 The column is compared/matched against a constant.
 If there are no more comparisons/matches then
 the filter can be replaced by the lookup of
 the constant.
 F2: the pattern has been matched and the
 constant has been looked up. If Frame has no
 more bindings than F2 (modulo unique
 variables), then the filter can be skipped. 
 
 Under rare circumstances (for instance: 
 not all constants mentioned in a filter are looked up.
 The filter can only be skipped if all constants
 are looked up.
 Don't try to handle filters that compare several
 The skip tag 'all' means that all filters are covered by the lookup.
 for match specifications (see match_spec_quals above).
 Comparing table. Cannot skip filters that match integers.
 Matching table. Skip filters regardless of operator.
 -> {TwoGens, ManyGens}
 Tries to find columns (possibly in the same table) that are equal.
 compared.
 Eq.classes .
 Matching table. It is possible that some objects read from the
 other table (the one with the objects to look up) contain
 integers. By making all variables imported it is ensured that
 comparisons are kept. See also Comparing Terms.
 Do what the join does: 
 As for lu_skip: sometimes it would be
 advantageously to assume some filter(s)
 occurring before the join filter had been run
 as well.
 "Run" the filter:
 kludge
 anonymous too
 Selects the guard filters. Other filters than guard filters are
 ignored when trying to find constants and join columns. Note: there
 must not occur any non-guard filter between a guard filter and the
 generator(s) the guard filter depends on. The reason is that such a
 filter could fail for some object(s) excluded by lookup or join. If
 the failing filter is placed _after_ the guard filter, the failing
 objects have already been filtered out by the guard filter.
 to be placed after further generators (the docs states otherwise, but 
 this seems to be common practice).
 Tuple tails are variables, never constants.
 is_bindable() has checked that E is normalisable. 
 template, records already expanded
 Makes test for equality simple:
 kludge for templates
 This is for join: chosing a constant could "hide" a variable.

 Ignoring "not B" and "not A" this is the same as "A or B"; 
 
 One must handle filters with care, both when joining and when
 looking up values. The reference is a nested loop: if the filter
 fails for some combination of values, it must fail also when
 looking up values or joining. In other words, the excluded
 combinations of values must not evaluate to anything but 'false'.
 Filters looking like guards are allowed to fail since for such
 filter the so called guard semantics ensures that the value is
 'false' if it is not 'true'. This behavior was inherited from the
 ordinary list comprehension, where it has been considered a bug
 semantics, and hard to change (at least in the qlc module).

 A special case is =/2. If there is a chance that the =/2 fails
 (badmatch) for some combination of values, that combination cannot
 be excluded. If the variable is bound only once, it is OK, but not
 twice (or more). The current implementation does not handle =/2 at
 all (except in generator patterns).
 In the transformed code there are no records in lookup values
 because records are expanded away in prep_expr.
 filter() tries to extract as much information about constant
 columns as possible. It ignores those parts of the filter that are
 uninteresting. safe_filter() on the other hand ensures that the
 Substitutions: 
 It is important that *the same* variables are introduced for
 columns in every frame. (When trying to find constant columns
 it doesn't matter, but when trying to find joined columns, the
 same variables have to be the representatives in every frame.)
 Do not handle the case where several
 because it is more or less undefined
 whether the table returns the given key
 rather, it would be strange if the table
 did not return the stored key upon
 request, but the 'lookup_fun' function
 may have to add the given key (see also
 seen as a bug.) Note: matching tables
 cannot skip the filter, but looking up
 one of the values should be OK.
 possibly empty
 D: columns occurring in every frame (path).
 Similar problems as described above.
 cons_tuple is used for representing {V1, ..., Vi | TupleTail}.

 Tests like "element(2, X) =:= a" are represented by "tuple tails":
 {_, a | _}. The tail may be unified later, when more information
 about the size of the tuple is known.
 Note: erl_expand_records ensures that all calls to element/2
 Partial evaluation.
 contradiction
 ignored
 Binaries are not handled at all (by unify).
 Note that a variable can be bound to several values, for instance:
 values.
 Binding a variable to several values makes the unification and
 dereferencing more complicated. An alternative would be not to try
 to find lookup values for such QLCs at all. That might have been a
 better design decision.
 Note: all variables are treated as imported. The dereferenced
 values must not depend on Imported.
 Ensure that imported variables are visible in the dereferenced
 value by pushing them to the end of the binding chain. Be careful
 not to introduce loops.
 Tuple tails are OK.
 "Free of integers" here means that there are not imported variables
 in V (which could take on integer values), but there may be other
 variables in V.
 Assumes that imported variables are representatives, if Value is a
 dereferenced value.
 Returns {..., Variable} if Variable is a tuple tail.
 tuple tail (always a variable)
 issues with anonymous variables.)
 don't need any test here
 Recognizes all QLCs on the form [T || P <- LE, F] such that
 the guard semantics implemented in filter/_ below. If one chooses
 not to have guard semantics, affected filters will have to be
 recognized and excluded here as well.
 -- R12B-3: {nil,L}
 R12B-4 --: {atom,L,v1}
 meant for redundant match spec
 Create qual_data (see qlc.erl):
 Create qual_data (see qlc.erl):
 The original code (in Source) is used for filters and the template
 since the translated code can have QLCs and we don't want them to
 be visible.
 Extra careful here or arguments will be lifted into a wide fun.
 The clause 'CE' was added in R11B. The version of the generated was
 however not incremented.
 This is the "guard semantics" used in ordinary list
 comprehension: if a filter looks like a guard test, it returns
 'false' rather than fails.
 Replace every element in IEs that is a member of Es by R, keep all
 other elements as they are.

 nested...
 nested...
 Every Anno is replaced by a unique number. The number is used in a
 table that holds data about the abstract node where Anno resides.
 In particular, the original location is kept there, so that the
 original abstract code can be re-created.
 generated code
 Variables that may shadow other variables are introduced in
 Variables) are now renamed. Each (new) occurrence in a pattern
 is assigned an index (integer), unique in the file. 

 name is the key), all variables occurring in the file
 is a member of Singletons), it is replaced by '_' (otherwise a
 warning for unused variable would erroneously be emitted). If
 tried (to avoid mixing up introduced names with existing ones).

 undo_no_shadows/2 re-creates the original code.
 Do it again, this time we know which variables are singletons.
 QLCs as well as LCs. It is OK to modify LCs as long as they
 occur within QLCs--the warning messages have already been found
 by compile_errors.
 cannot happen
 -> [Expr || _ <- []] on abstract format.
 Doesn't handle binaries very well, but don't bother for now.
 In code that has been run through erl_expand_records, a guard
 test will never contain calls without an explicit module
 prefix.  Unfortunately, this module runs *some* of the code
 through erl_expand_records, but not all of it.

 Therefore, we must set up our own list of local and imported functions
  Copyright Ericsson AB 2004 - 2017 . All Rights Reserved .
  Licensed under the Apache License , Version 2.0 ( the " License " ) ;
  distributed under the License is distributed on an " AS IS " BASIS ,
-module(qlc_pt).


-export([parse_transform/2, transform_from_evaluator/2, 
         transform_expression/2]).

-include_lib("stdlib/include/ms_transform.hrl").

-define(APIMOD, qlc).
-define(Q, q).

-define(QLC_Q(L1, L2, L3, L4, LC, Os), 
        {call,L1,{remote,L2,{atom,L3,?APIMOD},{atom,L4,?Q}},[LC | Os]}).
-define(IMP_Q(L1, L2, LC, Os), {call,L,{atom,L2,?Q},[LC | Os]}).

  qlc : q/1,2 , a query handle
        {lc,
        }).

-record(state, {imp,
		overridden,
                maxargs,
                records,
                xwarnings = [],
                intro_vars,
                node_info}).


-ifdef(debug).
-define(DEBUG(S, A), io:format(S, A)).
-else.
-define(DEBUG(S, A), ok).
-endif.

  erl_eval can not interpret funs with more than 20 arguments :
-define(EVAL_MAX_NUM_OF_ARGS, 20).
  Currently the compiler can handle at most 255 arguments .
-define(COMPILE_MAX_NUM_OF_ARGS, 250).

-define(QLC_FILE, qlc_current_file).


-spec(parse_transform(Forms, Options) -> Forms2 when
      Forms :: [erl_parse:abstract_form() | erl_parse:form_info()],
      Forms2 :: [erl_parse:abstract_form() | erl_parse:form_info()],
      Options :: [Option],
      Option :: type_checker | compile:option()).

parse_transform(Forms0, Options) ->
    ?DEBUG("qlc Parse Transform~n", []),
    Imported = is_qlc_q_imported(Forms0),
    {Forms, FormsNoShadows, State} = initiate(Forms0, Imported),
    NodeInfo = State#state.node_info,
    try
        case called_from_type_checker(Options) of
            true ->
                L = anno0(),
                {tuple,_,Fs0} = abstr(#qlc_lc{}, L),
                F = fun(_Id, LC, A) ->
                            Init = simple(L, 'V', LC, L),
                            {{tuple,L,set_field(#qlc_lc.lc, Fs0, Init)}, A}
                    end,
                {Forms1,ok} = qlc_mapfold(F, ok, Forms, State),
                Forms1;
            false ->
                case
                    compile_messages(Forms, FormsNoShadows, Options, State)
                of
                    {[],Warnings} ->
                        ?DEBUG("node info1 ~p~n",
                               [lists:sort(ets:tab2list(NodeInfo))]),
                        {NewForms, State1} =
                            transform(FormsNoShadows, State),
                        ExtraWs = State1#state.xwarnings,
                        {[],WForms} = no_duplicates(NewForms, [], Warnings,
                                                    ExtraWs, Options),
                        (restore_locations(WForms, State) ++
                         restore_anno(NewForms, NodeInfo));
                    {Errors,Warnings} ->
                        ?DEBUG("node info2 ~p~n",
                               [lists:sort(ets:tab2list(NodeInfo))]),
                        {EForms,WForms} = no_duplicates(FormsNoShadows, Errors,
                                                        Warnings, [],
                                                        Options),
                        restore_locations(EForms ++ WForms, State) ++ Forms0
                end
        end
    after
        true = ets:delete(NodeInfo)
    end.

-spec(transform_from_evaluator(LC, Bs) -> Return when
      LC :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct(),
      Return :: {ok, erl_parse:abstract_expr()}
              | {not_ok, {error, module(), Reason :: term()}}).

transform_from_evaluator(LC, Bindings) ->
    ?DEBUG("qlc Parse Transform (Evaluator Version)~n", []),
    transform_expression(LC, Bindings, false).

-spec(transform_expression(LC, Bs) -> Return when
      LC :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct(),
      Return :: {ok, erl_parse:abstract_expr()}
              | {not_ok, [{error, Reason :: term()}]}).

transform_expression(LC, Bindings) ->
    transform_expression(LC, Bindings, true).


called_from_type_checker(Options) ->
    lists:member(type_checker, Options).

transform_expression(LC, Bs0, WithLintErrors) ->
    L = anno1(),
    As = [{var,L,V} || {V,_Val} <- Bs0],
    Ar = length(As),
    F = {function,L,bar,Ar,[{clause,L,As,[],[?QLC_Q(L, L, L, L, LC, [])]}]},
    Forms0 = [{attribute,L,file,{"foo",L}},
              {attribute,L,module,foo}, F],
    {Forms, FormsNoShadows, State} = initiate(Forms0, false),
    NodeInfo = State#state.node_info,
    Options = [],
    try compile_messages(Forms, FormsNoShadows, Options, State) of
        {Errors0,_Warnings} ->
            case restore_locations(Errors0, State) of
                [] ->
                    {NewForms,_State1} = transform(FormsNoShadows, State),
                    NewForms1 = restore_anno(NewForms, NodeInfo),
                    {function,L,bar,Ar,[{clause,L,As,[],[NF]}]} =
                        lists:last(NewForms1),
                    {ok,NF};
                Errors when WithLintErrors ->
                    {not_ok,mforms(error, Errors)};
                Errors ->
                    [{error,Reason} | _] = mforms(error, Errors),
                    {not_ok, {error, ?APIMOD, Reason}}
            end
    after
        true = ets:delete(NodeInfo)
    end.

-ifdef(DEBUG).
-define(ILIM, 0).
-else.
-define(ILIM, 255).
-endif.

initiate(Forms0, Imported) ->
    NodeInfo = ets:new(?APIMOD, []),
    true = ets:insert(NodeInfo, {var_n, ?ILIM}),
    exclude_integers_from_unique_line_numbers(Forms0, NodeInfo),
    ?DEBUG("node info0 ~p~n",
           [lists:sort(ets:tab2list(NodeInfo))]),
    IsOverridden = set_up_overridden(Forms0),
    State0 = #state{imp = Imported,
		    overridden = IsOverridden,
                    maxargs = ?EVAL_MAX_NUM_OF_ARGS,
                    records = record_attributes(Forms0),
                    node_info = NodeInfo},
    Forms = save_anno(Forms0, NodeInfo),
    FormsNoShadows = no_shadows(Forms, State0),
    IntroVars = intro_variables(FormsNoShadows, State0),
    State = State0#state{intro_vars = IntroVars},
    {Forms, FormsNoShadows, State}.

exclude_integers_from_unique_line_numbers(Forms, NodeInfo) ->
    Integers = find_integers(Forms),
    lists:foreach(fun(I) -> ets:insert(NodeInfo, {I}) end, Integers).

find_integers(Forms) ->
    F = fun(A) ->
                Fs1 = map_anno(fun(_) -> A end, Forms),
                ordsets:from_list(integers(Fs1, []))
        end,
    ordsets:to_list(ordsets:intersection(F(anno0()), F(anno1()))).

integers([E | Es], L) ->
    integers(Es, integers(E, L));
integers(T, L) when is_tuple(T) ->
    integers(tuple_to_list(T), L);
integers(I, L) when is_integer(I), I > ?ILIM ->
    [I | L];
integers(_, L) ->
    L.

-define(I(I), {integer, L, I}).
-define(A(A), {atom, L, A}).
-define(V(V), {var, L, V}).
-define(ABST_NO_MORE, {nil, L}).
-define(ABST_MORE(Obj, Cont), {cons, L, Obj, Cont}).

  Qualifier identifier .
  The first one encountered in a QLC has no=1 .
-record(qid, {lcid,no}).

mforms(Tag, L) ->
    lists:sort([{Tag,M} || {_File,Ms} <- L, M <- Ms]).

no_duplicates(Forms, Errors, Warnings0, ExtraWarnings0, Options) ->
  validation as well as by qlc . Prefer the warnings from  :
   The Compiler and  do not agree on the location of errors .
   For now ,  's messages about failing patterns and filters
    ExtraWarnings = [W || W={_File,[{_,qlc,Tag}]} <-
                              ExtraWarnings0,
                    not lists:member(Tag, [nomatch_pattern,nomatch_filter])],
    Warnings1 = mforms(Warnings0) --
        ([{File,[{L,v3_core,nomatch}]} ||
             {File,[{L,qlc,M}]} <- mforms(ExtraWarnings),
             lists:member(M, [nomatch_pattern,nomatch_filter])]
         ++ 
         [{File,[{L,sys_core_fold,nomatch_guard}]} ||
             {File,[{L,qlc,M}]} <- mforms(ExtraWarnings),
             M =:= nomatch_filter]),
    Warnings = Warnings1 ++ ExtraWarnings,
    {Es1,Ws1} = compile_forms(Forms, Options),
    Es = mforms(Errors) -- mforms(Es1),
    Ws = mforms(Warnings) -- mforms(Ws1),
    {mforms2(error, Es),mforms2(warning, Ws)}.

mforms(L) ->
    lists:sort([{File,[M]} || {File,Ms} <- L, M <- Ms]).

mforms2(Tag, L) ->
    Line = anno0(),
    ML = lists:flatmap(fun({File,Ms}) ->
                               [[{attribute,Line,file,{File,0}}, {Tag,M}] ||
                                   M <- Ms]
                       end, lists:sort(L)),
    lists:flatten(lists:sort(ML)).

restore_locations([T | Ts], State) ->
    [restore_locations(T, State) | restore_locations(Ts, State)];
restore_locations(T, State) when is_tuple(T) ->
    list_to_tuple(restore_locations(tuple_to_list(T), State));
restore_locations(I, State) when I > ?ILIM ->
    restore_loc(I, State);
restore_locations(T, _State) ->
    T.

is_qlc_q_imported(Forms) ->
    [[] || {attribute,_,import,{?APIMOD,FAs}} <- Forms, {?Q,1} <- FAs] =/= [].

record_attributes(Forms) ->
    [A || A = {attribute, _, record, _D} <- Forms].

  Get the compile errors and warnings for the  as well as messages
compile_messages(Forms, FormsNoShadows, Options, State) ->
    BGenF = fun(_QId,{b_generate,Line,_P,_LE}=BGen, GA, A) ->
                    M = {loc(Line),?APIMOD,binary_generator},
                    {BGen,[{get(?QLC_FILE),[M]}|GA],A};
               (_QId, Q, GA, A) ->
                    {Q,GA,A}
            end,
    {_,BGens} = qual_fold(BGenF, [], [], Forms, State),
    GenForm = used_genvar_check(FormsNoShadows, State),
    ?DEBUG("GenForm = ~ts~n", [catch erl_pp:form(GenForm)]),
    {GEs,_} = compile_forms([GenForm], Options),
    UsedGenVarMsgs = used_genvar_messages(GEs, State),
    NodeInfo = State#state.node_info,
    WarnFun = fun(_Id, LC, A) -> {lc_nodes(LC, NodeInfo), A} end,
    {WForms,ok} = qlc_mapfold(WarnFun, ok, Forms, State),
    {Es,Ws} = compile_forms(WForms, Options),
    LcEs = lc_messages(Es, NodeInfo),
    LcWs = lc_messages(Ws, NodeInfo),
    Errors = badarg(Forms, State) ++ UsedGenVarMsgs++LcEs++BGens,
    Warnings = LcWs,
    {Errors,Warnings}.

badarg(Forms, State) ->
    F = fun(_Id, {lc,_L,_E,_Qs}=LC, Es) -> 
                {LC,Es};
           (Id, A, Es) -> 
                E = {get_lcid_line(Id),?APIMOD,not_a_query_list_comprehension},
                {A,[{get(?QLC_FILE), [E]} | Es]}
        end,
    {_,E0} = qlc_mapfold(F, [], Forms, State),
    E0.

lc_nodes(E, NodeInfo) ->
    map_anno(fun(Anno) ->
                     N = erl_anno:line(Anno),
                     [{N, Data}] = ets:lookup(NodeInfo, N),
                     NData = Data#{inside_lc => true},
                     true = ets:insert(NodeInfo, {N, NData}),
                     Anno
             end, E).

used_genvar_messages(MsL, S) ->
    [{File,[{Loc,?APIMOD,{used_generator_variable,V}}]}
       || {_, Ms} <- MsL,
           {XLoc,erl_lint,{unbound_var,_}} <- Ms,
           {Loc,File,V} <- [genvar_pos(XLoc, S)]].

lc_messages(MsL, NodeInfo) ->
    [{File,[{Loc,Mod,T} || {Loc,Mod,T} <- Ms, lc_loc(Loc, NodeInfo)]} ||
        {File,Ms} <- MsL].

lc_loc(N, NodeInfo) ->
    case ets:lookup(NodeInfo, N) of
        [{N, #{inside_lc := true}}] ->
            true;
        [{N, _}] ->
            false
    end.

genvar_pos(Location, S) ->
    case ets:lookup(S#state.node_info, Location) of
        [{Location, #{genvar_pos := Pos}}] ->
            Pos;
        [] ->
            Location
    end.

intro_variables(FormsNoShadows, State) ->
    NodeInfo = State#state.node_info,
    Fun = fun(QId, {T,_L,P0,_E0}=Q, {GVs,QIds}, Foo) when T =:= b_generate;
                                                          T =:= generate ->
                  PVs = qlc:var_ufold(fun({var,_,V}) -> {QId,V} end, P0),
                  {Q,{ordsets:to_list(PVs) ++ GVs,[{QId,[]} | QIds]},Foo};
             (QId, Filter0, {GVs,QIds}, Foo) ->
  template mentioning all variables occurring in F.
                  Vs = ordsets:to_list(qlc:vars(Filter0)),
                  AnyLine = anno0(),
                  Vars = [{var,AnyLine,V} || V <- Vs],
                  LC = embed_vars(Vars, AnyLine),
                  LC1 = intro_anno(LC, before, QId, NodeInfo),
                  LC2 = intro_anno(LC, 'after', QId, NodeInfo),
                  Filter = {block,AnyLine,[LC1,Filter0,LC2]},
                  {Filter,{GVs,[{QId,[]} | QIds]},Foo}
          end,
    Acc0 = {[],[]},
    {FForms,{GenVars,QIds}} = 
        qual_fold(Fun, Acc0, [], FormsNoShadows, State),
    Es0 = compile_errors(FForms),
    Before = [{QId,V} ||
                 {L,erl_lint,{unbound_var,V}} <- Es0,
                 {_L,{QId,before}} <- ets:lookup(NodeInfo, L)],
    After = [{QId,V} ||
                {L,erl_lint,{unbound_var,V}} <- Es0,
                {_L,{QId,'after'}} <- ets:lookup(NodeInfo, L)],
    Unsafe = [{QId,V} ||
                 {L,erl_lint,{unsafe_var,V,_Where}} <- Es0,
                 {_L,{QId,'after'}} <- ets:lookup(NodeInfo, L)],
    ?DEBUG("Before = ~p~n", [Before]),
    ?DEBUG("After = ~p~n", [After]),
    ?DEBUG("Unsafe = ~p~n", [Unsafe]),
    ?DEBUG("Filter ~p~n", [(Before -- After) -- Unsafe]),
    IV = (Before -- After) -- Unsafe,
    I1 = family(IV ++ GenVars),
    sofs:to_external(sofs:family_union(sofs:family(QIds), I1)).

intro_anno(LC, Where, QId, NodeInfo) ->
    Data = {QId,Where},
    Fun = fun(Anno) ->
                  Location = erl_anno:location(Anno),
                  true = ets:insert(NodeInfo, {Location,Data}),
                  Anno
          end,
    map_anno(Fun, save_anno(LC, NodeInfo)).

compile_errors(FormsNoShadows) ->
    case compile_forms(FormsNoShadows, []) of
        {[], _Warnings} ->
            [];
        {Errors, _Warnings} ->
            ?DEBUG("got errors ~tp~n", [Errors]),
            lists:flatmap(fun({_File,Es}) -> Es end, Errors)
    end.

compile_forms(Forms0, Options) ->
    Exclude = fun(eof) -> true;
                 (warning) -> true;
                 (error) -> true;
                 (_) -> false
              end,
    Forms = ([F || F <- Forms0, not Exclude(element(1, F))]
             ++ [{eof,0}]),
    try 
        case compile:noenv_forms(Forms, compile_options(Options)) of
            {ok, _ModName, Ws0} ->
                {[], Ws0};
            {error, Es0, Ws0} -> 
                {Es0, Ws0}
        end
    catch _:_ ->
        case erl_lint:module(Forms, lint_options(Options)) of
            {ok, Warnings} ->
                {[], Warnings};
            {error, Errors, Warnings} ->
                {Errors, Warnings}
        end
    end.

compile_options(Options) ->
    No = [report,report_errors,report_warnings,'P','E' | bitstr_options()],
    [strong_validation,return | skip_options(No, Options)].

lint_options(Options) ->
    skip_options(bitstr_options(), Options).

skip_options(Skip, Options) ->
    [O || O <- Options, not lists:member(O, Skip)].

bitstr_options() ->
    [binary_comprehension,bitlevel_binaries].    

  In LCs it is possible to use variables introduced in filters and
  but in QLCs this is not allowed .
  A brand new function is returned such that there is one expression
  for each ListExpr . The expression mentions all introduced variables
  occurring in ListExpr . Running the function through the compiler
used_genvar_check(FormsNoShadows, State) ->
    NodeInfo = State#state.node_info,
    F = fun(QId, {T, Ln, _P, LE}=Q, {QsIVs0, Exprs0}, IVsSoFar0)
                                   when T =:= b_generate; T =:= generate ->
                F = fun(Var) ->
                            {var, Anno0, OrigVar} =
                                undo_no_shadows(Var, State),
                            {var, Anno, _} = NewVar = save_anno(Var, NodeInfo),
                            Location0 = erl_anno:location(Anno0),
                            Location = erl_anno:location(Anno),
                            [{Location, Data}] =
                                ets:lookup(NodeInfo, Location),
                            Pos = {Location0,get(?QLC_FILE),OrigVar},
                            NData = Data#{genvar_pos => Pos},
                            true = ets:insert(NodeInfo, {Location, NData}),
                            NewVar
                    end,
                Vs = [Var || {var, _, V}=Var <- qlc:var_fold(F, [], LE),
                             lists:member(V, IVsSoFar0)],
                Exprs = case Vs of
                            [] -> Exprs0;
                            _ -> [embed_vars(Vs, Ln) | Exprs0]
                        end,
                {QsIVs,IVsSoFar} = q_intro_vars(QId, QsIVs0, IVsSoFar0),
                {Q, {QsIVs, Exprs}, IVsSoFar};
           (QId, Filter, {QsIVs0, Exprs}, IVsSoFar0) ->
                {QsIVs, IVsSoFar} = q_intro_vars(QId, QsIVs0, IVsSoFar0),
                {Filter, {QsIVs, Exprs}, IVsSoFar}
        end,
    Acc0 = {State#state.intro_vars, [{atom, anno0(), true}]},
    {_, {[], Exprs}} = qual_fold(F, Acc0, [], FormsNoShadows, State),
    FunctionNames = [Name || {function, _, Name, _, _} <- FormsNoShadows],
    UniqueFName = qlc:aux_name(used_genvar, 1, sets:from_list(FunctionNames)),
    A = anno0(),
    {function,A,UniqueFName,0,[{clause,A,[],[],lists:reverse(Exprs)}]}.
    
q_intro_vars(QId, [{QId, IVs} | QsIVs], IVsSoFar) -> {QsIVs, IVs ++ IVsSoFar}.


  The transformed code has two major parts : a fun where each
  qualifier is represented by one or more clauses , and a table where
  code , and to run the LEs before evaluation of the  ( and possibly
  modify the LEs should that be necessary ) . Only when doing a fast
  { join ,  , QualifierNumber1 , QualifierNumber2 ,  ,
  For each QLC , every filter is given a state number and every
  generator two state numbers ( one for initialization , one for
  first qualifier is given state number 2 . For every state except 0 ,
  The syntax of the value  returned from the fun is :
  Val = [ ] | [ term ( ) | Val ] | fun ( ) - > 
        Fun(3 , ... ,  , ... ) ;
     ( 3 , ... , [ ] , ... ) - >
                Fun(<next qualifier state > ... ,  , ... ) ;
                Fun(3 , ... ,  , ... ) ;
               Fun(<last generator loop state > , ... ) ;
  transform/2 replaces each  ( call to  : q/1 ) with a qlc_lc
  field returns { qlc_v1 , QFun , CodeF , Qdata , QOpt } such that :  is
  the above mentioned fun ; CodeF is a fun returning the original code
  for the template , every pattern , and every filter ; Qdata is the
  of one argument - an atom - which returns information about such
  - If the QLC has the form [ Var || Var < - LE ] and there are no
    options to qlc : q/2 , a tuple { simple_v1 , P , LEf , Line } is returned .

transform(FormsNoShadows, State) ->
    _ = erlang:system_flag(backtrace_depth, 500),
    IntroVars = State#state.intro_vars,
    AllVars = sets:from_list(ordsets:to_list(qlc:vars(FormsNoShadows))),
    ?DEBUG("AllVars = ~p~n", [sets:to_list(AllVars)]),
    F1 = fun(QId, {generate,_,P,LE}, Foo, {GoI,SI}) ->
                 {{QId,GoI,SI,{gen,P,LE}},Foo,{GoI + 3, SI + 2}};
            (QId, F, Foo, {GoI,SI}) ->
                 {{QId,GoI,SI,{fil,F}},Foo,{GoI + 2,SI + 1}}
         end,
    TemplS = qlc:template_state(),
    GoState = {TemplS + 1, TemplS + 1},
    {ModifiedForms1,_} = 
        qual_fold(F1, [], GoState, FormsNoShadows, State),

  This is for info/2 .  in filters and the template are
    {_,Source0} = qual_fold(fun(_QId, {generate,_,_P,_E}=Q, Dict, Foo) -> 
                                    {Q,Dict,Foo};
                               (QId, F, Dict, Foo) ->
                                    {F,dict:store(QId, F, Dict),Foo}
                            end, dict:new(), [], FormsNoShadows, State),
    {_,Source} = qlc_mapfold(fun(Id, {lc,_L,E,_Qs}=LC, Dict) ->
                                     {LC,dict:store(Id, E, Dict)}
                             end, Source0, FormsNoShadows, State),


    F2 = fun(Id, {lc,_L,E,Qs}, {IntroVs0,XWarn0}) ->
                 LcNo = get_lcid_no(Id),
                 LcL = get_lcid_line(Id),
                 [RL,Fun,Go,NGV,S0,RL0,Go0,AT,Err] = 
                     aux_vars(['RL','Fun','Go','C','S0','RL0','Go0','AT','E'],
                              LcNo, AllVars),
                 ?DEBUG("RL = ~p, Fun = ~p, Go = ~p~n", [RL, Fun, Go]),
                 {IntroVs, RestIntroVs} = lists:split(length(Qs), IntroVs0),
                 IntroVs_Qs = lists:zip(IntroVs, Qs),
                 F = fun({{QId,IVs}, {QId,GoI,SI,{gen,P,LE}}}, AllIVs0) ->
                             GV = aux_var('C', LcNo, QId#qid.no, 1, AllVars),
                             GenIVs = [GV | IVs],
                             {{QId,{GenIVs,{{gen,P,LE,GV},GoI,SI}}},
                              GenIVs ++ AllIVs0};
                        ({{QId,IVs}, {QId,GoI,SI,{fil,F}}}, AllIVs0) ->
                             {{QId,{IVs,{{fil,F},GoI,SI}}},
                              IVs++AllIVs0}
                     end,
                 {QCs, AllIVs} = lists:mapfoldl(F, [], IntroVs_Qs),

                 Dependencies = qualifier_dependencies(Qs, IntroVs),
                 L = no_compiler_warning(LcL),
                 {EqColumnConstants, EqualColumnConstants,
                  ExtraConsts, SizeInfo} =
                     constants_and_sizes(Qs, E, Dependencies, AllIVs, State),
                 {JoinInfo, XWarn} = 
                     join_kind(Qs, LcL, AllIVs, Dependencies, State),
  failing qualifiers ;  does it so much better .
                 FWarn = warn_failing_qualifiers(Qs, AllIVs, Dependencies, 
                                                 State),
                 JQs = join_quals(JoinInfo, QCs, L, LcNo, ExtraConsts, AllVars),
                 XQCs = QCs ++ JQs,
                 Cs0 = clauses(XQCs, RL, Fun, Go, NGV, Err, AllIVs, State),
                 Template = template(E, RL, Fun, Go, AT, L, AllIVs, State),
                 Fin = final(RL, AllIVs, L, State),
                 FunC = {'fun',L,{clauses,Fin ++ Template ++ Cs0}},
                 As0 = pack_args(abst_vars([S0, RL0, Fun, Go0 
                                            | replace(AllIVs, AllIVs, nil)], 
                                           L), L, State),
                 AsW = abst_vars([S0, RL0, Go0], L),
                 FunW = {'fun',L,{clauses,[{clause,L,AsW,[],
                                            [{match,L,{var,L,Fun},FunC},
                                             {call,L,{var,L,Fun},As0}]}]}},
                 {ok, OrigE0} = dict:find(Id, Source),
                 OrigE = undo_no_shadows(OrigE0, State),
                 QCode = qcode(OrigE, XQCs, Source, L, State),
                 Qdata = qdata(XQCs, L),
                 TemplateInfo = 
                     template_columns(Qs, E, AllIVs, Dependencies, State),
  ExtraConsts should be used by match_spec_quals .
                 MSQs = match_spec_quals(E, Dependencies, Qs, State),
                 Opt = opt_info(TemplateInfo, SizeInfo, JoinInfo, MSQs, L,
                                EqColumnConstants, EqualColumnConstants),
                 LCTuple = 
                     case qlc_kind(OrigE, Qs, State) of
                         qlc ->
                             {tuple,L,[?A(qlc_v1),FunW,QCode,Qdata,Opt]};
                         {simple, PL, LE, V} ->
                             Init = closure(LE, L),
                             simple(L, V, Init, PL)
                     end,
                 LCFun = {'fun',L,{clauses,[{clause,L,[],[],[LCTuple]}]}},
                 {tuple,_,Fs0} = abstr(#qlc_lc{}, L),
                 Fs = set_field(#qlc_lc.lc, Fs0, LCFun),
                 {{tuple,L,Fs},{RestIntroVs,FWarn++XWarn++XWarn0}}
         end,
    {NForms,{[],XW}} = qlc_mapfold(F2, {IntroVars,[]}, ModifiedForms1, State),
    display_forms(NForms),
    {NForms, State#state{xwarnings = XW}}.

join_kind(Qs, LcL, AllIVs, Dependencies, State) ->
    {EqualCols2, EqualColsN} = equal_columns(Qs, AllIVs, Dependencies, State),
    {MatchCols2, MatchColsN} = eq_columns(Qs, AllIVs, Dependencies, State),
    Tables = lists:usort
               ([T || {C,_Skip} <- EqualCols2, {T,_} <- C]
             ++ [T || {C,_Skip} <- EqualCols2, T <- C, is_integer(T)]),
    if 
        EqualColsN =/= []; MatchColsN =/= [] -> 
            {[], 
             [{get(?QLC_FILE),[{LcL,?APIMOD,too_complex_join}]}]};
        EqualCols2 =:= [], MatchCols2 =:= [] ->
            {[], []};
        length(Tables) > 2 -> 
            {[], 
             [{get(?QLC_FILE),[{LcL,?APIMOD,too_many_joins}]}]};
        EqualCols2 =:= MatchCols2 ->
            {EqualCols2, []};
        true -> 
            {{EqualCols2, MatchCols2}, []}
    end.

qlc_kind(OrigE, Qs, State) ->
    {OrigFilterData, OrigGeneratorData} =
        qual_data(undo_no_shadows(Qs, State)),
    OrigAllFilters = filters_as_one(OrigFilterData),
    {_FilterData, GeneratorData} = qual_data(Qs),
    case {OrigE, OrigAllFilters, OrigGeneratorData} of
        {{var,_,V}, {atom,_,true}, [{_,{gen,{var,PatternL,V},_LE}}]} ->
            [{_,{gen,_,LE}}] = GeneratorData,
        _ ->
            qlc
    end.

  A much weaker analysis than the one of  's .
warn_failing_qualifiers(Qualifiers, AllIVs, Dependencies, State) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),    
    Anon = 1,
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    {PFrame, _PatternVars} = 
        pattern_frame(GeneratorData, BindFun, Anon, State),
    {_, _, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    PFrames = frame2frames(PFrame),
    {_, Warnings} = 
        lists:foldl(fun({_QId,{fil,_Filter}}, {[]=Frames,Warnings}) ->
                            {Frames,Warnings};
                       ({_QId,{fil,Filter}}, {Frames,Warnings}) ->
                        case filter(reset_anno(Filter), Frames, BindFun,
                                    State, Imported) of
                            [] ->
                                {[],
                                 [{get(?QLC_FILE),
                                   [{loc(element(2, Filter)),?APIMOD,
                                     nomatch_filter}]} | Warnings]};
                            Frames1 -> 
                                {Frames1,Warnings}
                        end;
                   ({_QId,{gen,Pattern,_}}, {Frames,Warnings}) ->
                        case pattern(Pattern, Anon, [], BindFun, State) of
                            {failed, _, _} -> 
                                {Frames,
                                 [{get(?QLC_FILE),
                                   [{loc(element(2, Pattern)),?APIMOD,
                                     nomatch_pattern}]} | Warnings]};
                            _ ->
                                {Frames,Warnings}
                        end
                end, {PFrames,[]}, FilterData++GeneratorData),
    Warnings.

-define(TNO, 0).
-define(TID, #qid{lcid = template, no = ?TNO}).

opt_info(TemplateInfo, Sizes, JoinInfo, MSQs, L, 
         EqColumnConstants0, EqualColumnConstants0) ->
    SzCls = [{clause,L,[?I(C)],[],[?I(Sz)]} || {C,Sz} <- lists:sort(Sizes)]
            ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    S = [{size, {'fun', L, {clauses, SzCls}}}],
    J = case JoinInfo of [] -> []; _ -> [{join, abstr(JoinInfo, L)}] end,
  Superfluous clauses may be emitted :
    TCls0 = lists:append(
              [[{clause,L,[abstr(Col, L),EqType],[],
                 [abstr(TemplCols, L)]} ||
                   {Col,TemplCols} <- TemplateColumns]
               || {EqType, TemplateColumns} <- TemplateInfo]),
    TCls = lists:sort(TCls0) ++ [{clause,L,[?V('_'),?V('_')],[],[{nil,L}]}],
    T = [{template, {'fun', L, {clauses, TCls}}}],

    EqColumnConstants = opt_column_constants(EqColumnConstants0),
    CCs = opt_constants(L, EqColumnConstants),
    EqC = {constants,{'fun',L,{clauses,CCs}}},

    EqualColumnConstants = opt_column_constants(EqualColumnConstants0),
    ECCs = opt_constants(L, EqualColumnConstants),
    EqualC = {equal_constants,{'fun',L,{clauses,ECCs}}},
    C = [EqC | [EqualC || true <- [CCs =/= ECCs]]],

    ConstCols = [{IdNo,Col} || 
                    {{IdNo,Col},[_],_FilNs} <- EqualColumnConstants],
    ConstColsFamily = family_list(ConstCols),
    NSortedCols0 = [{IdNo,hd(lists:seq(1, length(Cols)+1)--Cols)} ||
                       {IdNo,Cols} <- ConstColsFamily],
    NCls = [{clause,L,[?I(IdNo)],[],[?I(N-1)]} ||
               {IdNo,N} <- NSortedCols0, N > 0]
           ++ [{clause,L,[?V('_')],[],[?I(0)]}],
    N = [{n_leading_constant_columns,{'fun',L,{clauses,NCls}}}],

    ConstCls = [{clause,L,[?I(IdNo)],[],[abstr(Cols,L)]} ||
                   {IdNo,Cols} <- ConstColsFamily] 
               ++ [{clause,L,[?V('_')],[],[{nil,L}]}],
    CC = [{constant_columns,{'fun',L,{clauses,ConstCls}}}],

    MSCls = [{clause,L,[?I(G)],[],[{tuple,L,[MS,abstr(Fs,L)]}]} ||
                {G,MS,Fs} <- MSQs]
          ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    MS = [{match_specs, {'fun',L,{clauses,MSCls}}}],

    Cls = [{clause,L,[?A(Tag)],[],[V]} || 
              {Tag,V} <- lists:append([J, S, T, C, N, CC, MS])]
          ++ [{clause,L,[?V('_')],[],[?A(undefined)]}],
    {'fun', L, {clauses, Cls}}.

opt_column_constants(ColumnConstants0) ->
    [CC || {{IdNo,_Col},Const,_FilNs}=CC <- ColumnConstants0,
           (IdNo =/= ?TNO) or (length(Const) =:= 1)].

opt_constants(L, ColumnConstants) ->
    Ns = lists:usort([IdNo || {{IdNo,_Col},_Const,_FilNs} <- ColumnConstants]),
    [{clause,L,[?I(IdNo)],[],[column_fun(ColumnConstants, IdNo, L)]}
     || IdNo <- Ns]
     ++ [{clause,L,[?V('_')],[],[?A(no_column_fun)]}].

abstr(Term, Anno) ->
    erl_parse:abstract(Term, loc(Anno)).

join_quals(JoinInfo, QCs, L, LcNo, ExtraConstants, AllVars) ->
    {LastGoI, LastSI} =
        lists:foldl(fun({_QId,{_QIVs,{{fil,_},GoI,SI}}}, 
                        {GoI0, _SI0}) when GoI >= GoI0 ->
                            {GoI + 2, SI + 1};
                       ({_QId,{_QIVs,{{gen,_,_,_},GoI,SI}}}, 
                        {GoI0, _SI0}) when GoI >= GoI0 ->
                            {GoI + 3, SI + 2};
                       (_, A) ->
                            A
                    end, {0, 0}, QCs),
    LastQId = lists:max([QId || {QId,{_QIVs,{_Q,_GoI,_SI}}} <- QCs]),
  Only two tables for the time being .
  the first of the two joined generators . Its introduced variables
  are the variables introduced by any of the two joined generators .
    QNums = case JoinInfo of
                {EqualCols, MatchCols} ->
                    EQs = join_qnums(EqualCols),
                    MQs = join_qnums(MatchCols),
                    [{Q1,Q2,'=:='} || {Q1,Q2} <- MQs] ++
                        [{Q1,Q2,'=='} || {Q1,Q2} <- EQs -- MQs];
                EqualCols ->
                    [{Q1,Q2,'=='} || {Q1,Q2} <- join_qnums(EqualCols)]
            end,
    LD = [begin 
              [{QId1,P1,GV1,QIVs1}] = 
                  [{QId,P,GV,QIVs} || 
                      {QId,{QIVs,{{gen,P,_,GV},_GoI,_SI}}} <- QCs, 
                      QId#qid.no =:= Q1],
              [{QId2,P2,QIVs2}] = 
                  [{QId,P,QIVs--[GV]} || 
                      {QId,{QIVs,{{gen,P,_,GV},_,_}}} <- QCs,
                      QId#qid.no =:= Q2],
              {QId1,Op,P1,GV1,QIVs1++QIVs2,QId2,P2}
          end || {Q1, Q2, Op} <- lists:usort(QNums)],
    Aux = abst_vars(aux_vars(['F','H','O','C'], LcNo, AllVars), L),
    F = fun({QId1,Op,P1,GV1,QIVs,QId2,P2}, {QId,GoI,SI}) ->
                AP1 = anon_pattern(P1),
                AP2 = anon_pattern(P2),
                Cs1 = join_handle_constants(QId1, ExtraConstants),
                Cs2 = join_handle_constants(QId2, ExtraConstants),
                H1 = join_handle(AP1, L, Aux, Cs1),
                H2 = join_handle(AP2, L, Aux, Cs2),
                Join = {join,Op,QId1#qid.no,QId2#qid.no,H1,H2,Cs1,Cs2},
                G = {NQId=QId#qid{no = QId#qid.no + 1},
                     {QIVs,{{gen,{cons,L,P1,P2},Join,GV1},GoI,SI}}},
                A = {NQId, GoI + 3, SI + 2},
                {G, A}
        end,
    {Qs, _} = lists:mapfoldl(F, {LastQId, LastGoI, LastSI}, LD),
    Qs.

join_qnums(Cols) ->
    lists:usort([{Q1, Q2} || {[{Q1,_C1}, {Q2,_C2}], _Skip} <- Cols]).

anon_pattern(P) ->
    MoreThanOnce = lists:usort(occ_vars(P) -- qlc:vars(P)),
    {AP, foo} = var_mapfold(fun({var, L, V}, A) ->
                                    case lists:member(V, MoreThanOnce) of
                                        true -> 
                                            {{var, L, V}, A};
                                        false ->
                                            {{var, L, '_'}, A}
                                    end
                            end, foo, P),
    AP.

join_handle(AP, L, [F, H, O, C], Constants) ->
    case {AP, Constants} of
        {{var, _, _}, []} ->
            {'fun',L,{clauses,[{clause,L,[H],[],[H]}]}};
        _ ->
            A = anno0(),
            G0 = [begin
                      Call = {call,A,{atom,A,element},[{integer,A,Col},O]},
                      list2op([{op,A,Op,Con,Call} || {Con,Op} <- Cs], 'or')
                  end || {Col,Cs} <- Constants],
            G = if G0 =:= [] -> G0; true -> [G0] end,
            CC1 = {clause,L,[AP],G,[{cons,L,O,closure({call,L,F,[F,C]},L)}]},
            CC2 = {clause,L,[?V('_')],[],[{call,L,F,[F,C]}]},
            Case = {'case',L,O,[CC1,CC2]},
            Cls = [{clause,L,[?V('_'),{nil,L}],[],[{nil,L}]},
                   {clause,L,[F,{cons,L,O,C}],[],[Case]},
                   {clause,L,[F,C],[[{call,L,?A(is_function),[C]}]],
                    [{call,L,F,[F,{call,L,C,[]}]}]},
                   {clause,L,[?V('_'),C],[],[C]}],
            Fun = {'fun', L, {clauses, Cls}},
            {'fun',L,{clauses,[{clause,L,[H],[],[{match,L,F,Fun}, 
                                                 closure({call,L,F,[F,H]}, 
                                                         L)]}]}}
    end.

join_handle_constants(QId, ExtraConstants) ->
    IdNo = QId#qid.no,
    case lists:keyfind(IdNo, 1, ExtraConstants) of
        {IdNo, ConstOps} ->
            ConstOps;
        false ->
            []
    end.

  outside ( before ) the QLC . Perhaps " parameter " would be a more


column_fun(Columns, QualifierNumber, LcL) ->
    A = anno0(),
    ColCls0 = 
        [begin
  at least one value to look up
             Vs1 = list2cons(Vs0),
             Fils1 = {tuple,A,[{atom,A,FTag},
                               lists:foldr
                                   (fun(F, Ac) -> {cons,A,{integer,A,F},Ac}
                                    end, {nil,A}, Fils)]},
             Tag = case ordsets:to_list(qlc:vars(Vs1)) of
                                length(Vs0) > 1 ->
                           usort_needed;
                       _ ->
                           values
                   end,
             Vs = {tuple,A,[{atom,A,Tag},Vs1,Fils1]},
             {clause,A,[erl_parse:abstract(Col)],[],[Vs]}
         end ||
            {{CIdNo,Col}, Vs0, {FTag,Fils}} <- Columns,
            CIdNo =:= QualifierNumber]
        ++ [{clause,A,[{var,A,'_'}],[],[{atom,A,false}]}],
    ColCls = set_anno(ColCls0, LcL),
    {'fun', LcL, {clauses, ColCls}}.

  Tries to find columns of the template that ( 1 ) are equal to ( or
  match ) or ( 2 ) match columns of the patterns of the generators . The
  - > [   , Equal | Match } ]
  EqType = abstract code for { _ | ' = = ' | ' = : = ' }

template_columns(Qs0, E0, AllIVs, Dependencies, State) ->
    E = expand_expr_records(pre_expand(E0), State),
    TemplateAsPattern = template_as_pattern(E),
    Qs = [TemplateAsPattern | Qs0],
    EqualColumns = equal_columns2(Qs, AllIVs, Dependencies, State),
    MatchColumns = eq_columns2(Qs, AllIVs, Dependencies, State),
    Equal = template_cols(EqualColumns), 
    Match = template_cols(MatchColumns),
    L = anno0(),
    if 
        Match =:= Equal -> 
            [{?V('_'), Match}];
        true -> 
            [{?A('=='), Equal}, {?A('=:='), Match}]
    end.

equal_columns2(Qualifiers, AllIVs, Dependencies, State) ->
    {JI, _Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State,_JoinOp = '=='),
    JI.

eq_columns2(Qualifiers, AllIVs, Dependencies, State) ->
    {JI, _SKip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=:='),
    JI.

template_cols(ColumnClasses) ->
    lists:sort([{{IdNo,Col}, lists:usort(Cs)} ||
                   Class <- ColumnClasses,
                   {IdNo,Col} <- Class,
                   IdNo =/= ?TNO,
                   [] =/= (Cs = [C || {?TNO,C} <- Class])]).

template_as_pattern(E) ->
    P = simple_template(E),
    {?TID,foo,foo,{gen,P,{nil,anno0()}}}.

simple_template({call,L,{remote,_,{atom,_,erlang},{atom,_,element}}=Call,
                 [{integer,_,I}=A1,A2]}) when I > 0 ->
    {call, L, Call, [A1, simple_template(A2)]};
simple_template({var, _, _}=E) ->
    E;
simple_template({tuple, L, Es}) ->
    {tuple, L, [simple_template(E) || E <- Es]};
simple_template({cons, L, H, T}) ->
    {cons, L, simple_template(H), simple_template(T)};
simple_template(E) ->
    case catch erl_parse:normalise(E) of
        {'EXIT', _} -> unique_var();
        _ -> E
    end.

  Qualifier QId ( a filter ) uses variables introduced in QId ' .
qualifier_dependencies(Qualifiers, IntroVs) ->
    Intro = sofs:relation([{IV,QId} || {QId,IVs} <- IntroVs, IV <- IVs]),
    {FilterData, _} = qual_data(Qualifiers),
    Used = sofs:relation([{QId,UV} ||
                             {QId,{fil,F}} <- FilterData,
                             UV <- qlc:vars(F)]),
    Depend = sofs:strict_relation(sofs:relative_product(Used, Intro)),
    G = sofs:family_to_digraph(sofs:relation_to_family(Depend)),
    Dep0 = [{V,digraph_utils:reachable_neighbours([V], G)} || 
               V <- digraph:vertices(G)],
    true = digraph:delete(G),
    FilterIds = sofs:set(filter_ids(Qualifiers)),
    Dep1 = sofs:restriction(sofs:family(Dep0), FilterIds),
    NoDep = sofs:constant_function(FilterIds, sofs:empty_set()),
    sofs:to_external(sofs:family_union(Dep1, NoDep)).

filter_ids(Qualifiers) ->
    {FilterData, _} = qual_data(Qualifiers),
    [QId || {QId,_} <- FilterData].

  - > [ { QualifierNumber , MatchSpec,[QualifierNumber ' ] }
  depend on QualifierNumber ( a generator Pattern < - LE ) only .
  MatchSpec is the match specification for [ Pattern ' || Pattern < - LE ,
  replaced by one match specification , otherwise a modified Pattern .
match_spec_quals(Template, Dependencies, Qualifiers, State) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    NoFilterGIds = [GId || {GId,_} <- GeneratorData] 
                   -- lists:flatmap(fun({_,GIds}) -> GIds end, Dependencies),
    Filters = filter_list(FilterData, Dependencies, State),
    Candidates = [{QId2#qid.no,Pattern,[Filter],F} || 
                     {QId,[QId2]} <- Dependencies,
                     {GQId,{gen,Pattern,_}} <- GeneratorData,
                     GQId =:= QId2,
                     FQId =:= QId] 
               ++ [{GId#qid.no,Pattern,[],{atom,anno0(),true}} ||
                      {GId,{gen,Pattern,_}} <- GeneratorData,
                      lists:member(GId, NoFilterGIds)],
    E = {nil, anno0()},
    GF = [{{GNum,Pattern},Filter} || 
             {GNum,Pattern,Filter,F} <- Candidates,
             no =/= try_ms(E, Pattern, F, State)],
    GFF = sofs:relation_to_family(sofs:relation(GF, 
                                                [{gnum_pattern,[filter]}])),
    GFFL = sofs:to_external(sofs:family_union(GFF)),
    try
        [{{GNum,Pattern}, GFilterData}] = GFFL,
        true = length(GFilterData) =:= length(FilterData),
        [_] = GeneratorData,
        AbstrMS = gen_ms(Template, Pattern, GFilterData, State),
  There is one generator and every filter uses some of the
        [{GNum, AbstrMS, all}]
    catch _:_ ->
        {TemplVar, _} = anon_var({var,anno0(),'_'}, 0),
        [one_gen_match_spec(GNum, Pattern, GFilterData, State, TemplVar) ||
            {{GNum,Pattern},GFilterData} <- GFFL]
    end.

one_gen_match_spec(GNum, Pattern0, GFilterData, State, TemplVar) ->
    {E, Pattern} = pattern_as_template(Pattern0, TemplVar),
    AbstrMS = gen_ms(E, Pattern, GFilterData, State),
    {GNum, AbstrMS, [FId#qid.no || {FId,_} <- GFilterData]}.

gen_ms(E, Pattern, GFilterData, State) ->
    {ok, MS, AMS} = try_ms(E, Pattern, filters_as_one(GFilterData), State),
    case MS of
        [{'$1',[true],['$1']}] ->
            {atom, anno0(), no_match_spec};
        _ ->
            AMS
    end.

  The pattern is accepted by ets : fun2ms/1 , that is , = /2 can only
pattern_as_template({var,_,'_'}, TemplVar) ->
    {TemplVar, TemplVar};
pattern_as_template({var,_,_}=V, _TemplVar) ->
    {V, V};
pattern_as_template({match,L,E,{var,_,'_'}}, TemplVar) ->
    {TemplVar, {match,L,E,TemplVar}};
pattern_as_template({match,L,{var,_,'_'},E}, TemplVar) ->
    {TemplVar, {match,L,E,TemplVar}};
pattern_as_template({match,_,_E,{var,_,_}=V}=P, _TemplVar) ->
    {V, P};
pattern_as_template({match,_,{var,_,_}=V,_E}=P, _TemplVar) ->
    {V, P};
pattern_as_template(E, TemplVar) ->
    L = anno0(),
    {TemplVar, {match, L, E, TemplVar}}.

  - > { ColumnConstants ,  , ExtraConstants }
  SizeInfo = [ { QualifierNumber , NumberOfColumns } ]
  Column = { QualifierNumber , ColumnNumber } }
  FilterNo is a filter that can be skipped at runtime provided constants
  ExtraConstants =
                          [ { AbstractConstant , AbstractOperator } ] } ] } ]
constants_and_sizes(Qualifiers0, E, Dependencies, AllIVs, State) ->
    TemplateAsPattern = template_as_pattern(E),
    Qualifiers = [TemplateAsPattern | Qualifiers0],
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    {Filter, Anon1, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    PatBindFun = fun(_Op, Value) -> is_bindable(Value) end,
    {PatternFrame, PatternVars} = 
        pattern_frame(GeneratorData, PatBindFun, Anon1, State),
    PatternFrames = frame2frames(PatternFrame),
    FilterFun = 
        fun(BindFun) -> 
              filter(Filter, PatternFrames, BindFun, State, Imported)
        end,
    SzFs = FilterFun(PatBindFun),

    SizeInfo = pattern_sizes(PatternVars, SzFs),
    SelectorFun = const_selector(Imported),
    PatternConstants = 
        lists:flatten(frames_to_columns(PatternFrames, PatternVars,
                                        deref_pattern(Imported),
                                        SelectorFun, Imported,
                                        '=:=')),

    {EqColumnConstants, _EqExtraConsts} = 
        constants(FilterFun, PatternVars, PatternConstants, PatternFrame,
                  FilterData, Dependencies, _LookupOp1 = '=:=', 
                  Imported, State),
    {EqualColumnConstants, EqualExtraConsts} = 
        constants(FilterFun, PatternVars, PatternConstants, PatternFrame,
                  FilterData, Dependencies, _LookupOp2 = '==', 
                  Imported, State),

    ExtraCon1 = 
        [{{GId,Col},{Val,Op}} ||
            {Consts,Op} <- [{EqualExtraConsts,'=='}],
            {{GId,Col},Val} <- Consts],
    ExtraConstants = 
      family_list([{GId, {Col,ValOps}} ||
                      {{GId,Col},ValOps} <- family_list(ExtraCon1)]),
    {EqColumnConstants, EqualColumnConstants, ExtraConstants, SizeInfo}.

constants(FilterFun, PatternVars, PatternConstants, PatternFrame, 
          FilterData, Dependencies, LookupOp, Imported, State) ->
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    Fs = FilterFun(BindFun),
    SelectorFun = const_selector(Imported),
    ColumnConstants0 = frames_to_columns(Fs, PatternVars, 
                                         deref_lookup(Imported, LookupOp),
                                         SelectorFun, Imported, LookupOp),
    ColumnConstants1 = lists:flatten(ColumnConstants0),
    ExtraConstants = 
       [{{GId,Col},Val} ||
           {{GId,Col},Vals} <- ColumnConstants1 -- PatternConstants,
           GId =/= ?TNO,
           Val <- Vals],
    ColumnConstants = lu_skip(ColumnConstants1, FilterData, PatternFrame,
                              PatternVars, Dependencies, State,
                              Imported, LookupOp),
    {ColumnConstants, ExtraConstants}.

  table matches keys . One way would be to look up the term both with

deref_lookup(Imported, '==') ->
    fun(PV, F) -> deref_values(PV, F, Imported) end;
deref_lookup(Imported, '=:=') ->
    BFun = fun(DV, Op) ->
                   Op =:= '=:=' orelse free_of_integers(DV, Imported)
           end,
    fun(PV, F) -> deref_values(PV, F, BFun, Imported) end.

lu_skip(ColConstants, FilterData, PatternFrame, PatternVars, 
        Dependencies, State, Imported, LookupOp) ->
    FailSelector = fun(_Frame) -> fun(Value) -> {yes, Value} end end,
    PatternFrames = frame2frames(PatternFrame),
    PatternColumns = 
        lists:flatten(frames_to_columns(PatternFrames, PatternVars,
                                        deref_pattern(Imported), FailSelector,
                                        Imported, LookupOp)),

  Note : ColFil can contain filters for columns that can not be
  Note : one filter at a time is tested ; only the pattern is
  ( an example : { { X , Y } } < - LE , X = : = 1 , Y = : = a ) .
    BindFun = fun(_Op, Value) -> is_bindable(Value) end,
    ColFil = [{Column, FId#qid.no} ||
                 {FId,{fil,Fil}} <- 
                     filter_list(FilterData, Dependencies, State),
                 [] =/= (SFs = safe_filter(reset_anno(Fil), PatternFrames,
                                           BindFun, State, Imported)),
                 {GId,PV} <- PatternVars,
                 [] =/= 
                    (Cols = hd(frames_to_columns(SFs, [{GId, PV}],
                                                 deref_lu_skip(LookupOp,
                                                               Imported),
                                                 const_selector(Imported),
                                                 Imported, LookupOp))),
  The filter must not test more than one column ( unless the
  ( an example : { X=1 } < - ... , X = : = 1 ) .
                 length(D = Cols -- PatternColumns) =:= 1,
                 {{_,Col} = Column, Constants} <- D,
                 lists:all(
                   fun(Frame) ->
                     {VarI, FrameI} = unify_column(Frame, PV, Col, BindFun,
                                                   Imported),
                     VarValues = deref_skip(VarI, FrameI, LookupOp, Imported),

                     {NV, F1} = unify_column(PatternFrame, PV, Col, BindFun,
                                             Imported),
                     F2 = unify_var_bindings(VarValues, '=:=', NV, F1, 
                                             BindFun, Imported, false),
  " X = : = 1 , X = : = U " , U imported ; only 1 is looked up ) ,
                     LookedUpConstants = 
                         case lists:keyfind(Column, 1, ColConstants) of
                             false -> [];
                             {Column, LUCs} -> LUCs
                         end,
  values equal . See also frames_to_columns ( ) .
                     length(VarValues) =< 1 andalso
                     (Constants -- LookedUpConstants =:= []) andalso
                     bindings_is_subset(Frame, F2, Imported)
                   end, SFs)],
    ColFils = family_list(ColFil),
  It does not imply that there is only one generator as is the case
    [{Col, Constants, skip_tag(Col, ColFils, FilterData)} ||
        {Col,Constants} <- ColConstants].

deref_skip(E, F, _LookupOp, Imported) ->
    deref(E, F, Imported).

deref_lu_skip('==', Imported) ->
    BFun = fun(DV, Op) ->
                   Op =:= '==' orelse free_of_integers(DV, Imported)
           end,
    fun(PV, F) -> deref_values(PV, F, BFun, Imported) end;
deref_lu_skip('=:=', Imported) ->
    fun(PV, F) -> deref_values(PV, F, Imported) end.

equal_columns(Qualifiers, AllIVs, Dependencies, State) ->
    {Cs, Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=='),
    join_gens(Cs, Qualifiers, Skip).

eq_columns(Qualifiers, AllIVs, Dependencies, State) ->
    {Cs, Skip} = 
        join_info(Qualifiers, AllIVs, Dependencies, State, _JoinOp = '=:='),
    join_gens(Cs, Qualifiers, Skip).

join_gens(Cs0, Qs, Skip) ->
    Cs = [family_list(C) || C <- Cs0],
    {FD, _GeneratorData} = qual_data(Qs),
    {join_gens2(lists:filter(fun(C) -> length(C) =:= 2 end, Cs), FD, Skip),
     join_gens2(lists:filter(fun(C) -> length(C) > 2 end, Cs), FD, Skip)}.

join_gens2(Cs0, FilterData, Skip) ->
    [{J, skip_tag(case lists:keyfind(J, 1, Skip) of
                      {J, FilL} ->
                          FilL;
                      false ->
                          []
                  end, FilterData)} ||
        J <- lists:append([qlc:all_selections(C) || C <- Cs0])].

skip_tag(FilList, FilterData) ->
    {if
         length(FilterData) =:= length(FilList) ->
             all;
         true ->
             some
     end, FilList}.

skip_tag(Col, ColFils, FilterData) ->
    case lists:keyfind(Col, 1, ColFils) of
        {Col, FilL} ->
            Tag = if
                      length(FilterData) =:= length(FilL) ->
                          all;
                      true ->
                          some
                  end,
            {Tag, FilL};
        false -> 
            {some,[]}
    end.

  If LookupOp is ' = : = ' then " equal " means that the columns are matched ;
  if LookupOp is ' = = ' then " equal " means that the columns are matched or
join_info(Qualifiers, AllIVs, Dependencies, State, JoinOp) ->
    {FilterData, GeneratorData} = qual_data(Qualifiers),
    {Filter, Anon1, Imported} = 
        filter_info(FilterData, AllIVs, Dependencies, State),
    BindFun = fun(_Op, V) -> bind_no_const(V, Imported) end,
    {PatternFrame, PatternVars} = 
        pattern_frame(GeneratorData, BindFun, Anon1, State),
    PatternFrames = frame2frames(PatternFrame),
    Fs = filter(Filter, PatternFrames, BindFun, State, Imported),
    SelectorFun = no_const_selector(Imported),
    Cols = frames_to_columns(Fs, PatternVars,
                             fun(PV1, F) -> deref_join(PV1, F, JoinOp) end,
                             SelectorFun, Imported, '=:='),
    JC = join_classes(Cols),
    Skip = join_skip(JC, FilterData, PatternFrame,
                     PatternVars, Dependencies, State, Imported, JoinOp),
    {JC, Skip}.

deref_join(E, Frame, '==') ->
    deref_values(E, Frame, _Imp = []);
deref_join(E, Frame, '=:=') ->
    deref_values(E, Frame, fun(_DV, Op) -> Op =:= '=:=' end, all).

join_classes(Cols0) ->
    ColVar = sofs:relation(lists:append(Cols0)),
    Cols = sofs:partition(2, ColVar),
    [[C || {C,_} <- Cs] || Cs <- sofs:to_external(Cols), length(Cs) > 1].

join_skip(JoinClasses, FilterData, PatternFrame, PatternVars, Dependencies,
          State, Imported, JoinOp) ->
    PatternFrames = frame2frames(PatternFrame),
    ColFil = [{JoinClass,FId#qid.no} ||
                 [{Q1,C1}, {Q2,C2}]=JoinClass <- JoinClasses,
                 {GId1, PV1} <- PatternVars,
                 GId1#qid.no =:= Q1,
                 {GId2, PV2} <- PatternVars,
                 GId2#qid.no =:= Q2,

  Select a filter that depends on the two generators :
                 {FId,{fil,Fil}} <- 
                     filter_list(FilterData, Dependencies, State),
                 {value,{_,GIds}} <- 
                     [lists:keysearch(FId, 1, Dependencies)],
                 GIds =:= lists:sort([GId1,GId2]),

                 begin
  element(C1 , G1 ) JoinOp element(C2 , G2 ) .
                     BindFun = fun(_Op, V) -> is_bindable(V) end,
                     {V1, JF1} = 
                       unify_column(PatternFrame, PV1, C1, BindFun, Imported),
                     {V2, JF2} = 
                         unify_column(JF1, PV2, C2, BindFun, Imported),
                     JF = unify(JoinOp, V1, V2, JF2, BindFun, Imported),

                     SFs = safe_filter(reset_anno(Fil), PatternFrames,
                                       BindFun, State, Imported),
                     lists:all(fun(Frame) -> 
                                       bindings_is_subset(Frame, JF, JImp)
                               end, SFs) andalso SFs =/= []
                 end],
    family_list(ColFil).

filter_info(FilterData, AllIVs, Dependencies, State) ->
    FilterList = filter_list(FilterData, Dependencies, State),
    Filter0 = reset_anno(filters_as_one(FilterList)),
    Anon0 = 0,
    {Filter, Anon1} = anon_var(Filter0, Anon0),
                                ordsets:from_list(AllIVs)), 
    {Filter, Anon1, Imported}.

  Note : guard filters using variables from one generator are allowed
filter_list(FilterData, Dependencies, State) ->
    sel_gf(FilterData, 1, Dependencies, State, [], []).

sel_gf([], _N, _Deps, _RDs, _Gens, _Gens1) ->
    [];
sel_gf([{#qid{no = N}=Id,{fil,F}}=Fil | FData], N, Deps, State, Gens, Gens1) ->
    case is_guard_test(F, State) of
        true ->
            {Id,GIds} = lists:keyfind(Id, 1, Deps),
            case length(GIds) =< 1 of
                true ->
                    case generators_in_scope(GIds, Gens1) of
                        true ->
                            [Fil|sel_gf(FData, N+1, Deps, State, Gens, Gens1)];
                        false ->
                            sel_gf(FData, N + 1, Deps, State, [], [])
                    end;
                false ->
                    case generators_in_scope(GIds, Gens) of
                        true ->
                            [Fil | sel_gf(FData, N + 1, Deps, State, Gens, [])];
                        false ->
                            sel_gf(FData, N + 1, Deps, State, [], [])
                    end
            end;
        false ->
            sel_gf(FData, N + 1, Deps, State, [], [])
    end;
sel_gf(FData, N, Deps, State, Gens, Gens1) ->
    sel_gf(FData, N + 1, Deps, State, [N | Gens], [N | Gens1]).

generators_in_scope(GenIds, GenNumbers) ->
    lists:all(fun(#qid{no=N}) -> lists:member(N, GenNumbers) end, GenIds).

pattern_frame(GeneratorData, BindFun, Anon1, State) ->
    Frame0 = [],
    {PatternFrame, _Anon2, PatternVars} =
        lists:foldl(fun({QId,{gen,Pattern,_}}, {F0,An0,PVs}) ->
                            {F1, An1, PV} = 
                                pattern(Pattern, An0, F0, BindFun, State),
                            {F1, An1, [{QId,PV} | PVs]}
                    end, {Frame0, Anon1, []}, GeneratorData),
    {PatternFrame, PatternVars}.
              
const_selector(Imported) ->
    selector(Imported, fun is_const/2).

no_const_selector(Imported) ->
    selector(Imported, fun(V, I) -> not is_const(V, I) end).

selector(Imported, TestFun) ->
    fun(_Frame) ->
            fun(Value) -> 
                    case TestFun(Value, Imported) of
                        true ->
                            {yes, Value};
                        false ->
                            no
                    end
            end
    end.

bind_no_const(Value, Imported) ->
    case is_const(Value, Imported) of
        true ->
            false;
        false ->
            is_bindable(Value)
    end.

is_const(Value, Imported) ->
    [] =:= ordsets:to_list(ordsets:subtract(qlc:vars(Value), Imported)).

is_bindable(Value) ->
    case normalise(Value) of
        {ok, _C} ->
            true;
        not_ok ->
            false
    end.

pattern(P0, AnonI, Frame0, BindFun, State) ->
    P1 = try 
             expand_pattern_records(P0, State)
         end,
    P2 = reset_anno(P1),
    {P3, AnonN} = anon_var(P2, AnonI),
    {P4, F1} = match_in_pattern(tuple2cons(P3), Frame0, BindFun),
    {var, _, PatternVar} = UniqueVar = unique_var(),
    F = unify('=:=', UniqueVar, P, F2, BindFun, _Imported = []),
    {F, AnonN, PatternVar}.

frame2frames(failed) ->
    [];
frame2frames(F) ->
    [F].

match_in_pattern({match, _, E10, E20}, F0, BF) ->
    {E1, F1} = match_in_pattern(E10, F0, BF),
    {E2, F} = match_in_pattern(E20, F1, BF),
    E = case BF('=:=', E1) of
            true -> E1;
            false -> E2
        end,
    {E, unify('=:=', E1, E2, F, BF, _Imported = [])};
match_in_pattern(T, F0, BF) when is_tuple(T) ->
    {L, F} = match_in_pattern(tuple_to_list(T), F0, BF),
    {list_to_tuple(L), F};
match_in_pattern([E0 | Es0], F0, BF) ->
    {E, F1} = match_in_pattern(E0, F0, BF),
    {Es, F} = match_in_pattern(Es0, F1, BF),
    {[E | Es], F};
match_in_pattern(E, F, _BF) ->
    {E, F}.

-define(ANON_VAR(N), N).

anon_var(E, AnonI) ->
    var_mapfold(fun({var, L, '_'}, N) ->
                        {{var, L, ?ANON_VAR(N)}, N+1};
                   (Var, N) -> {Var, N}
                end, AnonI, E).

reset_anno(T) ->
    set_anno(T, anno0()).

set_anno(T, A) ->
    map_anno(fun(_L) -> A end, T).

-record(fstate, {state, bind_fun, imported}).

filter(_E, []=Frames0, _BF, _State, _Imported) ->
    Frames0;
filter(E0, Frames0, BF, State, Imported) ->
    E = pre_expand(E0),
    FState = #fstate{state = State, bind_fun = BF, imported = Imported},
    filter1(E, Frames0, FState).

  One frame for each path through the and/or expression .
  " A xor B " is equal to " ( A and not B ) or ( not A and B ) " .
  " xor " can be handled just as " or " .
  kept for backward compatibility . Now it has become part of the 

filter1({op, _, Op, L0, R0}, Fs, FS) when Op =:= '=:='; Op =:= '==' ->
    #fstate{state = S, bind_fun = BF, imported = Imported} = FS,
    lists:flatmap(fun(F0) ->
                          {L, F1} = prep_expr(L0, F0, S, BF, Imported),
                          {R, F2} = prep_expr(R0, F1, S, BF, Imported),
                          case unify(Op, L, R, F2, BF, Imported) of
                              failed -> [];
                              F -> [F]
                          end
                  end, Fs);
filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'and'; Op =:= 'andalso' ->
    filter1(R, filter1(L, Fs, FS), FS);
filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'or'; 
                                        Op =:= 'orelse';
                                        Op =:= 'xor' ->
    filter1(L, Fs, FS) ++ filter1(R, Fs, FS);
filter1({atom,_,Atom}, _Fs, _FS) when Atom =/= true ->
    [];
filter1({call,L,{remote,_,{atom,_,erlang},{atom,_,is_record}},[T,R]},
        Fs, FS) ->
    filter1({op,L,'=:=',{call,L,{remote,L,{atom,L,erlang},{atom,L,element}},
                         [{integer,L,1},T]},R},
            Fs, FS);
  erlang : is_record/3 ( the size information is ignored ):
filter1({call,L,{remote,L1,{atom,_,erlang}=M,{atom,L2,is_record}},[T,R,_Sz]},
        Fs, FS) ->
    filter1({call,L,{remote,L1,M,{atom,L2,is_record}},[T,R]}, Fs, FS);
filter1(_E, Fs, _FS) ->
    Fs.

  bindings returned capture _ all _ aspects of the filter ( wrt BF ) .
safe_filter(_E, []=Frames0, _BF, _State, _Imported) ->
    Frames0;
safe_filter(E0, Frames0, BF, State, Imported) ->
    E = pre_expand(E0),
    FState = #fstate{state = State, bind_fun = BF, imported = Imported},
    safe_filter1(E, Frames0, FState).

safe_filter1({op, _, Op, L0, R0}, Fs, FS) when Op =:= '=:='; Op =:= '==' ->
    #fstate{state = S, bind_fun = BF, imported = Imported} = FS,
    lists:flatmap(fun(F0) ->
                          {L, F1} = prep_expr(L0, F0, S, BF, Imported),
                          {R, F2} = prep_expr(R0, F1, S, BF, Imported),
                          case safe_unify(Op, L, R, F2, BF, Imported) of
                              failed -> [];
                              F -> [F]
                          end
                  end, Fs);
safe_filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'and'; Op =:= 'andalso' ->
    safe_filter1(R, safe_filter1(L, Fs, FS), FS);
safe_filter1({op, _, Op, L, R}, Fs, FS) when Op =:= 'or'; Op =:= 'orelse' ->
    safe_filter1(L, Fs, FS) ++ safe_filter1(R, Fs, FS);
safe_filter1({atom,_,true}, Fs, _FS) ->
    Fs;
safe_filter1(_E, _Fs, _FS) ->
    [].

  M : F ( ) for { M , F } ( ) ;  : F ( ) for F ( ) ; is_record ( ) for record ( ) .
pre_expand({call,L1,{atom,L2,record},As}) ->
    pre_expand({call,L1,{atom,L2,is_record},As});
pre_expand({call,L,{atom,_,_}=F,As}) ->
    pre_expand({call,L,{remote,L,{atom,L,erlang},F},As});
pre_expand({call,L,{tuple,_,[M,F]},As}) ->
    pre_expand({call,L,{remote,L,M,F},As});
pre_expand(T) when is_tuple(T) ->
    list_to_tuple(pre_expand(tuple_to_list(T)));
pre_expand([E | Es]) ->
    [pre_expand(E) | pre_expand(Es)];
pre_expand(T) ->
    T.

  - > [ [ { { QualifierNumber , ColumnNumber } , [ Value ] } ] ]
frames_to_columns([], _PatternVars, _DerefFun, _SelectorFun, _Imp, _CompOp) ->
    [];
frames_to_columns(Fs, PatternVars, DerefFun, SelectorFun, Imp, CompOp) ->
    SizesVarsL =
        [begin 
             PatVar = {var,anno0(),PV},
             PatternSizes = [pattern_size([F], PatVar, false) || 
                                F <- Fs],
             MaxPZ = lists:max([0 | PatternSizes -- [undefined]]),
             Vars = pat_vars(MaxPZ),
             {PatternId#qid.no, PatVar, PatternSizes, Vars}
         end || {PatternId, PV} <- PatternVars],
    BF = fun(_Op, Value) -> is_bindable(Value) end,
    Fun = fun({_PatN, PatVar, PatSizes, Vars}, Frames) -> 
                  [unify('=:=', pat_tuple(Sz, Vars), PatVar, Frame, BF, Imp) ||
                      {Sz, Frame} <- lists:zip(PatSizes, Frames)]
          end,
    NFs = lists:foldl(Fun, Fs, SizesVarsL),
    [frames2cols(NFs, PatN, PatSizes, Vars, DerefFun, SelectorFun, CompOp) ||
        {PatN, _PatVar, PatSizes, Vars} <- SizesVarsL].

frames2cols(Fs, PatN, PatSizes, Vars, DerefFun, SelectorFun, CompOp) ->
    Rs = [ begin
               RL = [{{PatN,Col},cons2tuple(element(2, Const))} ||
                        {V, Col} <- lists:zip(lists:sublist(Vars, PatSz),
                                              lists:seq(1, PatSz)),
  values compare equal , e.g. " X = : = 1
  andalso X = = 1.0 " . Looking up both
  values or one of them wo n't always do
  or the one stored in the table . Or
  gb_table in qlc(3 ) ) . ( Not a very strong
  argument . " X = : = 1 " could ( should ? ) be
                        tl(Consts = DerefFun(V, F)) =:= [],
                        (Const = (SelectorFun(F))(hd(Consts))) =/= no],
            end || {F,PatSz} <- lists:zip(Fs, PatSizes)],
    Ss = sofs:from_sets(Rs),
    D = sofs:intersection(sofs:projection(fun(S) -> sofs:projection(1, S) end,
                                          Ss)),
    Cs = sofs:restriction(sofs:relation_to_family(sofs:union(Ss)), D),
    [C || {_,Vs}=C <- sofs:to_external(Cs), not col_ignore(Vs, CompOp)].

pat_vars(N) ->
    [unique_var() || _ <- lists:seq(1, N)].

pat_tuple(Sz, Vars) when is_integer(Sz), Sz > 0 ->
    TupleTail = unique_var(),
    {cons_tuple, list2cons(lists:sublist(Vars, Sz) ++ TupleTail)};
pat_tuple(_, _Vars) ->
    unique_var().

  Do not handle tests as " X = : = 1.0 orelse X = = 1 " either .
col_ignore(_Vs, '=:=') ->
    false;
col_ignore(Vs, '==') ->
    length(Vs) =/= length(lists:usort([element(2, normalise(V)) || V <- Vs])).

pattern_sizes(PatternVars, Fs) ->
    [{QId#qid.no, Size} || 
        {QId,PV} <- PatternVars,
        undefined =/= (Size = pattern_size(Fs, {var,anno0(),PV}, true))].

pattern_size(Fs, PatternVar, Exact) ->
    Fun = fun(F) -> (deref_pattern(_Imported = []))(PatternVar, F) end,
    Derefs = lists:flatmap(Fun, Fs),
    Szs = [pattern_sz(Cs, 0, Exact) || {cons_tuple, Cs} <- Derefs],
    case lists:usort(Szs) of
        [Sz] when is_integer(Sz), Sz >= 0 -> Sz;
        [] when not Exact -> 0;
        _  -> undefined
    end.

pattern_sz({cons,_,_C,E}, Col, Exact) ->
    pattern_sz(E, Col+1, Exact);
pattern_sz({nil,_}, Sz, _Exact) ->
    Sz;
pattern_sz(_, _Sz, true) ->
    undefined;
pattern_sz(_, Sz, false) ->
    Sz.

deref_pattern(Imported) ->
    fun(PV, F) -> deref_values(PV, F, Imported) end.

prep_expr(E, F, S, BF, Imported) ->
    element_calls(tuple2cons(expand_expr_records(E, S)), F, BF, Imported).

unify_column(Frame, Var, Col, BindFun, Imported) ->
    A = anno0(),
    Call = {call,A,{remote,A,{atom,A,erlang},{atom,A,element}},
	    [{integer,A,Col}, {var,A,Var}]},
    element_calls(Call, Frame, BindFun, Imported).

element_calls({call,_,{remote,_,{atom,_,erlang},{atom,_,element}},
               [{integer,_,I},Term0]}, F0, BF, Imported) when I > 0 ->
  have an explicit " erlang : " prefix .
    TupleTail = unique_var(),
    VarsL = [unique_var() || _ <- lists:seq(1, I)],
    Vars = VarsL ++ TupleTail,
    Tuple = {cons_tuple, list2cons(Vars)},
    VarI = lists:nth(I, VarsL),
    {Term, F} = element_calls(Term0, F0, BF, Imported),
    {VarI, unify('=:=', Tuple, Term, F, BF, Imported)};
element_calls(T, F0, BF, Imported) when is_tuple(T) ->
    {L, F} = element_calls(tuple_to_list(T), F0, BF, Imported),
    {list_to_tuple(L), F};
element_calls([E0 | Es0], F0, BF, Imported) ->
    {E, F1} = element_calls(E0, F0, BF, Imported),
    {Es, F} = element_calls(Es0, F1, BF, Imported),
    {[E | Es], F};
element_calls(E, F, _BF, _Imported) ->
    {E, F}.

unique_var() ->
    {var, anno0(), make_ref()}.

is_unique_var({var, _L, V}) ->
    is_reference(V).

expand_pattern_records(P, State) ->
    A = anno0(),
    E = {'case',A,{atom,A,true},[{clause,A,[P],[],[{atom,A,true}]}]},
    {'case',_,_,[{clause,A,[NP],_,_}]} = expand_expr_records(E, State),
    NP.

expand_expr_records(E, State) ->
    RecordDefs = State#state.records,
    A = anno1(),
    Forms0 = RecordDefs ++ [{function,A,foo,0,[{clause,A,[],[],[pe(E)]}]}],
    Forms = erl_expand_records:module(Forms0, [no_strict_record_tests]),
    {function,_,foo,0,[{clause,_,[],[],[NE]}]} = lists:last(Forms),
    NE.

pe({op,Line,Op,A}) ->
    erl_eval:partial_eval({op,Line,Op,pe(A)});
pe({op,Line,Op,L,R}) ->
    erl_eval:partial_eval({op,Line,Op,pe(L),pe(R)});
pe(T) when is_tuple(T) ->
    list_to_tuple(pe(tuple_to_list(T)));
pe([E | Es]) ->
    [pe(E) | pe(Es)];
pe(E) ->
    E.

unify(Op, E1, E2, F, BF, Imported) ->
    unify(Op, E1, E2, F, BF, Imported, false).

safe_unify(Op, E1, E2, F, BF, Imported) ->
    unify(Op, E1, E2, F, BF, Imported, true).

    failed;
unify(_Op, E, E, F, _BF, _Imported, _Safe) ->
    F;
unify(Op, {var, _, _}=Var, E2, F, BF, Imported, Safe) ->
    extend_frame(Op, Var, E2, F, BF, Imported, Safe);
unify(Op, E1, {var, _, _}=Var, F, BF, Imported, Safe) ->
    extend_frame(Op, Var, E1, F, BF, Imported, Safe);
unify(Op, {cons_tuple, Es1}, {cons_tuple, Es2}, F, BF, Imported, Safe) ->
    unify(Op, Es1, Es2, F, BF, Imported, Safe);
unify(Op, {cons, _, L1, R1}, {cons, _, L2, R2}, F, BF, Imported, Safe) ->
    E = unify(Op, L1, L2, F, BF, Imported, Safe),
    unify(Op, R1, R2, E, BF, Imported, Safe);
unify(Op, E1, E2, F, _BF, _Imported, Safe) ->
    try
      {ok, C1} = normalise(E1),
      {ok, C2} = normalise(E2),
      if 
          Op =:= '=:=', C1 =:= C2 ->
              F;
          Op =:= '==', C1 == C2 ->
              F;
          true ->
              failed
      end 
    catch error:_ when Safe -> failed;
    end.

  X = : = 3 , X = = 3.0 . As a consequence , deref ( ) returns a list of


-record(bind, {var, value, op}). 

extend_frame(Op, Var, Value, F, BF, Imported, Safe) ->
    case var_values(Var, F) of
        [] ->
            case Value of
                {var, _, _} ->
                    case var_values(Value, F) of
                        [] ->
                            add_binding(Op, Value, Var, F, BF, Imported, Safe);
                        ValsOps ->
                            maybe_add_binding(ValsOps, Op, Value, Var, F, 
                                              BF, Imported, Safe)
                    end;
                _ ->
                    add_binding(Op, Var, Value, F, BF, Imported, Safe)
            end;
        ValsOps ->
            maybe_add_binding(ValsOps, Op, Var, Value, F, BF, Imported, Safe)
    end.

maybe_add_binding(ValsOps, Op, Var, Value, F0, BF, Imported, Safe) ->
    case unify_var_bindings(ValsOps, Op, Value, F0, BF, Imported, Safe) of
        failed ->
            failed;
        F ->
            case already_bound(Op, Var, Value, F) of
                true -> 
                    F;
                false ->
                    add_binding(Op, Var, Value, F, BF, Imported, Safe)
            end
    end.

already_bound(Op, Var, Value, F) ->
    BFun = fun(_DV, BOp) ->  Op =:= BOp end,
    DerefValue = deref_value(Value, Op, F, BFun, all),
    DerefVar = deref_var(Var, F, BFun, all),
    DerefValue -- DerefVar =:= [].

unify_var_bindings([], _Op, _Value, F, _BF, _Imported, _Safe) ->
    F;
unify_var_bindings([{VarValue, Op2} | Bindings],
                   Op1, Value, F0, BF, Imported, Safe) ->
    Op = deref_op(Op1, Op2),
    case unify(Op, VarValue, Value, F0, BF, Imported, Safe) of
        failed ->
            failed;
        F ->
            unify_var_bindings(Bindings, Op1, Value, F, BF, Imported, Safe)
    end.

deref_op('=:=', '=:=') ->
    '=:=';
deref_op(_, _) ->
    '=='.

  Note : usort works ; { integer , L,3 } does not match { float , L,3.0 } .

var_values(Var, Frame) ->
    [{Value, Op} || 
        #bind{value = Value, op = Op} <- var_bindings(Var, Frame)].

deref_var(Var, Frame, Imported) ->
    deref_var(Var, Frame, fun(_DV, _Op) -> true end, Imported).

deref_var(Var, Frame, BFun, Imported) ->
    lists:usort([ValOp || 
                    #bind{value = Value, op = Op} <- var_bindings(Var, Frame),
                    ValOp <- deref_value(Value, Op, Frame, BFun, Imported)]).

deref_value(Value, Op, Frame, BFun, Imported) ->
    lists:usort([{Val,value_op(ValOp, Op, Imported)} || 
                    {Val,_Op}=ValOp <- deref(Value, Frame, BFun, Imported)]).

add_binding(Op, Var0, Value0, F, BF, Imported, Safe) ->
    {Var, Value} = maybe_swap_var_value(Var0, Value0, F, Imported),
    case BF(Op, Value) of
        true ->
            add_binding2(Var, Value, Op, F);
        false when Safe ->
            failed;
        false when not Safe ->
            F
    end.

add_binding2(Var, Value, Op, F) ->
    case occurs(Var, Value, F) of
        true ->
            failed;
        false ->
            [#bind{var = Var, value = Value, op = Op} | F]
    end.

maybe_swap_var_value(Var, Value, Frame, Imported) ->
    case do_swap_var_value(Var, Value, Frame, Imported) of
        true ->
            {Value, Var};
        false ->
            {Var, Value}
    end.

do_swap_var_value({var, _, V1}=Var1, {var, _, V2}=Var2, F, Imported) ->
    case swap_vv(Var1, Var2, F) of
        [] ->
            case swap_vv(Var2, Var1, F) of
                [] ->
                    ordsets:is_element(V1, Imported) andalso 
                        not ordsets:is_element(V2, Imported);
                _Bs ->
                    true
            end;                
        _Bs ->
           false
    end;
do_swap_var_value(_, _, _F, _Imp) ->
    false.

swap_vv(V1, V2, F) ->
    [V || #bind{value = V} <- var_bindings(V1, F), V =:= V2].

normalise(E) ->
    case catch erl_parse:normalise(var2const(cons2tuple(E))) of
        {'EXIT', _} ->
            not_ok;
        C ->
            {ok, C}
    end.

occurs(V, V, _F) ->
    true;
occurs(V, {var, _, _} = Var, F) ->
    lists:any(fun(B) -> occurs(V, B#bind.value, F) end, var_bindings(Var, F));
occurs(V, T, F) when is_tuple(T) ->
    lists:any(fun(E) -> occurs(V, E, F) end, tuple_to_list(T));
occurs(V, [E | Es], F) ->
    occurs(V, E, F) orelse occurs(V, Es, F);
occurs(_V, _E, _F) ->
    false.

deref_values(E, Frame, Imported) ->
    deref_values(E, Frame, fun(_DV, _Op) -> true end, Imported).

deref_values(E, Frame, BFun, Imported) ->
    lists:usort([V || 
                    {V, Op} <- deref(E, Frame, BFun, Imported),
                    BFun(V, Op)]).

deref(E, F, Imp) ->
    BFun = fun(_DV, _Op) -> true end,
    deref(E, F, BFun, Imp).

deref({var, _, _}=V, F, BFun, Imp) ->
    DBs = lists:flatmap(fun(B) -> deref_binding(B, F, BFun, Imp) 
                        end, var_bindings(V, F)),
    case DBs of
        [] ->
            [{V, '=:='}];
        _ ->
            lists:usort(DBs)
    end;
deref(T, F, BFun, Imp) when is_tuple(T) ->
    [{list_to_tuple(DL), Op} || 
        {DL, Op} <- deref(tuple_to_list(T), F, BFun, Imp)];
deref(Es, F, BFun, Imp) when is_list(Es) ->
    L = [deref(C, F, BFun, Imp) || C <- Es],
    lists:usort([deref_list(S) || S <- all_comb(L)]);
deref(E, _F, _BFun, _Imp) ->
    [{E, '=:='}].

var_bindings(Var, F) ->
    [B || #bind{var = V}=B <- F, V =:= Var].

deref_binding(Bind, Frame, BFun, Imp) ->
    #bind{value = Value, op = Op0} = Bind,
    [{Val, Op} ||
        {Val, _Op}=ValOp <- deref(Value, Frame, BFun, Imp),
        BFun(Val, Op = value_op(ValOp, Op0, Imp))].
    
deref_list(L) ->
    Op = case lists:usort([Op || {_Val, Op} <- L]) of
             ['=:='] ->
                 '=:=';
             _ ->
                 '=='
         end,
    {[V || {V, _Op} <- L], Op}.

value_op({_V, '=='}, _BindOp, _Imp) ->
    '==';
value_op({_V, '=:='}, _BindOp='=:=', _Imp) ->
    '=:=';
value_op({V, '=:='}, _BindOp='==', Imp) ->
    case free_of_integers(V, Imp) of
        true ->
            '=:=';
        false ->
            '=='
    end.

all_comb([]) ->
    [[]];
all_comb([Cs | ICs]) ->
    [[C | L] || C <- Cs, L <- all_comb(ICs)].

free_of_integers(V, Imported) ->
    not has_integer(V) andalso not has_imported_vars(V, Imported).

has_imported_vars(Value, all) ->
    qlc:vars(Value) =/= [];
has_imported_vars(Value, Imported) ->
    [Var || Var <- qlc:vars(Value), lists:member(Var, Imported)] =/= [].

has_integer(Abstr) ->
    try
        has_int(Abstr)
    catch throw:true -> true
    end.

has_int({integer,_,I}) when float(I) == I ->
    throw(true);
has_int({float,_,F}) when round(F) == F ->
    throw(true);
has_int(T) when is_tuple(T) ->
    has_int(tuple_to_list(T));
has_int([E | Es]) ->
    has_int(E), 
    has_int(Es);
has_int(_) ->
    false.

tuple2cons({tuple, _, Es}) ->
    {cons_tuple, list2cons(tuple2cons(Es))};
tuple2cons(T) when is_tuple(T) ->
    list_to_tuple(tuple2cons(tuple_to_list(T)));
tuple2cons([E | Es]) ->
    [tuple2cons(E) | tuple2cons(Es)];
tuple2cons(E) ->
    E.

list2cons([E | Es]) ->
    {cons, anno0(), E, list2cons(Es)};
list2cons([]) ->
    {nil, anno0()};
list2cons(E) ->
    E.

cons2tuple({cons_tuple, Es}) ->
    {tuple, anno0(), cons2list(Es)};
cons2tuple(T) when is_tuple(T) ->
    list_to_tuple(cons2tuple(tuple_to_list(T)));
cons2tuple([E | Es]) ->
    [cons2tuple(E) | cons2tuple(Es)];
cons2tuple(E) ->
    E.

cons2list({cons, _, L, R}) ->
    [cons2tuple(L) | cons2list(R)];
cons2list({nil, _}) ->
    [];
    [cons2tuple(E)].

  Returns true if all bindings in F1 also occur in F2 .
  Viewing F1 and F2 as sets , the fact that F1 is a subset of F2 iff
  F1 union F2 is equal to F2 is used . ( This should take care of
bindings_is_subset(F1, F2, Imported) ->
  Extend F2 with the bindings in F1 :
    F = lists:foldl(fun(#bind{var = V, value = Value, op = Op}, Frame) ->
                            unify(Op, V, Value, Frame, BF, Imported)
                    end, F2, F1),
    bindings_subset(F, F2, Imported) andalso bindings_subset(F2, F, Imported).

bindings_subset(F1, F2, Imp) ->
    Vars = lists:usort([V || #bind{var = V} <- F1, not is_unique_var(V)]),
    lists:all(fun(V) ->
                      deref_var(V, F1, Imp) =:= deref_var(V, F2, Imp)
              end, Vars).

  ets : fun2ms(fun(P ) when F - > T end ) is a match spec . This is OK with
try_ms(E, P, Fltr, State) ->
    L = anno1(),
    Fun =  {'fun',L,{clauses,[{clause,L,[P],[[Fltr]],[E]}]}},
    Expr = {call,L,{remote,L,{atom,L,ets},{atom,L,fun2ms}},[Fun]},
    Form = {function,L,foo,0,[{clause,L,[],[],[Expr]}]},
    X = ms_transform:parse_transform(State#state.records ++ [Form], []),
    case catch 
        begin
            {function,L,foo,0,[{clause,L,[],[],[MS0]}]} = lists:last(X),
            MS = erl_parse:normalise(var2const(MS0)),
            XMS = ets:match_spec_compile(MS),
            true = ets:is_compiled_ms(XMS),
            {ok, MS, MS0} 
        end of
        {'EXIT', _Reason} ->
            no;
        Reply ->
            Reply
    end.

filters_as_one([]) ->
    {atom, anno0(), true};
filters_as_one(FilterData) ->
    [{_,{fil,Filter1}} | Filters] = lists:reverse(FilterData),
    lists:foldr(fun({_QId,{fil,Filter}}, AbstF) ->
                        {op,anno0(),'andalso',Filter,AbstF}
                end, Filter1, Filters).

qual_data(Qualifiers) ->
    F = fun(T) -> 
                [{QId,Q} || {QId,_,_,Q} <- Qualifiers, element(1,Q) =:= T]
        end,
    {F(fil), F(gen)}.

set_field(Pos, Fs, Data) ->
    lists:sublist(Fs, Pos-1) ++ [Data] ++ lists:nthtail(Pos, Fs).

qdata([{#qid{no = QIdNo},{_QIVs,{{gen,_P,LE,_GV},GoI,SI}}} | QCs], L) ->
    Init = case LE of 
               {join, Op, Q1, Q2, H1, H2, Cs1_0, Cs2_0} ->
                   Cs1 = qcon(Cs1_0),
                   Cs2 = qcon(Cs2_0),
                   CF = closure({tuple,L,[Cs1,Cs2,Compat]}, L),
                   {tuple,L,[?A(join),?A(Op),?I(Q1),?I(Q2),H1,H2,CF]};
               _ ->
                   closure(LE, L)
           end,
    {cons,L,{tuple,L,[?I(QIdNo),?I(GoI),?I(SI),{tuple,L,[?A(gen),Init]}]},
     qdata(QCs, L)};
qdata([{#qid{no = QIdNo},{_QIVs,{{fil,_F},GoI,SI}}} | QCs], L) ->
    {cons,L,{tuple,L,[?I(QIdNo),?I(GoI),?I(SI),?A(fil)]},qdata(QCs, L)};
qdata([], L) ->
    {nil,L}.

qcon(Cs) ->
    A = anno0(),
    list2cons([{tuple,A,[{integer,A,Col},list2cons(qcon1(ConstOps))]} ||
                  {Col,ConstOps} <- Cs]).

qcon1(ConstOps) ->
    A = anno0(),
    [{tuple,A,[Const,abstr(Op, A)]} || {Const,Op} <- ConstOps].

qcode(E, QCs, Source, L, State) ->
    CL = [begin
              Bin = term_to_binary(C, [compressed]),
              {bin, L, [{bin_element, L, 
                         {string, L, binary_to_list(Bin)},
                         default, default}]}
          end || {_,C} <- lists:keysort(1, [{qlc:template_state(),E} | 
                                            qcode(QCs, Source, State)])],
    {'fun', L, {clauses, [{clause, L, [], [], [{tuple, L, CL}]}]}}.

qcode([{_QId, {_QIvs, {{gen,P,_LE,_GV}, GoI, _SI}}} | QCs], Source, State) ->
    [{GoI,undo_no_shadows(P, State)} | qcode(QCs, Source, State)];
qcode([{QId, {_QIVs, {{fil,_F}, GoI, _SI}}} | QCs], Source, State) ->
    {ok,OrigF} = dict:find(QId, Source),
    [{GoI,undo_no_shadows(OrigF, State)} | qcode(QCs, Source, State)];
qcode([], _Source, _State) ->
    [].

closure(Code, L) ->
    {'fun',L,{clauses,[{clause,L,[],[],[Code]}]}}.

simple(L, Var, Init, Anno) ->
    {tuple,L,[?A(simple_v1),?A(Var),Init,abstr(loc(Anno), Anno)]}.

clauses([{QId,{QIVs,{QualData,GoI,S}}} | QCs], RL, Fun, Go, NGV, E, IVs,St) ->
    ?DEBUG("QIVs = ~p~n", [QIVs]),
    ?DEBUG("IVs = ~p~n", [IVs]),
    ?DEBUG("GoI = ~p, S = ~p~n", [GoI, S]),
    L = no_compiler_warning(get_lcid_line(QId#qid.lcid)),
    Cs = case QualData of
             {gen,P,_LE,GV} ->
                 generator(S, QIVs, P, GV, NGV, E, IVs, RL, Fun, Go,GoI,L,St);
             {fil,F} ->
                 filter(F, L, QIVs, S, RL, Fun, Go, GoI, IVs, St)
         end,
    Cs ++ clauses(QCs, RL, Fun, Go, NGV, E, IVs, St);
clauses([], _RL, _Fun, _Go, _NGV, _IVs, _E, _St) ->
    [].

final(RL, IVs, L, State) ->
    IAs = replace(IVs, IVs, '_'),
    AsL = pack_args([?I(0) | abst_vars([RL, '_', '_'] ++ IAs, L)], L, State),
    Grd = [is_list_c(RL, L)],
    Rev = {call,L,{remote,L,?A(lists),?A(reverse)},[?V(RL)]},
    CL = {clause,L,AsL,[Grd],[Rev]},
    AsF = pack_args([?I(0) | abst_vars(['_', '_', '_'] ++ IAs, L)], L, State),
    CF = {clause,L,AsF,[],[?ABST_NO_MORE]},
    [CL, CF].

template(E, RL, Fun, Go, AT, L, IVs, State) ->
    I = qlc:template_state(), GoI = qlc:template_state(),
    ARL = {cons,L,E,abst_vars(RL, L)},
    Next = next(Go, GoI, L),
    As0 = abst_vars([RL, Fun, Go] ++ IVs, L),
    As = pack_args([?I(I) | As0], L, State),
    NAs = pack_args([Next, ARL] ++ abst_vars([Fun, Go] ++ IVs, L), L, State),
    Grd = [is_list_c(RL, L)],
    CL = {clause,L,As,[Grd],[{call,L,?V(Fun),NAs}]},

    F = case split_args([Next | As0], L, State) of
            {ArgsL, ArgsT} -> 
                Call = {call,L,?V(Fun),ArgsL++[{var,L,AT}]},
                {block,L,
                 [{match,L,{var,L,AT},ArgsT},
                  {'fun',L,{clauses,[{clause,L,[],[],[Call]}]}}]};
            FNAs ->
                {'fun',L,{clauses,[{clause,L,[],[],[{call,L,?V(Fun),FNAs}]}]}}
        end,
    CF = {clause,L,As,[],[?ABST_MORE(E, F)]},
    [CL,CF].

generator(S, QIVs, P, GV, NGV, E, IVs, RL, Fun, Go, GoI, L, State) ->
    ComAs = abst_vars([RL, Fun, Go], L),
    InitC = generator_init(S, L, GV, RL, Fun, Go, GoI, IVs, State),
    As = [?I(S + 1)| ComAs ++ abst_vars(replace(QIVs -- [GV], IVs, '_'), L)],

    MatchS = next(Go, GoI + 1, L),
    AsM0 = [MatchS | ComAs ++ abst_vars(replace([GV], IVs, NGV), L)],
    AsM = pack_args(AsM0, L, State),

    ContS = ?I(S + 1),
    QIVs__GV = QIVs -- [GV],
    Tmp = replace([GV], replace(QIVs__GV, IVs, nil), NGV),
    AsC = pack_args([ContS | ComAs ++ abst_vars(Tmp, L)], L, State),

    DoneS = next(Go, GoI, L),
    AsD0 = [DoneS | ComAs ++ abst_vars(replace(QIVs, IVs, nil), L)],
    AsD = pack_args(AsD0, L, State),

    CsL = generator_list(P, GV, NGV, As, AsM, AsC, AsD, Fun, L, State),
    CsF = generator_cont(P, GV, NGV, E, As, AsM, AsC, AsD, Fun, L, State),
    [InitC | CsL ++ CsF].
    
generator_init(S, L, GV, RL, Fun, Go, GoI, IVs, State) ->
    As0 = abst_vars([RL, Fun, Go] ++ replace([GV], IVs, '_'), L),
    As = pack_args([?I(S) | As0], L, State),
    Next = next(Go, GoI + 2, L),
    NAs = pack_args([?I(S + 1) | replace([?V('_')], As0, Next)], L, State),
    {clause,L,As,[],[{call,L,?V(Fun),NAs}]}.

generator_list(P, GV, NGV, As, AsM, AsC, AsD, Fun, L, State) ->
    As1 = pack_args(replace([?V(GV)], As, {cons,L,P,?V(NGV)}), L, State),
    As2 = pack_args(replace([?V(GV)], As, {cons,L,?V('_'),?V(NGV)}), L,State),
    As3 = pack_args(replace([?V(GV)], As, {nil,L}), L, State),
    CM = {clause,L,As1,[],[{call,L,?V(Fun),AsM}]},
    CC = {clause,L,As2,[],[{call,L,?V(Fun),AsC}]},
    CD = {clause,L,As3,[],[{call,L,?V(Fun),AsD}]},
    [CM, CC, CD].

generator_cont(P, GV, NGV, E, As0, AsM, AsC, AsD, Fun, L, State) ->
    As = pack_args(As0, L, State),
    CF1 = ?ABST_MORE(P, ?V(NGV)),
    CF2 = ?ABST_MORE(?V('_'), ?V(NGV)),
    CF3 = ?ABST_NO_MORE,
    CF4 = ?V(E),
    CM = {clause,L,[CF1],[],[{call,L,?V(Fun),AsM}]},
    CC = {clause,L,[CF2],[],[{call,L,?V(Fun),AsC}]},
    CD = {clause,L,[CF3],[],[{call,L,?V(Fun),AsD}]},
    CE = {clause,L,[CF4],[],[CF4]},
    Cls = [CM, CC, CD, CE],
    B = {'case',L,{call,L,?V(GV),[]},Cls},
    [{clause,L,As,[],[B]}].
    
filter(E, L, QIVs, S, RL, Fun, Go, GoI, IVs, State) ->
    IAs = replace(QIVs, IVs, '_'),
    As = pack_args([?I(S) | abst_vars([RL, Fun, Go] ++ IAs, L)], L, State),
    NAs = abst_vars([RL, Fun, Go] ++ IVs, L),
    TNext = next(Go, GoI + 1, L),
    FNext = next(Go, GoI, L),
    NAsT = pack_args([TNext | NAs], L, State),
    NAsF = pack_args([FNext | NAs], L, State),
    Body = case is_guard_test(E, State) of
               true -> 
                   CT = {clause,L,[],[[E]],[{call,L,?V(Fun),NAsT}]},
                   CF = {clause,L,[],[[?A(true)]],[{call,L,?V(Fun),NAsF}]},
                   [{'if',L,[CT,CF]}];
               false -> 
                   CT = {clause,L,[?A(true)],[],[{call,L,?V(Fun),NAsT}]},
                   CF = {clause,L,[?A(false)],[],[{call,L,?V(Fun),NAsF}]},
                   [{'case',L,E,[CT,CF]}]
           end,
    [{clause,L,As,[],Body}].
    
pack_args(Args, L, State) ->
    case split_args(Args, L, State) of
        {ArgsL, ArgsT} ->
            ArgsL ++ [ArgsT];
        _ ->
            Args
    end.

split_args(Args, L, State) when length(Args) > State#state.maxargs ->
    {lists:sublist(Args, State#state.maxargs-1), 
     {tuple,L,lists:nthtail(State#state.maxargs-1, Args)}};
split_args(Args, _L, _State) ->
    Args.
    
replace(Es, IEs, R) ->
    [case lists:member(E, Es) of
         true -> R; 
         false -> E 
     end || E <- IEs].

is_list_c(V, L) ->
    {call,L,?A(is_list),[?V(V)]}.

next(Go, GoI, L) ->
    {call,L,?A(element),[?I(GoI),?V(Go)]}.

aux_vars(Vars, LcN, AllVars) ->
    [aux_var(Name, LcN, 0, 1, AllVars) || Name <- Vars].

aux_var(Name, LcN, QN, N, AllVars) ->
    qlc:aux_name(lists:concat([Name, LcN, '_', QN, '_']), N, AllVars).

no_compiler_warning(L) ->
    Anno = erl_anno:new(L),
    erl_anno:set_generated(true, Anno).

loc(A) ->
    erl_anno:location(A).

list2op([E], _Op) ->
    E;
list2op([E | Es], Op) ->
    {op,anno0(),Op,E,list2op(Es, Op)}.

anno0() ->
    erl_anno:new(0).

anno1() ->
    erl_anno:new(1).


qual_fold(Fun, GlobAcc0, Acc0, Forms, State) ->
    F = fun(Id, {lc,L,E,Qs0}, GA0) ->
                {Qs,GA,_NA} = qual_fold(Qs0, Fun, GA0, Acc0, Id, 1, []),
                {{lc,L,E,Qs},GA};
           (_Id, Expr, GA) ->
                {Expr,GA}
        end,
    qlc_mapfold(F, GlobAcc0, Forms, State).

qual_fold([Q0 | Qs], F, GA0, A0, Id, No, NQs) ->
    QId = qid(Id, No),
    {Q,GA,A} = F(QId, Q0, GA0, A0),
    qual_fold(Qs, F, GA, A, Id, No + 1, [Q | NQs]);
qual_fold([], _F, GA, A, _Id, _No, NQs) ->
    {lists:reverse(NQs),GA,A}.

qlc_mapfold(Fun, Acc0, Forms0, State) ->
    {Forms, A, _NNo} = qlcmf(Forms0, Fun, State#state.imp, Acc0, 1),
    erase(?QLC_FILE),
    {Forms, A}.

qlcmf([E0 | Es0], F, Imp, A0, No0) ->
    {E, A1, No1} = qlcmf(E0, F, Imp, A0, No0),
    {Es, A, No} = qlcmf(Es0, F, Imp, A1, No1),
    {[E | Es], A, No};
qlcmf(?QLC_Q(L1, L2, L3, L4, LC0, Os0), F, Imp, A0, No0) when length(Os0) < 2 ->
    {Os, A1, No1} = qlcmf(Os0, F, Imp, A0, No0),
    NL = make_lcid(L1, No),
    {T, A} = F(NL, LC, A2),
    {?QLC_Q(L1, L2, L3, L4, T, Os), A, No + 1};
qlcmf(?IMP_Q(L1, L2, LC0, Os0), F, Imp=true, A0, No0) when length(Os0) < 2 ->
    {Os, A1, No1} = qlcmf(Os0, F, Imp, A0, No0),
    NL = make_lcid(L, No),
    {T, A} = F(NL, LC, A2),
    {?IMP_Q(L1, L2, T, Os), A, No + 1};
qlcmf({attribute,_L,file,{File,_Line}}=Attr, _F, _Imp, A, No) ->
    put(?QLC_FILE, File),
    {Attr, A, No};
qlcmf(T, F, Imp, A0, No0) when is_tuple(T) ->
    {TL, A, No} = qlcmf(tuple_to_list(T), F, Imp, A0, No0),
    {list_to_tuple(TL), A, No};
qlcmf(T, _F, _Imp, A, No) ->
    {T, A, No}.

occ_vars(E) ->
    qlc:var_fold(fun({var,_L,V}) -> V end, [], E).

save_anno(Abstr, NodeInfo) ->
    F = fun(Anno) ->
                N = next_slot(NodeInfo),
                Location = erl_anno:location(Anno),
                Data = {N, #{location => Location}},
                true = ets:insert(NodeInfo, Data),
                erl_anno:new(N)
        end,
    map_anno(F, Abstr).

next_slot(T) ->
    I = ets:update_counter(T, var_n, 1),
    case ets:lookup(T, I) of
        [] ->
            I;
        _ ->
            next_slot(T)
    end.

restore_anno(Abstr, NodeInfo) ->
    F = fun(Anno) ->
                Location = erl_anno:location(Anno),
                case ets:lookup(NodeInfo, Location) of
                    [{Location, Data}] ->
                        OrigLocation = maps:get(location, Data),
                        erl_anno:set_location(OrigLocation, Anno);
                        Anno;
                    [] ->
                        Anno
                end
        end,
    map_anno(F, Abstr).

restore_loc(Location, #state{node_info = NodeInfo}) ->
  case ets:lookup(NodeInfo, Location) of
      [{Location, #{location := OrigLocation}}] ->
          OrigLocation;
      [{Location}] ->
          Location;
      [] ->
          Location
  end.

no_shadows(Forms0, State) ->
  LCs and Funs . Such variables ( call them SV , Shadowing
  The state { LastIndex , ActiveVars , UsedVars , AllVars , Singletons , State }
  holds the last index used for each SV ( LastIndex ) , the SVs in
  the current scope ( ActiveVars ) , used SVs ( UsedVars , the indexed
  (  ) , and all singletons . If an SV is not used ( that is ,
  the indexed name of an SV occurs in the file , next index is
  The original names of variables are kept in a table in State .
    AllVars = sets:from_list(ordsets:to_list(qlc:vars(Forms0))),
    ?DEBUG("nos AllVars = ~p~n", [sets:to_list(AllVars)]),
    VFun = fun(_Id, LC, Vs) -> nos(LC, Vs) end,
    LI = ets:new(?APIMOD,[]),
    UV = ets:new(?APIMOD,[]),
    D0 = dict:new(),
    S1 = {LI, D0, UV, AllVars, [], State},
    _ = qlc_mapfold(VFun, S1, Forms0, State),
    ?DEBUG("UsedIntroVars = ~p~n", [ets:match_object(UV, '_')]),
    Singletons = ets:select(UV, ets:fun2ms(fun({K,0}) -> K  end)),
    ?DEBUG("Singletons: ~p~n", [Singletons]),
    true = ets:delete_all_objects(LI),
    true = ets:delete_all_objects(UV),
    S2 = {LI, D0, UV, AllVars, Singletons, State},
    {Forms,_} = qlc_mapfold(VFun, S2, Forms0, State),
    true = ets:delete(LI),
    true = ets:delete(UV),
    Forms.

nos([E0 | Es0], S0) ->
    {E, S1} = nos(E0, S0),
    {Es, S} = nos(Es0, S1),
    {[E | Es], S};
nos({'fun',L,{clauses,Cs}}, S) ->
    NCs = [begin
               {H, S1} = nos_pattern(H0, S),
               {[G, B], _} = nos([G0, B0], S1),
               {clause,Ln,H,G,B}
           end || {clause,Ln,H0,G0,B0} <- Cs],
    {{'fun',L,{clauses,NCs}}, S};
nos({named_fun,Loc,Name,Cs}, S) ->
    {{var,NLoc,NName}, S1} = case Name of
                                 '_' ->
                                     S;
                                 Name ->
                                     nos_pattern({var,Loc,Name}, S)
                               end,
    NCs = [begin
               {H, S2} = nos_pattern(H0, S1),
               {[G, B], _} = nos([G0, B0], S2),
               {clause,CLoc,H,G,B}
           end || {clause,CLoc,H0,G0,B0} <- Cs],
    {{named_fun,NLoc,NName,NCs}, S};
nos({lc,L,E0,Qs0}, S) ->
    F = fun({T,Ln,P0,LE0}, QS0) when T =:= b_generate; T =:= generate -> 
                {LE, _} = nos(LE0, QS0),
                {P, QS} = nos_pattern(P0, QS0),
                {{T,Ln,P,LE}, QS};
           (Filter, QS) -> 
                nos(Filter, QS)
        end,
    {Qs, S1} = lists:mapfoldl(F, S, Qs0),
    {E, _} = nos(E0, S1),
    {{lc,L,E,Qs}, S};
nos({var,L,V}=Var, {_LI,Vs,UV,_A,_Sg,State}=S) when V =/= '_' ->
    case used_var(V, Vs, UV) of
        {true, VN} ->
            nos_var(L, V, State),
            {{var,L,VN}, S};
        false ->
            {Var, S}
    end;
nos(T, S0) when is_tuple(T) ->
    {TL, S} = nos(tuple_to_list(T), S0),
    {list_to_tuple(TL), S};
nos(T, S) ->
    {T, S}.

nos_pattern(P, S) ->
    {T, NS, _} = nos_pattern(P, S, []),
    {T, NS}.

nos_pattern([P0 | Ps0], S0, PVs0) ->
    {P, S1, PVs1} = nos_pattern(P0, S0, PVs0),
    {Ps, S, PVs} = nos_pattern(Ps0, S1, PVs1),
    {[P | Ps], S, PVs};
nos_pattern({var,L,V}, {LI,Vs0,UV,A,Sg,State}, PVs0) when V =/= '_' ->
    {Name, Vs, PVs} = 
        case lists:keyfind(V, 1, PVs0) of
            {V, VN} ->
                _ = used_var(V, Vs0, UV), 
                {VN, Vs0, PVs0};
            false -> 
                {VN, Vs1} = next_var(V, Vs0, A, LI, UV),
                N = case lists:member(VN, Sg) of
                        true -> '_';
                        false -> VN
                    end,
                {N, Vs1, [{V,VN} | PVs0]}
        end,
    nos_var(L, V, State),
    {{var,L,Name}, {LI,Vs,UV,A,Sg,State}, PVs};
nos_pattern(T, S0, PVs0) when is_tuple(T) ->
    {TL, S, PVs} = nos_pattern(tuple_to_list(T), S0, PVs0),
    {list_to_tuple(TL), S, PVs};
nos_pattern(T, S, PVs) ->
    {T, S, PVs}.

nos_var(Anno, Name, State) ->
    NodeInfo = State#state.node_info,
    Location = erl_anno:location(Anno),
    case ets:lookup(NodeInfo, Location) of
        [{Location, #{name := _}}] ->
            true;
        [{Location, Data}] ->
            true = ets:insert(NodeInfo, {Location, Data#{name => Name}});
            true
    end.

used_var(V, Vs, UV) ->
    case dict:find(V, Vs) of
        {ok,Value} ->
            VN = qlc:name_suffix(V, Value),
            _ = ets:update_counter(UV, VN, 1),
            {true, VN};
        error -> false
    end.

next_var(V, Vs, AllVars, LI, UV) ->
    NValue = case ets:lookup(LI, V) of
                 [{V, Value}] -> Value + 1;
                 [] -> 1
             end,
    true = ets:insert(LI, {V, NValue}),
    VN = qlc:name_suffix(V, NValue),
    case sets:is_element(VN, AllVars) of
        true -> next_var(V, Vs, AllVars, LI, UV);
        false -> true = ets:insert(UV, {VN, 0}),
                 NVs = dict:store(V, NValue, Vs),
                 {VN, NVs}
    end.

undo_no_shadows(E, State) ->
    var_map(fun(Anno) -> undo_no_shadows1(Anno, State) end, E).

undo_no_shadows1({var, Anno, _}=Var, State) ->
    Location = erl_anno:location(Anno),
    NodeInfo = State#state.node_info,
    case ets:lookup(NodeInfo, Location) of
        [{Location, #{name := Name}}] ->
            {var, Anno, Name};
        _ ->
            Var
    end.

  QLC identifier .
  The first one encountered in the file has No=1 .

make_lcid(Anno, No) when is_integer(No), No > 0 ->
    {No, erl_anno:line(Anno)}.

get_lcid_no({No, _Line}) ->
    No.

get_lcid_line({_No, Line}) ->
    Line.

qid(LCId, No) ->
    #qid{no = No, lcid = LCId}.

abst_vars([V | Vs], L) ->
    [abst_vars(V, L) | abst_vars(Vs, L)];
abst_vars([], _L) ->
    [];
abst_vars(nil, L) ->
    {nil,L};
abst_vars(V, L) ->
    {var,L,V}.

embed_vars(Vars, L) ->
    embed_expr({tuple,L,Vars}, L).

embed_expr(Expr, L) ->
    {lc,L,Expr,[{generate,L,{var,L,'_'},{nil,L}}]}.

var2const(E) ->
    var_map(fun({var, L, V}) -> {atom, L, V} end, E).

var_map(F, {var, _, _}=V) ->
    F(V);
var_map(F, {named_fun,NLoc,NName,Cs}) ->
    {var,Loc,Name} = F({var,NLoc,NName}),
    {named_fun,Loc,Name,var_map(F, Cs)};
var_map(F, T) when is_tuple(T) ->
    list_to_tuple(var_map(F, tuple_to_list(T)));
var_map(F, [E | Es]) ->
    [var_map(F, E) | var_map(F, Es)];
var_map(_F, E) ->
    E.

var_mapfold(F, A, {var, _, _}=V) ->
    F(V, A);
var_mapfold(F, A0, T) when is_tuple(T) ->
    {L, A} = var_mapfold(F, A0, tuple_to_list(T)),
    {list_to_tuple(L), A};
var_mapfold(F, A0, [E0 | Es0]) ->
    {E, A1} = var_mapfold(F, A0, E0),
    {Es, A} = var_mapfold(F, A1, Es0),
    {[E | Es], A};
var_mapfold(_F, A, E) ->
    {E, A}.

map_anno(F, AbstrList) when is_list(AbstrList) ->
    [map_anno1(F, Abstr) || Abstr <- AbstrList];
map_anno(F, Abstr) ->
    map_anno1(F, Abstr).

map_anno1(F, Abstr) ->
    erl_parse:map_anno(F, Abstr).

family_list(L) ->
    sofs:to_external(family(L)).

family(L) ->
    sofs:relation_to_family(sofs:relation(L)).

is_guard_test(E, #state{records = RDs, overridden = IsOverridden}) ->
    erl_lint:is_guard_test(E, RDs, IsOverridden).

  that will override a BIF with the same name .

set_up_overridden(Forms) ->
    Locals = [{Name,Arity} || {function,_,Name,Arity,_} <- Forms],
    Imports0 = [Fs || {attribute,_,import,Fs} <- Forms],
    Imports1 = lists:flatten(Imports0),
    Imports2 = [Fs || {_,Fs} <- Imports1],
    Imports = lists:flatten(Imports2),
    Overridden = gb_sets:from_list(Imports ++ Locals),
    fun(FA) -> gb_sets:is_element(FA, Overridden) end.

-ifdef(debug).
display_forms(Forms) ->
    io:format("Forms ***~n"),
    lists:foreach(fun(Form) ->
                          io:format("~ts~n", [catch erl_pp:form(Form)])
                  end, Forms),
    io:format("End Forms ***~n").
-else.
display_forms(_) ->
    ok.
-endif.

