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%% Copyright (c) 2015-2016 Christopher Meiklejohn. All Rights Reserved.
%% Copyright (c) 2007-2012 Basho Technologies, Inc. All Rights Reserved.
%% This file is provided to you 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
%% Unless required by applicable law or agreed to in writing,
%% software distributed under the License is distributed on an
%% KIND, either express or implied. See the License for the
%% specific language governing permissions and limitations
%% under the License.
%% -------------------------------------------------------------------
%% @doc ORSet CRDT: observed-remove set with tombstones
%% @reference Marc Shapiro, Nuno Preguiça, Carlos Baquero, Marek Zawirski (2011)
%% A comprehensive study of Convergent and Commutative
%% Replicated Data Types.
%% []
-author("Vitor Enes Duarte <>").
-define(TYPE, ?MODULE).
-export([new/0, new/1]).
-export([mutate/3, delta_mutate/3, merge/2]).
-export([query/1, equal/2, is_bottom/1,
is_inflation/2, is_strict_inflation/2,
-export([join_decomposition/1, delta/2, digest/1]).
-export([encode/2, decode/2]).
-export_type([state_orset/0, state_orset_op/0]).
-opaque state_orset() :: {?TYPE, payload()}.
-type payload() :: orddict:orddict().
-type element() :: term().
-type token() :: term().
-type state_orset_op() :: {add, element()} |
{add_by_token, token(), element()} |
{add_all, [element()]} |
{rmv, element()} |
{rmv_all, [element()]}.
%% @doc Create a new, empty `state_orset()'
-spec new() -> state_orset().
new() ->
{?TYPE, orddict:new()}.
%% @doc Create a new, empty `state_orset()'
-spec new([term()]) -> state_orset().
new([]) ->
%% @doc Mutate a `state_orset()'.
-spec mutate(state_orset_op(), type:id(), state_orset()) ->
{ok, state_orset()}.
mutate(Op, Actor, {?TYPE, _ORSet}=CRDT) ->
state_type:mutate(Op, Actor, CRDT).
%% @doc Delta-mutate a `state_orset()'.
%% The first argument can be:
%% - `{add, element()}'
%% - `{add_by_token, token(), element()}'
%% - `{rmv, element()}'
%% The second argument is the replica id.
%% The third argument is the `state_orset()' to be inflated.
-spec delta_mutate(state_orset_op(), type:id(), state_orset()) ->
{ok, state_orset()}.
delta_mutate({add, Elem}, Actor, {?TYPE, _}=ORSet) ->
Token = unique(Actor),
delta_mutate({add_by_token, Token, Elem}, Actor, ORSet);
%% @doc Returns a new `state_orset()' with only one element in
%% the dictionary. This element maps to a dictionary with
%% only one token tagged as true (token active)
delta_mutate({add_by_token, Token, Elem}, _Actor, {?TYPE, _ORSet}) ->
Tokens = orddict:store(Token, true, orddict:new()),
Delta = orddict:store(Elem, Tokens, orddict:new()),
{ok, {?TYPE, Delta}};
%% @doc Returns a new `state_orset()' with the elements passed as argument
%% as keys in the dictionary.
delta_mutate({add_all, Elems}, Actor, {?TYPE, _ORSet}) ->
Delta = lists:foldl(
fun(Elem, Acc) ->
Token = unique(Actor),
Tokens = orddict:store(Token, true, orddict:new()),
orddict:store(Elem, Tokens, Acc)
{ok, {?TYPE, Delta}};
%% @doc Returns a new `state_orset()' with only one element in
%% the dictionary mapping all current tokens to false (inactive).
delta_mutate({rmv, Elem}, _Actor, {?TYPE, ORSet}) ->
Delta = case orddict:find(Elem, ORSet) of
{ok, Tokens} ->
InactiveTokens = [{Token, false} || {Token, _Active} <- orddict:to_list(Tokens)],
orddict:store(Elem, InactiveTokens, orddict:new());
error ->
{ok, {?TYPE, Delta}};
%% @doc Removes a list of elements passed as input.
delta_mutate({rmv_all, Elems}, Actor, {?TYPE, _}=ORSet) ->
{?TYPE, DeltaGroup} = lists:foldl(
fun(Elem, DeltaGroupAcc) ->
case delta_mutate({rmv, Elem}, Actor, ORSet) of
{ok, {?TYPE, Delta}} ->
merge({?TYPE, Delta}, DeltaGroupAcc)
{ok, {?TYPE, DeltaGroup}}.
%% @doc Returns the value of the `state_orset()'.
%% This value is a set with all the elements in the `state_orset()'
%% that have at least one token still marked as active (true).
-spec query(state_orset()) -> sets:set(element()).
query({?TYPE, ORSet}) ->
fun(Elem, Tokens, Acc) ->
ActiveTokens = [Token || {Token, true} <- orddict:to_list(Tokens)],
case length(ActiveTokens) > 0 of
true ->
sets:add_element(Elem, Acc);
false ->
%% @doc Merge two `state_orset()'.
%% The keys (elements) of the resulting `state_orset()' are the union
%% of keys of both `state_orset()' passed as input.
%% When one of the elements is present in both `state_orset()',
%% the respective tokens are merged respecting the following rule:
%% - if a token is only present in on of the `state_orset()',
%% its value is preserved
%% - if a token is present in both `state_orset()' its value will be:
%% * active (true) if both were active before
%% * inactive (false) otherwise
-spec merge(state_orset(), state_orset()) -> state_orset().
merge({?TYPE, ORSet1}, {?TYPE, ORSet2}) ->
ORSet = orddict:merge(
fun(_Elem, Tokens1, Tokens2) ->
fun(_Token, Active1, Active2) ->
Active1 andalso Active2
{?TYPE, ORSet}.
%% @doc Equality for `state_orset()'.
%% Since everything is ordered, == should work.
-spec equal(state_orset(), state_orset()) -> boolean().
equal({?TYPE, ORSet1}, {?TYPE, ORSet2}) ->
ORSet1 == ORSet2.
%% @doc Check if an ORSet is bottom.
-spec is_bottom(state_orset()) -> boolean().
is_bottom({?TYPE, ORSet}) ->
%% @doc Given two `state_orset()', check if the second is and inflation
%% of the first.
%% The second is an inflation if, at least, has all the elements
%% of the first.
%% Also, for each element, we have an inflation if all the tokens
%% present in the first `state_orset()' are present in the second and
%% the value (activeness) is:
%% - active on both
%% - inactive on both
%% - first active and second inactive
-spec is_inflation(state_orset(), state_orset()) -> boolean().
is_inflation({?TYPE, ORSet1}, {?TYPE, ORSet2}) ->
fun({Elem, Tokens1}) ->
case orddict:find(Elem, ORSet2) of
%% if element is found, compare tokens
{ok, Tokens2} ->
fun({Token, Active1}) ->
case orddict:find(Token, Tokens2) of
%% if token is found, compare activeness
{ok, Active2} ->
%% (both active or both inactive)
%% orelse (first active and second inactive)
(Active1 == Active2)
orelse (Active1 andalso (not Active2));
%% if not found, not an inflation
error ->
%% if not found, not an inflation
error ->
%% @todo get back here later
is_inflation({cardinality, Value}, {?TYPE, _}=CRDT) ->
sets:size(query(CRDT)) >= Value.
%% @doc Check for strict inflation.
-spec is_strict_inflation(state_orset(), state_orset()) -> boolean().
is_strict_inflation({?TYPE, _}=CRDT1, {?TYPE, _}=CRDT2) ->
state_type:is_strict_inflation(CRDT1, CRDT2);
%% @todo get back here later
is_strict_inflation({cardinality, Value}, {?TYPE, _}=CRDT) ->
sets:size(query(CRDT)) > Value.
%% @doc Check for irreducible strict inflation.
-spec irreducible_is_strict_inflation(state_orset(),
state_type:digest()) ->
irreducible_is_strict_inflation({?TYPE, [{Elem, [{Token, Active}]}]},
{state, {?TYPE, ORSet}}) ->
case orddict:find(Elem, ORSet) of
{ok, Tokens} ->
case orddict:find(Token, Tokens) of
{ok, IsActive} ->
%% It will inflate if the token is active in
%% the current state (`true')
%% and the irreducible state has the token
%% inactive (`false')
IsActive andalso not Active;
error ->
%% If the token is not there, it will inflate
error ->
%% If the element is not there, it will inflate
-spec digest(state_orset()) -> state_type:digest().
digest({?TYPE, _}=CRDT) ->
{state, CRDT}.
%% @doc Join decomposition for `state_orset()'.
-spec join_decomposition(state_orset()) -> [state_orset()].
join_decomposition({?TYPE, ORSet}) ->
fun(Elem, Tokens, Acc) ->
Decomp = [{?TYPE, [{Elem, orddict:store(Token, Active, orddict:new())}]} || {Token, Active} <- orddict:to_list(Tokens)],
lists:append(Decomp, Acc)
%% @doc Delta calculation for `state_orset()'.
-spec delta(state_orset(), state_type:digest()) -> state_orset().
delta({?TYPE, _}=A, B) ->
state_type:delta(A, B).
-spec encode(state_type:format(), state_orset()) -> binary().
encode(erlang, {?TYPE, _}=CRDT) ->
-spec decode(state_type:format(), binary()) -> state_orset().
decode(erlang, Binary) ->
{?TYPE, _} = CRDT = erlang:binary_to_term(Binary),
%% private
unique(_Actor) ->
%% ===================================================================
%% EUnit tests
%% ===================================================================
new_test() ->
?assertEqual({?TYPE, orddict:new()}, new()).
query_test() ->
Set0 = new(),
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
?assertEqual(sets:new(), query(Set0)),
?assertEqual(sets:from_list([<<"a">>]), query(Set1)).
delta_add_test() ->
Actor = 1,
Set0 = new(),
{ok, {?TYPE, Delta1}} = delta_mutate({add_by_token, <<"token1">>, <<"a">>}, Actor, Set0),
Set1 = merge({?TYPE, Delta1}, Set0),
{ok, {?TYPE, Delta2}} = delta_mutate({add_by_token, <<"token2">>, <<"a">>}, Actor, Set1),
Set2 = merge({?TYPE, Delta2}, Set1),
{ok, {?TYPE, Delta3}} = delta_mutate({add_by_token, <<"token3">>, <<"b">>}, Actor, Set2),
Set3 = merge({?TYPE, Delta3}, Set2),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]}, {?TYPE, Delta1}),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]}, Set1),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token2">>, true}]}]}, {?TYPE, Delta2}),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}, {<<"token2">>, true}]}]}, Set2),
?assertEqual({?TYPE, [{<<"b">>, [{<<"token3">>, true}]}]}, {?TYPE, Delta3}),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}, {<<"token2">>, true}]}, {<<"b">>, [{<<"token3">>, true}]}]}, Set3).
add_test() ->
Actor = 1,
Set0 = new(),
{ok, Set1} = mutate({add_by_token, <<"token1">>, <<"a">>}, Actor, Set0),
{ok, Set2} = mutate({add_by_token, <<"token2">>, <<"a">>}, Actor, Set1),
{ok, Set3} = mutate({add_by_token, <<"token3">>, <<"b">>}, Actor, Set2),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]}, Set1),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}, {<<"token2">>, true}]}]}, Set2),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, true}, {<<"token2">>, true}]}, {<<"b">>, [{<<"token3">>, true}]}]}, Set3).
rmv_test() ->
Actor = 1,
Set0 = new(),
{ok, Set1} = mutate({add, <<"a">>}, Actor, Set0),
{ok, Set1} = mutate({rmv, <<"b">>}, Actor, Set1),
{ok, Set2} = mutate({rmv, <<"a">>}, Actor, Set1),
?assertEqual(sets:new(), query(Set2)).
add_all_test() ->
Actor = 1,
Set0 = new(),
{ok, Set1} = mutate({add_all, []}, Actor, Set0),
{ok, Set2} = mutate({add_all, [<<"a">>, <<"b">>]}, Actor, Set0),
{ok, Set3} = mutate({add_all, [<<"b">>, <<"c">>]}, Actor, Set2),
?assertEqual(sets:new(), query(Set1)),
?assertEqual(sets:from_list([<<"a">>, <<"b">>]), query(Set2)),
?assertEqual(sets:from_list([<<"a">>, <<"b">>, <<"c">>]), query(Set3)).
remove_all_test() ->
Actor = 1,
Set0 = new(),
{ok, Set1} = mutate({add_all, [<<"a">>, <<"b">>, <<"c">>]}, Actor, Set0),
{ok, Set2} = mutate({rmv_all, [<<"a">>, <<"c">>]}, Actor, Set1),
{ok, Set3} = mutate({rmv_all, [<<"b">>, <<"d">>]}, Actor, Set2),
{ok, Set4} = mutate({rmv_all, [<<"b">>, <<"a">>]}, Actor, Set2),
?assertEqual(sets:from_list([<<"b">>]), query(Set2)),
?assertEqual(sets:new(), query(Set3)),
?assertEqual(sets:new(), query(Set4)).
merge_idempotent_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set2 = {?TYPE, [{<<"b">>, [{<<"token2">>, true}]}]},
Set3 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Set4 = merge(Set1, Set1),
Set5 = merge(Set2, Set2),
Set6 = merge(Set3, Set3),
?assertEqual(Set1, Set4),
?assertEqual(Set2, Set5),
?assertEqual(Set3, Set6).
merge_commutative_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set2 = {?TYPE, [{<<"b">>, [{<<"token2">>, true}]}]},
Set3 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Set4 = merge(Set1, Set2),
Set5 = merge(Set2, Set1),
Set6 = merge(Set1, Set3),
Set7 = merge(Set3, Set1),
Set8 = merge(Set2, Set3),
Set9 = merge(Set3, Set2),
Set10 = merge(Set1, merge(Set2, Set3)),
Set1_2 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}, {<<"b">>, [{<<"token2">>, true}]}]},
Set1_3 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Set2_3 = Set3,
?assertEqual(Set1_2, Set4),
?assertEqual(Set1_2, Set5),
?assertEqual(Set1_3, Set6),
?assertEqual(Set1_3, Set7),
?assertEqual(Set2_3, Set8),
?assertEqual(Set2_3, Set9),
?assertEqual(Set1_3, Set10).
merge_delta_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
Delta1 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Delta2 = {?TYPE, [{<<"b">>, [{<<"token2">>, true}]}]},
Set2 = merge(Delta1, Set1),
Set3 = merge(Set1, Delta1),
DeltaGroup = merge(Delta1, Delta2),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]}, Set2),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]}, Set3),
?assertEqual({?TYPE, [{<<"a">>, [{<<"token1">>, false}]}, {<<"b">>, [{<<"token2">>, true}]}]}, DeltaGroup).
equal_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
Set2 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set3 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
?assert(equal(Set1, Set1)),
?assert(equal(Set2, Set2)),
?assert(equal(Set3, Set3)),
?assertNot(equal(Set1, Set2)),
?assertNot(equal(Set1, Set3)),
?assertNot(equal(Set2, Set3)).
is_bottom_test() ->
Set0 = new(),
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
is_inflation_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
Set2 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set3 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
?assert(is_inflation(Set1, Set1)),
?assert(is_inflation(Set1, Set2)),
?assertNot(is_inflation(Set2, Set1)),
?assert(is_inflation(Set1, Set3)),
?assertNot(is_inflation(Set2, Set3)),
?assertNot(is_inflation(Set3, Set2)),
%% check inflation with merge
?assert(state_type:is_inflation(Set1, Set1)),
?assert(state_type:is_inflation(Set1, Set2)),
?assertNot(state_type:is_inflation(Set2, Set1)),
?assert(state_type:is_inflation(Set1, Set3)),
?assertNot(state_type:is_inflation(Set2, Set3)),
?assertNot(state_type:is_inflation(Set3, Set2)).
is_strict_inflation_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
Set2 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set3 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
?assertNot(is_strict_inflation(Set1, Set1)),
?assert(is_strict_inflation(Set1, Set2)),
?assertNot(is_strict_inflation(Set2, Set1)),
?assert(is_strict_inflation(Set1, Set3)),
?assertNot(is_strict_inflation(Set2, Set3)),
?assertNot(is_strict_inflation(Set3, Set2)).
irreducible_is_strict_inflation_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Digest = digest(Set1),
Irreducible1 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Irreducible2 = {?TYPE, [{<<"b">>, [{<<"token2">>, false}]}]},
Irreducible3 = {?TYPE, [{<<"b">>, [{<<"token3">>, false}]}]},
Irreducible4 = {?TYPE, [{<<"c">>, [{<<"token4">>, true}]}]},
?assert(irreducible_is_strict_inflation(Irreducible1, Digest)),
?assertNot(irreducible_is_strict_inflation(Irreducible2, Digest)),
?assert(irreducible_is_strict_inflation(Irreducible3, Digest)),
?assert(irreducible_is_strict_inflation(Irreducible4, Digest)).
join_decomposition_test() ->
Set1 = {?TYPE, [{<<"a">>, [{<<"token1">>, false}]}]},
Set2 = {?TYPE, [{<<"a">>, [{<<"token1">>, true}, {<<"token3">>, false}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Decomp1 = join_decomposition(Set1),
Decomp2 = join_decomposition(Set2),
List = [{?TYPE, [{<<"a">>, [{<<"token1">>, true}]}]},
{?TYPE, [{<<"a">>, [{<<"token3">>, false}]}]},
{?TYPE, [{<<"b">>, [{<<"token2">>, false}]}]}],
?assertEqual([Set1], Decomp1),
?assertEqual(lists:sort(List), lists:sort(Decomp2)).
encode_decode_test() ->
Set = {?TYPE, [{<<"a">>, [{<<"token1">>, true}]}, {<<"b">>, [{<<"token2">>, false}]}]},
Binary = encode(erlang, Set),
ESet = decode(erlang, Binary),
?assertEqual(Set, ESet).
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