%%
%% %CopyrightBegin%
%%
%% Copyright Ericsson AB 2004-2015. 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
%%
%%     http://www.apache.org/licenses/LICENSE-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.
-record(qlc_lc,     % qlc:q/1,2, a query handle
        {lc,
         opt        % #qlc_opt
        }).

-record(state, {imp,
                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 cannot 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()],
      Forms2 :: [erl_parse:abstract_form()],
      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) -> Expr when
      LC :: erl_parse:abstract_expr(),
      Expr :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct()).

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

-spec(transform_expression(LC, Bs) -> Expr when
      LC :: erl_parse:abstract_expr(),
      Expr :: erl_parse:abstract_expr(),
      Bs :: erl_eval:binding_struct()).

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))]),
    State0 = #state{imp = Imported,
                    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 = erl_parse: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 qlc:
    %%  The Compiler and qlc do not agree on the location of errors.
    %%  For now, qlc'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 QLC 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) ->
    erl_parse: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,
    erl_parse: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,anno0()}]),
    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 QLC (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, Op, QualifierNumber1, QualifierNumber2, PatternFilter1,
%% 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 Val returned from the fun is:
%% Val = [] | [term() | Val] | fun() -> Val
%% 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>, ..., Val, ...); % arguments are bound
%%    (3, ..., [_ | Val], ...) -> % pattern does not match
%%       Fun(3, ..., Val, ...);
%%    (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, ...);
%%           [_ | Val] -> 
%%               Fun(3, ..., Val, ...);
%%           [] ->
%%              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 QLC (call to qlc: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: QFun 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. QLCs 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; Dialyzer 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 Dialyzer'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
             true = Vs0 =/= [], % 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.
%% -> [{EqType,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, SizeInfo, 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 cannot 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) ->
    RDs = State#state.records,
    sel_gf(FilterData, 1, Dependencies, RDs, [], []).

sel_gf([], _N, _Deps, _RDs, _Gens, _Gens1) ->
    [];
sel_gf([{#qid{no = N}=Id,{fil,F}}=Fil | FData], N, Deps, RDs, Gens, Gens1) ->
    case erl_lint:is_guard_test(F, RDs) 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, RDs, Gens, Gens1)];
                        false ->
                            sel_gf(FData, N + 1, Deps, RDs, [], [])
                    end;
                false ->
                    case generators_in_scope(GIds, Gens) of
                        true ->
                            [Fil | sel_gf(FData, N + 1, Deps, RDs, Gens, [])];
                        false ->
                            sel_gf(FData, N + 1, Deps, RDs, [], [])
                    end
            end;
        false ->
            sel_gf(FData, N + 1, Deps, RDs, [], [])
    end;
sel_gf(FData, N, Deps, RDs, Gens, Gens1) ->
    sel_gf(FData, N + 1, Deps, RDs, [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) ->
    erl_parse: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 QLC
%% 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}(); erlang: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 won'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,{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 ->
    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({call,L1,{atom,_,element}=E,As}, F0, BF, Imported) ->
    %% erl_expand_records should add "erlang:"...
    element_calls({call,L1,{remote,L1,{atom,L1,erlang},E}, As}, F0, 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(),
    Forms = RecordDefs ++ [{function,A,foo,0,[{clause,A,[],[],[pe(E)]}]}],
    [{function,_,foo,0,[{clause,_,[],[],[NE]}]}] = 
        erl_expand_records:module(Forms, [no_strict_record_tests]),
    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 erl_lint:is_guard_test(E, State#state.records) 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,
    erl_parse: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,
    erl_parse: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
    %% (AllVars), 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}.

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

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

-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.

