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-rw-r--r--lib/stdlib/doc/src/c.xml8
-rw-r--r--lib/stdlib/doc/src/gb_sets.xml13
-rw-r--r--lib/stdlib/doc/src/gb_trees.xml13
-rw-r--r--lib/stdlib/doc/src/maps.xml22
-rw-r--r--lib/stdlib/src/c.erl23
-rw-r--r--lib/stdlib/src/gb_sets.erl24
-rw-r--r--lib/stdlib/src/gb_trees.erl31
-rw-r--r--lib/stdlib/src/maps.erl21
-rw-r--r--lib/stdlib/src/shell_default.erl3
-rw-r--r--lib/stdlib/test/dict_SUITE.erl50
-rw-r--r--lib/stdlib/test/dict_test_lib.erl5
-rw-r--r--lib/stdlib/test/maps_SUITE.erl14
-rw-r--r--lib/stdlib/test/sets_SUITE.erl44
-rw-r--r--lib/stdlib/test/sets_test_lib.erl5
14 files changed, 252 insertions, 24 deletions
diff --git a/lib/stdlib/doc/src/c.xml b/lib/stdlib/doc/src/c.xml
index b49fa6ad67..b43d4786ae 100644
--- a/lib/stdlib/doc/src/c.xml
+++ b/lib/stdlib/doc/src/c.xml
@@ -232,6 +232,14 @@ compile:file(<anno>File</anno>, <anno>Options</anno> ++ [report_errors, report_w
</desc>
</func>
<func>
+ <name name="uptime" arity="0"/>
+ <fsummary>Print node uptime</fsummary>
+ <desc>
+ <p>Prints the node uptime (as given by
+ <c>erlang:statistics(wall_clock)</c>), in human-readable form.</p>
+ </desc>
+ </func>
+ <func>
<name>xm(ModSpec) -> void()</name>
<fsummary>Cross reference check a module</fsummary>
<type>
diff --git a/lib/stdlib/doc/src/gb_sets.xml b/lib/stdlib/doc/src/gb_sets.xml
index ea96c14472..405bae5698 100644
--- a/lib/stdlib/doc/src/gb_sets.xml
+++ b/lib/stdlib/doc/src/gb_sets.xml
@@ -4,7 +4,7 @@
<erlref>
<header>
<copyright>
- <year>2001</year><year>2014</year>
+ <year>2001</year><year>2015</year>
<holder>Ericsson AB. All Rights Reserved.</holder>
</copyright>
<legalnotice>
@@ -306,6 +306,17 @@
</desc>
</func>
<func>
+ <name name="iterator_from" arity="2"/>
+ <fsummary>Return an iterator for a set starting from a specified element</fsummary>
+ <desc>
+ <p>Returns an iterator that can be used for traversing the
+ entries of <c><anno>Set</anno></c>; see <c>next/1</c>.
+ The difference as compared to the iterator returned by
+ <c>iterator/1</c> is that the first element greater than
+ or equal to <c><anno>Element</anno></c> is returned.</p>
+ </desc>
+ </func>
+ <func>
<name name="largest" arity="1"/>
<fsummary>Return largest element</fsummary>
<desc>
diff --git a/lib/stdlib/doc/src/gb_trees.xml b/lib/stdlib/doc/src/gb_trees.xml
index b2f237e1d7..82167e1083 100644
--- a/lib/stdlib/doc/src/gb_trees.xml
+++ b/lib/stdlib/doc/src/gb_trees.xml
@@ -4,7 +4,7 @@
<erlref>
<header>
<copyright>
- <year>2001</year><year>2014</year>
+ <year>2001</year><year>2015</year>
<holder>Ericsson AB. All Rights Reserved.</holder>
</copyright>
<legalnotice>
@@ -183,6 +183,17 @@
</desc>
</func>
<func>
+ <name name="iterator_from" arity="2"/>
+ <fsummary>Return an iterator for a tree starting from specified key</fsummary>
+ <desc>
+ <p>Returns an iterator that can be used for traversing the
+ entries of <c><anno>Tree</anno></c>; see <c>next/1</c>.
+ The difference as compared to the iterator returned by
+ <c>iterator/1</c> is that the first key greater than
+ or equal to <c><anno>Key</anno></c> is returned.</p>
+ </desc>
+ </func>
+ <func>
<name name="keys" arity="1"/>
<fsummary>Return a list of the keys in a tree</fsummary>
<desc>
diff --git a/lib/stdlib/doc/src/maps.xml b/lib/stdlib/doc/src/maps.xml
index e46068230a..7345a9357a 100644
--- a/lib/stdlib/doc/src/maps.xml
+++ b/lib/stdlib/doc/src/maps.xml
@@ -33,6 +33,28 @@
<funcs>
<func>
+ <name name="filter" arity="2"/>
+ <fsummary>Choose pairs which satisfy a predicate</fsummary>
+ <desc>
+ <p>
+ Returns a map <c><anno>Map2</anno></c> for which predicate
+ <c><anno>Pred</anno></c> holds true in <c><anno>Map1</anno></c>.
+ </p>
+ <p>
+ The call will fail with a <c>{badmap,Map}</c> exception if
+ <c><anno>Map1</anno></c> is not a map or with <c>badarg</c> if
+ <c><anno>Pred</anno></c> is not a function of arity 2.
+ </p>
+ <p>Example:</p>
+ <code type="none">
+> M = #{a => 2, b => 3, c=> 4, "a" => 1, "b" => 2, "c" => 4},
+ Pred = fun(K,V) -> is_atom(K) andalso (V rem 2) =:= 0 end,
+ maps:filter(Pred,M).
+#{a => 2,c => 4} </code>
+ </desc>
+ </func>
+
+ <func>
<name name="find" arity="2"/>
<fsummary></fsummary>
<desc>
diff --git a/lib/stdlib/src/c.erl b/lib/stdlib/src/c.erl
index 9860adf04d..d5b24d3c32 100644
--- a/lib/stdlib/src/c.erl
+++ b/lib/stdlib/src/c.erl
@@ -27,7 +27,7 @@
lc_batch/0, lc_batch/1,
i/3,pid/3,m/0,m/1,
bt/1, q/0,
- erlangrc/0,erlangrc/1,bi/1, flush/0, regs/0,
+ erlangrc/0,erlangrc/1,bi/1, flush/0, regs/0, uptime/0,
nregs/0,pwd/0,ls/0,ls/1,cd/1,memory/1,memory/0, xm/1]).
-export([display_info/1]).
@@ -65,6 +65,7 @@ help() ->
"q() -- quit - shorthand for init:stop()\n"
"regs() -- information about registered processes\n"
"nregs() -- information about all registered processes\n"
+ "uptime() -- print node uptime\n"
"xm(M) -- cross reference check a module\n"
"y(File) -- generate a Yecc parser\n">>).
@@ -774,6 +775,26 @@ memory() -> erlang:memory().
memory(TypeSpec) -> erlang:memory(TypeSpec).
%%
+%% uptime/0
+%%
+
+-spec uptime() -> 'ok'.
+
+uptime() ->
+ io:format("~s~n", [uptime(get_uptime())]).
+
+uptime({D, {H, M, S}}) ->
+ lists:flatten(
+ [[ io_lib:format("~p days, ", [D]) || D > 0 ],
+ [ io_lib:format("~p hours, ", [H]) || D+H > 0 ],
+ [ io_lib:format("~p minutes and ", [M]) || D+H+M > 0 ],
+ io_lib:format("~p seconds", [S])]).
+
+get_uptime() ->
+ {UpTime, _} = erlang:statistics(wall_clock),
+ calendar:seconds_to_daystime(UpTime div 1000).
+
+%%
%% Cross Reference Check
%%
%%-spec xm(module() | file:filename()) -> xref:m/1 return
diff --git a/lib/stdlib/src/gb_sets.erl b/lib/stdlib/src/gb_sets.erl
index 393fb07229..d3fbd542f7 100644
--- a/lib/stdlib/src/gb_sets.erl
+++ b/lib/stdlib/src/gb_sets.erl
@@ -137,6 +137,10 @@
%% approach is that it does not require the complete list of all
%% elements to be built in memory at one time.
%%
+%% - iterator_from(X, S): returns an iterator that can be used for
+%% traversing the elements of set S greater than or equal to X;
+%% see `next'.
+%%
%% - next(T): returns {X, T1} where X is the smallest element referred
%% to by the iterator T, and T1 is the new iterator to be used for
%% traversing the remaining elements, or the atom `none' if no
@@ -157,8 +161,8 @@
insert/2, add/2, delete/2, delete_any/2, balance/1, union/2,
union/1, intersection/2, intersection/1, is_disjoint/2, difference/2,
is_subset/2, to_list/1, from_list/1, from_ordset/1, smallest/1,
- largest/1, take_smallest/1, take_largest/1, iterator/1, next/1,
- filter/2, fold/3, is_set/1]).
+ largest/1, take_smallest/1, take_largest/1, iterator/1,
+ iterator_from/2, next/1, filter/2, fold/3, is_set/1]).
%% `sets' compatibility aliases:
@@ -500,6 +504,22 @@ iterator({_, L, _} = T, As) ->
iterator(nil, As) ->
As.
+-spec iterator_from(Element, Set) -> Iter when
+ Set :: set(Element),
+ Iter :: iter(Element).
+
+iterator_from(S, {_, T}) ->
+ iterator_from(S, T, []).
+
+iterator_from(S, {K, _, T}, As) when K < S ->
+ iterator_from(S, T, As);
+iterator_from(_, {_, nil, _} = T, As) ->
+ [T | As];
+iterator_from(S, {_, L, _} = T, As) ->
+ iterator_from(S, L, [T | As]);
+iterator_from(_, nil, As) ->
+ As.
+
-spec next(Iter1) -> {Element, Iter2} | 'none' when
Iter1 :: iter(Element),
Iter2 :: iter(Element).
diff --git a/lib/stdlib/src/gb_trees.erl b/lib/stdlib/src/gb_trees.erl
index 7069b61873..259e8f718b 100644
--- a/lib/stdlib/src/gb_trees.erl
+++ b/lib/stdlib/src/gb_trees.erl
@@ -1,7 +1,7 @@
%%
%% %CopyrightBegin%
%%
-%% Copyright Ericsson AB 2001-2014. All Rights Reserved.
+%% Copyright Ericsson AB 2001-2015. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
@@ -102,6 +102,10 @@
%% approach is that it does not require the complete list of all
%% elements to be built in memory at one time.
%%
+%% - iterator_from(K, T): returns an iterator that can be used for
+%% traversing the entries of tree T with key greater than or
+%% equal to K; see `next'.
+%%
%% - next(S): returns {X, V, S1} where X is the smallest key referred to
%% by the iterator S, and S1 is the new iterator to be used for
%% traversing the remaining entries, or the atom `none' if no entries
@@ -117,7 +121,7 @@
update/3, enter/3, delete/2, delete_any/2, balance/1,
is_defined/2, keys/1, values/1, to_list/1, from_orddict/1,
smallest/1, largest/1, take_smallest/1, take_largest/1,
- iterator/1, next/1, map/2]).
+ iterator/1, iterator_from/2, next/1, map/2]).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -529,6 +533,29 @@ iterator({_, _, L, _} = T, As) ->
iterator(nil, As) ->
As.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+-spec iterator_from(Key, Tree) -> Iter when
+ Tree :: tree(Key, Value),
+ Iter :: iter(Key, Value).
+
+iterator_from(S, {_, T}) ->
+ iterator_1_from(S, T).
+
+iterator_1_from(S, T) ->
+ iterator_from(S, T, []).
+
+iterator_from(S, {K, _, _, T}, As) when K < S ->
+ iterator_from(S, T, As);
+iterator_from(_, {_, _, nil, _} = T, As) ->
+ [T | As];
+iterator_from(S, {_, _, L, _} = T, As) ->
+ iterator_from(S, L, [T | As]);
+iterator_from(_, nil, As) ->
+ As.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
-spec next(Iter1) -> 'none' | {Key, Value, Iter2} when
Iter1 :: iter(Key, Value),
Iter2 :: iter(Key, Value).
diff --git a/lib/stdlib/src/maps.erl b/lib/stdlib/src/maps.erl
index 3877c150ec..533ff08726 100644
--- a/lib/stdlib/src/maps.erl
+++ b/lib/stdlib/src/maps.erl
@@ -19,7 +19,8 @@
-module(maps).
--export([get/3,fold/3, map/2, size/1,
+-export([get/3,filter/2,fold/3, map/2,
+ size/1,
without/2, with/2]).
@@ -145,6 +146,19 @@ get(Key,Map,Default) ->
erlang:error({badmap,Map},[Key,Map,Default]).
+-spec filter(Pred,Map1) -> Map2 when
+ Pred :: fun((Key, Value) -> boolean()),
+ Key :: term(),
+ Value :: term(),
+ Map1 :: map(),
+ Map2 :: map().
+
+filter(Pred,Map) when is_function(Pred,2), is_map(Map) ->
+ maps:from_list([{K,V}||{K,V}<-maps:to_list(Map),Pred(K,V)]);
+filter(Pred,Map) ->
+ erlang:error(error_type(Map),[Pred,Map]).
+
+
-spec fold(Fun,Init,Map) -> Acc when
Fun :: fun((K, V, AccIn) -> AccOut),
Init :: term(),
@@ -169,10 +183,7 @@ fold(Fun,Init,Map) ->
V2 :: term().
map(Fun,Map) when is_function(Fun, 2), is_map(Map) ->
- maps:from_list(lists:map(fun
- ({K,V}) ->
- {K,Fun(K,V)}
- end,maps:to_list(Map)));
+ maps:from_list([{K,Fun(K,V)}||{K,V}<-maps:to_list(Map)]);
map(Fun,Map) ->
erlang:error(error_type(Map),[Fun,Map]).
diff --git a/lib/stdlib/src/shell_default.erl b/lib/stdlib/src/shell_default.erl
index 3fe359af0e..0fca7ff8c7 100644
--- a/lib/stdlib/src/shell_default.erl
+++ b/lib/stdlib/src/shell_default.erl
@@ -23,7 +23,7 @@
-module(shell_default).
-export([help/0,lc/1,c/1,c/2,nc/1,nl/1,l/1,i/0,pid/3,i/3,m/0,m/1,
- memory/0,memory/1,
+ memory/0,memory/1,uptime/0,
erlangrc/1,bi/1, regs/0, flush/0,pwd/0,ls/0,ls/1,cd/1,
y/1, y/2,
xm/1, bt/1, q/0,
@@ -92,6 +92,7 @@ pid(X,Y,Z) -> c:pid(X,Y,Z).
pwd() -> c:pwd().
q() -> c:q().
regs() -> c:regs().
+uptime() -> c:uptime().
xm(Mod) -> c:xm(Mod).
y(File) -> c:y(File).
y(File, Opts) -> c:y(File, Opts).
diff --git a/lib/stdlib/test/dict_SUITE.erl b/lib/stdlib/test/dict_SUITE.erl
index 69814e12ce..ab624e8dd2 100644
--- a/lib/stdlib/test/dict_SUITE.erl
+++ b/lib/stdlib/test/dict_SUITE.erl
@@ -1,7 +1,7 @@
%%
%% %CopyrightBegin%
%%
-%% Copyright Ericsson AB 2008-2013. All Rights Reserved.
+%% Copyright Ericsson AB 2008-2015. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
@@ -25,16 +25,16 @@
-export([all/0, suite/0,groups/0,init_per_suite/1, end_per_suite/1,
init_per_group/2,end_per_group/2,
init_per_testcase/2,end_per_testcase/2,
- create/1,store/1]).
+ create/1,store/1,iterate/1]).
-include_lib("test_server/include/test_server.hrl").
--import(lists, [foldl/3,reverse/1]).
+-import(lists, [foldl/3]).
suite() -> [{ct_hooks,[ts_install_cth]}].
all() ->
- [create, store].
+ [create, store, iterate].
groups() ->
[].
@@ -93,6 +93,48 @@ store_1(List, M) ->
D0.
%%%
+%%% Test specifics for gb_trees.
+%%%
+
+iterate(Config) when is_list(Config) ->
+ test_all(fun iterate_1/1).
+
+iterate_1(M) ->
+ case M(module, []) of
+ gb_trees -> iterate_2(M);
+ _ -> ok
+ end,
+ M(empty, []).
+
+iterate_2(M) ->
+ random:seed(1, 2, 42),
+ iter_tree(M, 1000).
+
+iter_tree(_M, 0) ->
+ ok;
+iter_tree(M, N) ->
+ L = [{I, I} || I <- lists:seq(1, N)],
+ T = M(from_list, L),
+ L = lists:reverse(iterate_tree(M, T)),
+ R = random:uniform(N),
+ KV = lists:reverse(iterate_tree_from(M, R, T)),
+ KV = [P || P={K,_} <- L, K >= R],
+ iter_tree(M, N-1).
+
+iterate_tree(M, Tree) ->
+ I = M(iterator, Tree),
+ iterate_tree_1(M, M(next, I), []).
+
+iterate_tree_from(M, Start, Tree) ->
+ I = M(iterator_from, {Start, Tree}),
+ iterate_tree_1(M, M(next, I), []).
+
+iterate_tree_1(_, none, R) ->
+ R;
+iterate_tree_1(M, {K, V, I}, R) ->
+ iterate_tree_1(M, M(next, I), [{K, V} | R]).
+
+%%%
%%% Helper functions.
%%%
diff --git a/lib/stdlib/test/dict_test_lib.erl b/lib/stdlib/test/dict_test_lib.erl
index 4fdb4fa0bd..81d26ce5f8 100644
--- a/lib/stdlib/test/dict_test_lib.erl
+++ b/lib/stdlib/test/dict_test_lib.erl
@@ -1,7 +1,7 @@
%%
%% %CopyrightBegin%
%%
-%% Copyright Ericsson AB 2008-2013. All Rights Reserved.
+%% Copyright Ericsson AB 2008-2015. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
@@ -29,6 +29,9 @@ new(Mod, Eq) ->
(module, []) -> Mod;
(size, D) -> Mod:size(D);
(is_empty, D) -> Mod:is_empty(D);
+ (iterator, S) -> Mod:iterator(S);
+ (iterator_from, {Start, S}) -> Mod:iterator_from(Start, S);
+ (next, I) -> Mod:next(I);
(to_list, D) -> to_list(Mod, D)
end.
diff --git a/lib/stdlib/test/maps_SUITE.erl b/lib/stdlib/test/maps_SUITE.erl
index 1d9c041a74..21e146ae3d 100644
--- a/lib/stdlib/test/maps_SUITE.erl
+++ b/lib/stdlib/test/maps_SUITE.erl
@@ -34,7 +34,7 @@
-export([init_per_testcase/2]).
-export([end_per_testcase/2]).
--export([t_get_3/1,
+-export([t_get_3/1, t_filter_2/1,
t_fold_3/1,t_map_2/1,t_size_1/1,
t_with_2/1,t_without_2/1]).
@@ -45,7 +45,7 @@ suite() ->
[{ct_hooks, [ts_install_cth]}].
all() ->
- [t_get_3,
+ [t_get_3,t_filter_2,
t_fold_3,t_map_2,t_size_1,
t_with_2,t_without_2].
@@ -99,6 +99,16 @@ t_with_2(_Config) ->
?badarg(with,[a,#{}]) = (catch maps:with(a,#{})),
ok.
+t_filter_2(Config) when is_list(Config) ->
+ M = #{a => 2, b => 3, c=> 4, "a" => 1, "b" => 2, "c" => 4},
+ Pred1 = fun(K,V) -> is_atom(K) andalso (V rem 2) =:= 0 end,
+ Pred2 = fun(K,V) -> is_list(K) andalso (V rem 2) =:= 0 end,
+ #{a := 2,c := 4} = maps:filter(Pred1,M),
+ #{"b" := 2,"c" := 4} = maps:filter(Pred2,M),
+ %% error case
+ ?badmap(a,filter,[_,a]) = (catch maps:filter(fun(_,_) -> ok end,id(a))),
+ ?badarg(filter,[<<>>,#{}]) = (catch maps:filter(id(<<>>),#{})),
+ ok.
t_fold_3(Config) when is_list(Config) ->
Vs = lists:seq(1,200),
diff --git a/lib/stdlib/test/sets_SUITE.erl b/lib/stdlib/test/sets_SUITE.erl
index c0cf1fc7e8..24f5d65f82 100644
--- a/lib/stdlib/test/sets_SUITE.erl
+++ b/lib/stdlib/test/sets_SUITE.erl
@@ -1,7 +1,7 @@
%%
%% %CopyrightBegin%
%%
-%% Copyright Ericsson AB 2004-2013. All Rights Reserved.
+%% Copyright Ericsson AB 2004-2015. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
@@ -28,7 +28,7 @@
create/1,add_element/1,del_element/1,
subtract/1,intersection/1,union/1,is_subset/1,
is_set/1,fold/1,filter/1,
- take_smallest/1,take_largest/1]).
+ take_smallest/1,take_largest/1, iterate/1]).
-include_lib("test_server/include/test_server.hrl").
@@ -48,7 +48,7 @@ suite() -> [{ct_hooks,[ts_install_cth]}].
all() ->
[create, add_element, del_element, subtract,
intersection, union, is_subset, is_set, fold, filter,
- take_smallest, take_largest].
+ take_smallest, take_largest, iterate].
groups() ->
[].
@@ -426,6 +426,44 @@ take_largest_3(S0, List0, M) ->
take_largest_3(S, List, M)
end.
+iterate(Config) when is_list(Config) ->
+ test_all(fun iterate_1/1).
+
+iterate_1(M) ->
+ case M(module, []) of
+ gb_sets -> iterate_2(M);
+ _ -> ok
+ end,
+ M(empty, []).
+
+iterate_2(M) ->
+ random:seed(1, 2, 42),
+ iter_set(M, 1000).
+
+iter_set(_M, 0) ->
+ ok;
+iter_set(M, N) ->
+ L = [I || I <- lists:seq(1, N)],
+ T = M(from_list, L),
+ L = lists:reverse(iterate_set(M, T)),
+ R = random:uniform(N),
+ S = lists:reverse(iterate_set(M, R, T)),
+ S = [E || E <- L, E >= R],
+ iter_set(M, N-1).
+
+iterate_set(M, Set) ->
+ I = M(iterator, Set),
+ iterate_set_1(M, M(next, I), []).
+
+iterate_set(M, Start, Set) ->
+ I = M(iterator_from, {Start, Set}),
+ iterate_set_1(M, M(next, I), []).
+
+iterate_set_1(_, none, R) ->
+ R;
+iterate_set_1(M, {E, I}, R) ->
+ iterate_set_1(M, M(next, I), [E | R]).
+
%%%
%%% Helper functions.
%%%
diff --git a/lib/stdlib/test/sets_test_lib.erl b/lib/stdlib/test/sets_test_lib.erl
index 86f009a8f9..772139406d 100644
--- a/lib/stdlib/test/sets_test_lib.erl
+++ b/lib/stdlib/test/sets_test_lib.erl
@@ -1,7 +1,7 @@
%%
%% %CopyrightBegin%
%%
-%% Copyright Ericsson AB 2004-2013. All Rights Reserved.
+%% Copyright Ericsson AB 2004-2015. All Rights Reserved.
%%
%% The contents of this file are subject to the Erlang Public License,
%% Version 1.1, (the "License"); you may not use this file except in
@@ -34,7 +34,10 @@ new(Mod, Eq) ->
(is_empty, S) -> is_empty(Mod, S);
(is_set, S) -> Mod:is_set(S);
(is_subset, {S,Set}) -> is_subset(Mod, Eq, S, Set);
+ (iterator, S) -> Mod:iterator(S);
+ (iterator_from, {Start, S}) -> Mod:iterator_from(Start, S);
(module, []) -> Mod;
+ (next, I) -> Mod:next(I);
(singleton, E) -> singleton(Mod, E);
(size, S) -> Mod:size(S);
(subtract, {S1,S2}) -> subtract(Mod, S1, S2);