{"metadata":{"image":[],"title":"","description":""},"api":{"url":"","auth":"required","results":{"codes":[]},"settings":"","params":[]},"next":{"description":"","pages":[]},"title":"Set-Theoretic Operations","type":"basic","slug":"set-theoretic-operations","excerpt":"How can you combine collections together?","body":"We explore the set-theoretic operations provided by Lasp.  Each of these functions takes, as input, a two source collections and creates a single output collection.  The output will be maintained as the input is modified, and these operators can be chained arbitrarily.  \n[block:api-header]\n{\n  \"title\": \"Product Operation\"\n}\n[/block]\nLet's start by creating two input collections and an output collection.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"1> {ok, {LeftId, _, _, _}} = lasp:declare({<<\\\"left\\\">>, state_orset}, state_orset).              \\n{ok,{{<<\\\"left\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               1}]}],\\n     {state_orset,[]}}}\\n2> {ok, {RightId, _, _, _}} = lasp:declare({<<\\\"right\\\">>, state_orset}, state_orset).\\n{ok,{{<<\\\"right\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               1}]}],\\n     {state_orset,[]}}}\\n3> {ok, {ProductId, _, _, _}} = lasp:declare({<<\\\"product\\\">>, state_orset}, state_orset).\\n{ok,{{<<\\\"product\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               1}]}],\\n     {state_orset,[]}}}\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\nNow, let's instruct the system to compute the Cartesian product of these two collections, and place the output in it's own collection.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"4> lasp:product(LeftId, RightId, ProductId).\\nok\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\nNow, let's insert some values into the collections.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"5> lasp:update(LeftId, {add, 1}, self()).\\n{ok,{{<<\\\"left\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               2}]}],\\n     {state_orset,[{1,\\n                    [{<<238,140,18,224,53,159,36,82,45,233,15,19,116,65,95,\\n                        234,...>>,\\n                      true}]}]}}}\\n6> lasp:update(RightId, {add, 1}, self()).\\n{ok,{{<<\\\"right\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               2}]}],\\n     {state_orset,[{1,\\n                    [{<<255,58,60,173,193,138,15,227,94,88,201,220,12,106,56,\\n                        116,...>>,\\n                      true}]}]}}}\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\nLet's verify we have the right result: in this case it will be a collection of pairs, represented as Erlang tuples.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"7> {ok, ProductResult} = lasp:query(ProductId), sets:to_list(ProductResult).\\n[{1,1}]\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\n\n[block:api-header]\n{\n  \"title\": \"Union\"\n}\n[/block]\nNow, we can also use these initial collections to perform a union.\n\nLet's declare a place for the results.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"8> {ok, {UnionId, _, _, _}} = lasp:declare({<<\\\"union\\\">>, state_orset}, state_orset).    \\n{ok,{{<<\\\"union\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               1}]}],\\n     {state_orset,[]}}}\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\nLet's perform the union.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"9> lasp:union(LeftId, RightId, UnionId).\\nok\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\nFinally, let's look at the output.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"10> {ok, UnionResult} = lasp:query(UnionId), sets:to_list(UnionResult).           \\n[1]\",\n      \"language\": \"erlang\"\n    }\n  ]\n}\n[/block]\n\n[block:api-header]\n{\n  \"title\": \"Intersection\"\n}\n[/block]\nIntersection operates in a similar way as well.\n[block:code]\n{\n  \"codes\": [\n    {\n      \"code\": \"11> {ok, {IntersectionId, _, _, _}} = lasp:declare({<<\\\"intersection\\\">>, state_orset}, state_orset).\\n{ok,{{<<\\\"intersection\\\">>,state_orset},\\n     state_orset,\\n     [{clock,[{<<170,227,142,126,63,64,19,227,195,66,39,125,58,\\n                 195,75,134,148,109,168,...>>,\\n               1}]}],\\n     {state_orset,[]}}}\\n12> lasp:intersection(LeftId, RightId, IntersectionId).                \\nok\\n13> {ok, IntersectionResult} = lasp:query(IntersectionId), sets:to_list(IntersectionResult).\\n[1]\",\n      \"language\": \"erlang\"\n    }\n  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