Accumulators

Accumulators are special types of variables that accumulate information about the graph during its traversal and exploration. Because they are a unique and important feature of the GSQL query language, we devote a separate section to their introduction, but additional detail on their usage will be covered in other sections, the SELECT Statement section in particular.

This section covers the following subset of the EBNF language definitions:

EBNF for accumulators
accumDeclStmt :=
          accumType localAccumName ["=" constant]
                    ["," localAccumName ["=" constant]]*
        | accumType globalAccumName ["=" constant]
                    ["," globalAccumName ["=" constant]]*
localAccumName := "@"accumName;
globalAccumName := "@@"accumName;


accumType := "SumAccum" "<" ( INT | FLOAT | DOUBLE | STRING | STRING COMPRESS) ">"
       | "MaxAccum" "<" ( INT | FLOAT | DOUBLE ) ">"
       | "MinAccum" "<" ( INT | FLOAT | DOUBLE ) ">"
       | "AvgAccum"
       | "OrAccum"
       | "AndAccum"
       | "BitwiseOrAccum"
       | "BitwiseAndAccum"
       | "ListAccum" "<" type ">"
       | "SetAccum"  "<" elementType ">"
       | "BagAccum"  "<" elementType ">"
       | "MapAccum"  "<" elementType "," (baseType | accumType | tupleType) ">"
       | "HeapAccum" "<" tupleType ">" "(" simpleSize "," fieldName [ASC | DESC]
                                          ["," fieldName [ASC | DESC]]* ")"
       | "GroupByAccum" "<" elementType fieldName ["," elementType fieldName]* ,
		                     accumType fieldName ["," accumType fieldName]* ">"
       | "ArrayAccum" "<" accumName ">"

elementType := baseType | tupleType | STRING COMPRESS

gAccumAccumStmt := globalAccumName "+=" expr

accumClause := ACCUM DMLSubStmtList

postAccumClause := "POST-ACCUM" DMLSubStmtList

There are a number of different types of accumulators, each providing specific accumulation functions. Accumulators are declared to have one of two types of association: global or vertex-attached.

More technically, accumulators are mutable mutex (mutual exclusion) variables shared among all the graph computation threads exploring the graph within a given query. To improve performance, the graph processing engine employs multithreaded processing. Modification of accumulators is coordinated at run-time so the accumulation operator works correctly (i.e., mutually exclusively) across all threads.

This is particularly relevant in the ACCUM clause. During traversal of the graph, the selected set of edges or vertices is partitioned among a group of threads. These threads have shared mutually exclusive access to the accumulators.

Declaration of Accumulators

Global accumulators can be declared anywhere in the query. Vertex-attached accumulators can be declared anywhere in the query except for in a FOREACH loop or WHILE loop. Accumulators are block-scoped and can only be accessed in the block where they are declared.

The name of a vertex-attached accumulator begins with a single @.The name of a global accumulator begins with @@.

EBNF for Accumulator Declaration
accumDeclStmt := accumType localAccumName ["=" expr]
                    ["," localAccumName ["=" expr]]*
               | accumType globalAccumName ["=" expr]
                    ["," globalAccumName ["=" expr]]*
localAccumName := "@"accumName;
globalAccumName := "@@"accumName;

Vertex-attached Accumulators

Vertex-attached accumulators are mutable state variables that are attached to each vertex in the graph for the duration of the query’s lifetime. They act as run-time attributes of a vertex. They are shared, mutually exclusively, among all query processes.

Vertex-attached accumulators can be set to a value with the = operator. Additionally, the operator =` can be used to update the state of the accumulator; the function of `= depends on the accumulator type. Vertex-attached accumulators can only be accessed or updated (via = or +=) in an ACCUM or POST-ACCUM clause within a SELECT statement or by a PRINT statement.

In the example below, there are two accumulators attached to each vertex. The initial value of an accumulator of a given type is predefined, however it can be changed at declaration as in the accumulator @weight below. All vertex-attached accumulator names have a single leading at-sign @.

Vertex-Attached Accumulators
SumAccum<INT>   @neighbors;
MaxAccum<FLOAT> @weight = 2.8;

If there is a graph with 10 vertices, then there is an instance of @neighbors and @weight for each vertex (hence 10 of each, and 20 total accumulator instances). These are accessed via the dot operator on a vertex variable or a vertex alias (e.g., v.@neighbor). The accumulator operator += only impacts the accumulator for the specific vertex being referenced. A statement such as v1.@neighbors += 1will only impact v1 's @neighbors and not the @neighbors for other vertices.

Global accumulators

A global accumulator is a single mutable accumulator that can be accessed or updated within a query. The names of global accumulators start with a double at-sign @@.

Global Accumulators
SumAccum<INT>   @@totalNeighbors;
MaxAccum<FLOAT> @@entropy = 1.0;

Global accumulators can only be assigned (using the = operator) outside a SELECT block (i.e., not within an ACCUM or POST-ACCUM clause). Global accumulators can be accessed or updated via the accumulate operator += anywhere within a query, including inside a SELECT block.

The accumulation operation for global accumulators in an ACCUM clause executes once for each process. That is:

  • if the FROM clause uses an edge-induced selection (introduced in Section "`SELECT` Statement"), the ACCUM clause executes one process for each edge in the selected edge set.

  • If the FROM clause uses a vertex-induced selection (introduced in Section "`SELECT` Statement"), the ACCUM clause executes one process for each vertex in the selected vertex set.

Since global accumulators are shared in a mutually exclusive manner among processes, they behave very differently than a non-accumulator variable (see the Declaration Statements section for more details) in an ACCUM clause.

Take the following code example. The global accumulator @@globalRelationshipCount is accumulated for every Works_For edge traversed since it is shared among processes. Conversely, Relationship_Count appears to have only been incremented once.

This is because a non-accumulator variable is not shared among processes. Each process has its own separate unshared copy of Relationship_Count and increments the original value by one. (E.g., each process increments Relationship_Count from 0 to 1.) There is no accumulation and the final value is one.

Example

  • Query

  • Results

Global Variable vs Global Accumulator
// Count the total number of employment relationships for all companies
CREATE QUERY count_employment_relationships() FOR GRAPH Work_Net SYNTAX V2 {

    INT local_relationship_count;
    SumAccum<INT> @@global_relationship_count;

    start = {Company.*};

    companies = SELECT s FROM start:s -(Works_For)- :t
        ACCUM @@global_relationship_count += 1,
        local_relationship_count = local_relationship_count + 1;

    PRINT local_relationship_count;
    PRINT @@global_relationship_count;
}
countEmploymentRelationship.json Results
GSQL > RUN QUERY count_employment_relationships()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"local_relationship_count": 1},
    {"@@global_relationship_count": 17}
  ]
}

Accumulator Types

The following are the accumulator types we currently support. Each type of accumulator supports one or more data types.

EBNF for Accumulator Types
accumType := "SumAccum" "<" ( INT | FLOAT | DOUBLE | STRING | STRING COMPRESS) ">"
		   | "MaxAccum" "<" ( INT | FLOAT | DOUBLE ) ">"
 	     | "MinAccum" "<" ( INT | FLOAT | DOUBLE ) ">"
     	 | "AvgAccum"
		   | "OrAccum"
		   | "AndAccum"
       | "BitwiseOrAccum"
       | "BitwiseAndAccum"
		   | "ListAccum" "<" type ">"
		   | "SetAccum"  "<" elementType ">"
		   | "BagAccum"  "<" elementType ">"
       | "MapAccum"  "<" elementType "," (baseType | accumType | tupleType) ">"
       | "HeapAccum" "<" tupleType ">" "(" simpleSize "," fieleName [ASC | DESC]
                               ["," fieldName [ASC | DESC]]* ")"
		   | "GroupByAccum" "<" elementType fieldName ["," elementType fieldName]* ,
		                        accumType fieldName ["," accumType fieldName]* ">"
       | "ArrayAccum" "<" accumName ">"

elementType := baseType | tupleType | STRING COMPRESS

gAccumAccumStmt := globaAccumName "+=" expr

The accumulators fall into two major groups :

  • Scalar Accumulators store a single value:

    • SumAccum

    • MinAccum, MaxAccum

    • AvgAccum

    • AndAccum, OrAccum

    • BitwiseAndAccum, BitwiseOrAccum

  • Collection Accumulators store a set of values:

    • ListAccum

    • SetAccum

    • BagAccum

    • MapAccum

    • ArrayAccum

    • HeapAccum

    • GroupByAccum

The details of each accumulator type are summarized in this table. The Accumulation Operation column explains how the accumulator exampleAccum is updated when the statement exampleAccum += newVal is executed. Following the table are example queries for each accumulator type.

Table 1. Accumulator Types and Their Accumulation Behavior
Accumulator type (Case Sensitive) Default Initial Value Accumulation operation

SumAccum<INT>

0

Adds right operand to SumAccum.

SumAccum<FLOAT or DOUBLE>

0.0

Adds right operand to SumAccum.

SumAccum<STRING>

Empty string

Concatenates SumAccum and right operand.

MaxAccum<INT>

INT_MIN

Updates the value of MaxAccum to the greater between MaxAccum and right operand.

MaxAccum<FLOAT or DOUBLE>

FLOAT_MIN or DOUBLE_MIN

Updates the value of MaxAccum to the greater between MaxAccum and right operand.

MaxAccum<STRING>

Empty string

Updates the value of MaxAccum to the greater between MaxAccum and right operand according to UTF-8 lexicographical ordering.

MaxAccum<VERTEX>

Vertex with internal ID 0

Updates the value of MaxAccum to the vertex with greater internal ID between MaxAccum and right operand.

MaxAccum<tupleType>

Default for each field of the tuple

Updates the value of MaxAccum to the greater between MaxAccum and right operand. tupleType is a user-defined sequence of base types. Ordering is hierarchical, using the leftmost field of the tuple first, then the next field, and so on.

MinAccum<INT>

INT_MAX

Updates the value of MinAccum to the lesser between MinAccum and right operand.

MinAccum<FLOAT or DOUBLE>

FLOAT_MAX or DOUBLE_MAX

Updates the value of MinAccum to the lesser between MinAccum and right operand.

MinAccum<STRING>

empty string

Updates the value of MinAccum to the lesser between MinAccum and right operand according to UTF-8 lexicographical ordering.

MinAccum<VERTEX>

unknown

Updates the value of MinAccum to the vertex with lesser internal ID between MinAccum and right operand.

MinAccum<tupleType>

Default for each field of the tuple

Updates the value of MinAccum to the lesser between MinAccum and right operand. tupleType is a user-defined sequence of baseTypes. Ordering is hierarchical, using the leftmost field of the tuple first, then the next field, and so on.

AvgAccum

0.0 (double precision)

Updates AvgAccum to double precision average of right operand and all previous values accumulated to AvgAccum

AndAccum

True

Updates AndAccum to boolean AND of right operand and AndAccum.

OrAccum

False

Updates OrAccum to boolean OR of right operand and AndAccum.

BitwiseAndAccum

-1 (INT) = 64-bit sequence of 1s

Updates BitwiseAndAccum to boolean AND of right operand and BitwiseAndAccum.

BitwiseOrAccum

0 (INT) = 64-bit sequence of 0s

Updates BitwiseOrAccum to boolean OR of right operand and BitwiseORAccum.

ListAccum< type >

Empty list

Appends right operand to end of ListAccum.

SetAccum< type >

empty set

Updates SetAccum to union of right operand and SetAccum. right operand can be a single value or a set/bag.

BagAccum<type>

Empty bag

Updates BagAccum to union of right operand and BagAccum. Right operand can be a single value or a set/bag.

MapAccum< type, type >

Empty map

Adds or updates a key-value pair of MapAccum.

ArrayAccum< accumType >

Empty list

See the ArrayAccum section below for details.

HeapAccum< tuple >(heapSize, sortKey)

Empty heap

Inserts right operand into HeapAccum, maintaining the heap in sorted order, according to the sort key(s) and size limit declared for this HeapAccum.

GroupByAccum< type [, type] , accumType [, accumType]* >

Empty group by map

Adds or updates a key:value pair GroupByAccum. See Section GroupByAccum for more details.

SumAccum

The SumAccum type computes and stores the cumulative sum of numeric values or the cumulative concatenation of text values. The output of a SumAccum is a single numeric or string value. SumAccum variables operate on values of type INT, UINT, FLOAT, DOUBLE, or STRING only.

The =` operator updates the accumulator's state. For `INT`, `FLOAT`, and `DOUBLE` types, `= arg performs a numeric addition, while for the STRING value type += arg concatenates arg to the current value of the SumAccum.

Example

  • Query

  • Results

SumAccum Example
CREATE QUERY sum_accum_ex() FOR GRAPH Minimal_Net {

    SumAccum<INT>    @@int_accum;
    SumAccum<FLOAT>  @@float_accum;
    SumAccum<DOUBLE> @@double_accum;
    SumAccum<STRING> @@string_accum;

    @@int_accum  = 1;
    @@int_accum += 1;

    @@float_accum = @@int_accum;
    @@float_accum = @@float_accum / 3;

    @@double_accum  = @@float_accum * 8;
    @@double_accum += -1;

    @@string_accum  = "Hello ";
    @@string_accum += "World";

    PRINT @@int_accum;
    PRINT @@float_accum;
    PRINT @@double_accum;
    PRINT @@string_accum;
}
sumAccumEx.json Result
GSQL > RUN QUERY sum_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@int_accum": 2},
    {"@@float_accum": 0.66667},
    {"@@double_accum": 4.33333},
    {"@@string_accum": "Hello World"}
  ]
}

MinAccum / MaxAccum

The MinAccum and MaxAccum types calculate and store the cumulative minimum or the cumulative maximum of a series of values. The output of a MinAccum or a MaxAccum is a single value of the type that was passed in. MinAccum and MaxAccum variables operate on values of type INT, UINT, FLOAT, DOUBLE, STRING, TUPLE, and VERTEX (with optional specific vertex type) only.

For MinAccum, += arg checks if the current value held is less than arg and stores the smaller of the two. MaxAccum behaves the same, with the exception that it checks for and stores the greater instead of the lesser of the two.

Example

  • Query

  • Results

MinAccum and MaxAccum Example
CREATE QUERY min_max_accum_ex() FOR GRAPH Minimal_Net {

    MinAccum<INT> @@min_accum;
    MaxAccum<FLOAT> @@max_accum;

    @@min_accum += 40;
    @@min_accum += 20;
    @@min_accum += -10;

    @@max_accum += -1.1;
    @@max_accum += 2.5;
    @@max_accum += 2.8;

    PRINT @@min_accum;
    PRINT @@max_accum;
}
GSQL > RUN QUERY min_max_accum_Ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@min_accum": -10},
    {"@@max_accum": 2.8}
  ]
}

String minimum and maximum values are based on their UTF-8 codes, which is a multilingual superset of the ASCII codes. Within ASCII, a is less than z, uppercase is less than lowercase, and digits are less than alphabetic characters.

MinAccum and MaxAccum operating on VERTEX types have a special comparison. They do not compare vertex ids, but TigerGraph internal ids, which might not be in the same order as the external ids. Comparing internal ids is much faster, so MinAccum/MaxAccum<VERTEX> provides an efficient way to compare and select vertices. This is helpful for some graph algorithms that require the vertices to be numbered and sortable. For example, the following query returns one post from each person. The returned vertex is not necessarily the vertex with the alphabetically largest id.

  • Query

  • Results

This query returns one random post vertex from each person

CREATE QUERY min_max_accum_vertex() FOR GRAPH Social_Net api("v2") {

  MaxAccum<VERTEX> @max_vertex;
  all_user = {Person.*};
  all_user = SELECT src
            FROM all_user:src -(Posted>)- Post:tgt
            ACCUM src.@max_vertex += tgt
            ORDER BY src.id;
  PRINT all_user[all_user.@max_vertex]; // api v2
}
minMaxAccuxVertex.json Result
GSQL > RUN QUERY min_max_accum_vertex()
{
  "error": false,
  "message": "",
  "version": {
    "edition": "developer",
    "schema": 0,
    "api": "v2"
  },
  "results": [{"allUser": [
    {
      "v_id": "person1",
      "attributes": {"allUser.@maxVertex": "0"},
      "v_type": "person"
    },
    {
      "v_id": "person2",
      "attributes": {"allUser.@maxVertex": "1"},
      "v_type": "person"
    },
    {
      "v_id": "person3",
      "attributes": {"allUser.@maxVertex": "2"},
      "v_type": "person"
    },
    {
      "v_id": "person4",
      "attributes": {"allUser.@maxVertex": "3"},
      "v_type": "person"
    },
    {
      "v_id": "person5",
      "attributes": {"allUser.@maxVertex": "11"},
      "v_type": "person"
    },
    {
      "v_id": "person6",
      "attributes": {"allUser.@maxVertex": "10"},
      "v_type": "person"
    },
    {
      "v_id": "person7",
      "attributes": {"allUser.@maxVertex": "9"},
      "v_type": "person"
    },
    {
      "v_id": "person8",
      "attributes": {"allUser.@maxVertex": "7"},
      "v_type": "person"
    }
  ]}]
}

Tuple data types are treated as hierarchical structures, where the first field used for ordering is the leftmost one. When a tuple is used as an element of a MinAccum or MaxAccum, tuple fields can be directly accessed from the accumulator. For example, if we have the following tuple type and MaxAccum :

TYPEDEF TUPLE <FLOAT weight> Edge_Weight
MinAccum<EDGE_WEIGHT> @@acc_test;

Then the weight field of the tuple can be accessed directly from the MinAccum through the dot operator(.):

@@acc_test.weight // Will return the weight field value for the EDGE_WEIGHT
                 // type tuple stored in the MaxAccum

AvgAccum

The AvgAccum type calculates and stores the cumulative mean of a series of numeric values. Internally, its state information includes the sum value of all inputs and a count of how many input values it has accumulated. The output is the mean value; the sum and the count values are not accessible to the user.

The data type of an AvgAccum variable is not declared; all AvgAccum accumulators accept inputs of type INT, UINT, FLOAT, and DOUBLE. The output is always DOUBLE type.

The += arg operation updates the AvgAccum variable’s state to be the mean of all the previous arguments along with the current argument. The = arg operation clears the previously accumulated state and sets the new state to be arg with a count of one.

Example

  • Query

  • Results

AvgAccum Example
CREATE QUERY avg_accum_ex() FOR GRAPH Minimal_Net {

    AvgAccum @@average_accum;

    @@average_accum += 10;
    @@average_accum += 5.5; // avg = (10+5.5) / 2.0
    @@average_accum += -1;  // avg = (10+5.5-1) / 3.0

    PRINT @@average_accum;  // 4.8333...

    @@average_accum = 99;   // reset
    @@average_accum += 101; // avg = (99 + 101) / 2

    PRINT @@average_accum;  // 100
}
GSQL > RUN QUERY avg_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@average_accum": 4.83333},
    {"@@average_accum": 100}
  ]
}

AndAccum / OrAccum

The AndAccum and OrAccum types calculate and store the cumulative result of a series of boolean operations. The output of an AndAccum or an OrAccum is a single boolean value (TRUE or FALSE). AndAccum and OrAccum variables operate on boolean values only. The data type does not need to be declared.

For AndAccum, += arg updates the state to be the logical AND between the current boolean state and arg. OrAccum behaves the same, with the exception that it stores the result of a logical OR operation.

Example

  • Query

  • Results

AndAccum and OrAccum Example
CREATE QUERY and_or_accum_ex() FOR GRAPH Minimal_Net {

    AndAccum @@and_accum_var; // (default value = TRUE)
    OrAccum  @@or_accum_var;  // (default value = FALSE)

    @@and_accum_var += TRUE;  // T and T = T
    @@and_accum_var += FALSE; // T and F = F
    @@and_accum_var += TRUE;  // F and T = F

    PRINT @@and_accum_var;

    @@or_accum_var += FALSE;  // F or F == F
    @@or_accum_var += TRUE;   // F or T == T
    @@or_accum_var += FALSE;  // T or F == T

    PRINT @@or_accum_var;
}
GSQL > RUN QUERY and_or_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@and_accum_var": false},
    {"@@or_accum_var": true}
  ]
}

BitwiseAndAccum / BitwiseOrAccum

The BitwiseAndAccum and BitwiseOrAccum types calculate and store the cumulative result of a series of bitwise boolean operations and store the resulting bit sequences. The default length for both BitwiseAndAccum and BitwiseOrAccum is 64 bit. You can specify the length of both types by appending the desired length in angle brackets<>.

Fundamental to understanding and using bitwise operations is the knowledge that integers are stored in base-2 representation as a 64-bit sequence of 1s and 0s. "Bitwise" means that each bit is treated as a separate boolean value, with 1 representing true and 0 representing false. Hence, an integer is equivalent to a sequence of boolean values. Computing the Bitwise AND of two numbers A and B means computing the bit sequence C where the \(j_{th}\) bit of C, denoted \(C_j\), is equal to \(A_j\) AND \(B_j\).

Declaration

A bitwise accumulator has different declaration syntax depending on its length:

  • When a bitwise accumulator length is less than or equal to 64 bit, it’s assigned using one integer. The integer is converted to a 64-bit sequence of 1s and 0s. Overflow on the left is ignored.

  • When a bitwise accumulator length is longer than 64 bit, it’s assigned using an array of two integers. Each integer is converted to a 64-bit sequence of 1s and 0s. The integer in the second position will take up the first 64 bits from the right of the sequence, and the integer on the left will take up the remaining bits. Any overflowing bits will be ignored.

For example, if you are declaring an 80-bit BitwiseAndAccum:

@@bit80<80> = [123, 456]

456 represents the 64-bit sequence 0000….000111001000 (zeros omitted), and 123 represents the 64-bit sequence 0000000000…00001111011 (zeros omitted).

When the two integers are joined together, the 64-bit sequence on the right (456) takes up the 64 bits from the right. The 64-bit sequence on the left (123) takes up the remaining 16 bits and the overflow on the left is ignored.

The resulting BitwiseAndAccum prints as below:

0000000001111011 (16bits in total) 0000000...000111001000 (64bits in total)

Accumulation behavior

For BitwiseAndAccum, += arg updates the accumulator’s state to be the Bitwise AND of the current state and arg. BitwiseOrAccum behaves the same, with the exception that it computes a Bitwise OR.

Bitwise Operations and Negative Integers

Most computer systems represent negative integers using "2’s complement" format, where the uppermost bit has special significance. Operations that affect the uppermost bit are crossing the boundary between positive and negative numbers, and vice versa.

Functions

This is a list of methods of BitwiseAndAccum and BitwiseOrAccum. If a method returns an BitwiseAndAccum or BitwiseOrAccum, it returns the same type as the instance that calls the method.

Table 2. Bitwise accumulator functions
Function Return type Accessor/Mutator Description

.reset()

None.

Mutator

Sets all bits to 0.

.cardinality()

INT

Accessor

Returns the number of 1s.

.get( index )

INT

Accessor

Returns the 1 or 0 at the provided index.

  • index: INT. The position of the bit value to return.

.set( )

None.

Mutator

Sets all bits to 1.

.set( index, value )

None.

Mutator

Sets the bit at the provided index to the desire value.

  • index: INT. The position of the bit

  • value: BOOL. The value of the bit.

.flip( index )

None.

Mutator

Flips the bit at the specified index. If the bit is 0, changes it to 1 and vice versa.

.flip( fromIndex [, toIndex ] )

None.

Mutator

Flips the bits in the specified range.

.xor ( accum )

None.

Mutator

Compares two bitwise accumulators of the same length. Returns a Bitwise accumulator whose every bit is the exclusive OR result between the two bitwise accumulators.

.and ( accum )

None.

Mutator

Compares two bitwise accumulators of the same length. Returns a bitwise accumulator whose every bit is the AND result between the two bitwise accumulators.

.or ( accum )

None.

Mutator

Compares two bitwise accumulators of the same length. Returns a Bitwise accumulator whose every bit is the OR result between the two bitwise accumulators.

Example

  • Query

  • Results

CREATE QUERY bitwise_accum_ex() FOR GRAPH Minimal_Net {

    BitwiseAndAccum @@bw_and_accum_var; // default value = 64-bits of 1 = -1 (INT)
    BitwiseOrAccum    @@bw_or_accum_var;    // default value = 64-bits of 0 = 0 (INT))

    // 11110000 = 240
    // 00001111 =    15
    // 10101010 = 170
    // 01010101 =    85

    // BitwiseAndAccum
    @@bw_and_accum_var += 170; // 11111111 & 10101010 -> 10101010
    @@bw_and_accum_var +=    85; // 10101010 & 01010101 -> 00000000
    PRINT @@bw_and_accum_var;    // 0

    @@bw_and_accum_var = 15;     // reset to 00001111
    @@bw_and_accum_var += 85;    // 00001111 & 01010101 -> 00000101
    PRINT @@bw_and_accum_var;    // 5

    // BitwiseOrAccum
    @@bw_or_accum_var += 170; // 00000000 | 10101010 -> 10101010
    @@bw_or_accum_var +=    85; // 10101010 | 01010101 -> 11111111 = 255
    PRINT @@bw_or_accum_var;    // 255

    @@bw_or_accum_var = 15;     // reset to 00001111
    @@bw_or_accum_var += 85;    // 00001111 | 01010101 -> 01011111 = 95
    PRINT @@bw_or_accum_var;    // 95
}
GSQL > RUN QUERY bitwise_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@bw_and_accum_var": "0000000000000000000000000000000000000000000000000000000000000000"},
    {"@@bw_and_accum_var": "0000000000000000000000000000000000000000000000000000000000000101"},
    {"@@bw_or_accum_var": "0000000000000000000000000000000000000000000000000000000011111111"},
    {"@@bw_or_accum_var": "0000000000000000000000000000000000000000000000000000000001011111"}
  ]
}

ListAccum

The ListAccum type maintains a sequential collection of elements. The output of a ListAccum is a list of values in the order the elements were added. The element type can be any base type, tuple, or STRING COMPRESS. Additionally, a ListAccum can contain a nested collection of type ListAccum. Nesting of ListAccums is limited to a depth of three.

The += arg operation appends arg to the end of the list. In this case, arg may be either a single element or another ListAccum.

ListAccum supports two additional operations:

  • @list1 + @list2 creates a new ListAccum, which contains the elements of @list1 followed by the elements of @list2. The two ListAccums must have identical data types.

  • @list1 * @list2 (STRING data only) generates a new list of strings consisting of all permutations of an element of the first list followed by an element of the second list.

ListAccum also supports the following class functions.

Functions that modify the ListAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function (T is the element type) Return type Accessor / Mutator Description

.size()

INT

Accessor

Returns the number of elements in the list.

.contains( T val )

BOOL

Accessor

Returns true if the list does contain value, and false if it doesn’t.

.get( INT idx )

T

Accessor

Returns the value at the given index position in the list. The index begins at 0. If the index is out of bound (including any negative value), the default value of the element type is returned.

.clear()

VOID

Mutator

Clears the list so it becomes empty with size 0.

.update (INT index, T value )

VOID

Mutator

Assigns value to the list element at position index.

.remove(INT index)

VOID

Mutator

Removes value at the specified index. If the index is invalid, the function will do nothing.

.removeOne(T value)

VOID

Mutator

Removes the first matching value. If there is no matching value, the function will do nothing.

.removeAll(T value)

VOID

Mutator

Removes all matching values. If there is no matching value, the function will do nothing.

Examples

  • Query

  • Results

CREATE QUERY list_accum_ex() FOR GRAPH Minimal_Net {

    ListAccum<INT> @@int_list_accum;
    ListAccum<STRING> @@string_list_accum;
    ListAccum<STRING> @@string_multiply_list_accum;
    ListAccum<STRING> @@string_addition_accum;
    ListAccum<STRING> @@letter_list_accum;
    ListAccum<ListAccum<STRING>> @@nested_list_accum;

    @@int_list_accum = [1,3,5];
    @@int_list_accum += [7,9];
    @@int_list_accum += 11;
    @@int_list_accum += 13;
    @@int_list_accum += 15;

    PRINT @@int_list_accum;
    PRINT @@int_list_accum.get(0), @@int_list_accum.get(1);
    PRINT @@int_list_accum.get(8); // Out of bound: default value of int: 0

    // Other built-in functions
    PRINT @@int_list_accum.size();
    PRINT @@int_list_accum.contains(2);
    PRINT @@int_list_accum.contains(3);

    @@string_list_accum += "Hello";
    @@string_list_accum += "World";

    PRINT @@string_list_accum; // ["Hello","World"]

    @@letter_list_accum += "a";
    @@letter_list_accum += "b";

    // ListA + ListB produces a new list equivalent to ListB appended to ListA.
    // Ex: [a,b,c] + [d,e,f] => [a,b,c,d,e,f]
    @@string_addition_accum = @@string_list_accum + @@letter_list_accum;

    PRINT @@string_addition_accum;

    // Multiplication produces a list of all list-to-list element combinations (STRING TYPE ONLY)
    // Ex: [a,b] * [c,d] = [ac, ad, bc, bd]
    @@string_multiply_list_accum = @@string_list_accum * @@letter_list_accum;

    PRINT @@string_multiply_list_accum;

    // Two dimensional list (3 dimensions is possible as well)
    @@nested_list_accum += [["foo", "bar"], ["Big", "Bang", "Theory"], ["String", "Theory"]];

    PRINT @@nested_list_accum;
    PRINT @@nested_list_accum.get(0);
    PRINT @@nested_list_accum.get(0).get(1);
}
GSQL > RUN QUERY list_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@int_list_accum": [
      1,
      3,
      5,
      7,
      9,
      11,
      13,
      15
    ]},
    {
      "@@int_list_accum.get(1)": 3,
      "@@int_list_accum.get(0)": 1
    },
    {"@@int_list_accum.get(8)": 0},
    {"@@int_list_accum.size()": 8},
    {"@@int_list_accum.contains(2)": false},
    {"@@int_list_accum.contains(3)": true},
    {"@@string_list_accum": [
      "Hello",
      "World"
    ]},
    {"@@string_addition_accum": [
      "Hello",
      "World",
      "a",
      "b"
    ]},
    {"@@string_multiply_list_accum": [
      "Helloa",
      "Worlda",
      "Hellob",
      "Worldb"
    ]},
    {"@@nested_list_accum": [
      [
        "foo",
        "bar"
      ],
      [
        "Big",
        "Bang",
        "Theory"
      ],
      [
        "String",
        "Theory"
      ]
    ]},
    {"@@nested_list_accum.get(0)": [
      "foo",
      "bar"
    ]},
    {"@@nested_list_accum.get(0).get(1)": "bar"}
  ]
}

  • Query

  • Results

Example for update function on a global ListAccum
CREATE QUERY list_accum_update_ex() FOR GRAPH Work_Net {

    // Global List_accum
    ListAccum<INT> @@int_list_accum;
    ListAccum<STRING> @@string_list_accum;
    ListAccum<BOOL> @@pass_fail;

    @@int_list_accum += [0,2,4,6,8];
    @@string_list_accum += ["apple","banana","carrot","daikon"];

    // Global update at Query-Body Level
    @@pass_fail += @@int_list_accum.update(1,-99);
    @@pass_fail += @@int_list_accum.update(@@int_list_accum.size()-1,40);    // last element
    @@pass_fail += @@string_list_accum.update(0,"zero"); // first element
    @@pass_fail += @@string_list_accum.update(4,"four"); // FAIL: out-of-range

    PRINT @@int_list_accum, @@string_list_accum, @@pass_fail;
}
Results in listAccumUpdateEx.json
GSQL > RUN QUERY list_accum_update_ex()
{
  "error": false,
  "message": "",
  "version": {
    "edition": "developer",
    "schema": 0,
    "api": "v2"
  },
  "results": [{
    "@@passFail": [ true, true, true, false ],
    "@@intListAccum": [ 0, -99, 4, 6, 40 ],
    "@@stringListAccum": [ "zero", "banana", "carrot", "daikon" ]
  }]
}

  • Query

  • Results

Example for update function on a vertex-attached ListAccum
CREATE QUERY list_accum_update_ex2(SET<VERTEX<Person>> seed) FOR GRAPH Work_Net api("v2") {

    // Each person has an LIST<INT> of skills and a LIST<STRING> of interests.
    // This function copies their lists into ListAccums, and then udpates the last
    // int with -99 and updates the last string with "fizz".
    ListAccum<INT> @int_list;
    ListAccum<STRING> @string_list;
    ListAccum<STRING> @@int_fails, @@str_fails;

    S0 (Person) = seed;
    S1 = SELECT s
        FROM S0:s
        ACCUM
            s.@int_list = s.skill_list,
            s.@string_list = s.interest_list
        POST-ACCUM
            INT len = s.@int_list.size(),
            IF NOT s.@int_list.update(len-1,-99) THEN
                @@int_fails += s.id END,
                INT len2 = s.@string_list.size(),
            IF NOT s.@string_list.update(len2-1,"fizz") THEN
                @@str_fails += s.id
            END
        ;
    PRINT S1[S1.skill_list, S1.interest_list, S1.@int_list, S1.@string_list]; // api v2
    PRINT @@int_fails, @@str_fails;
}
// RUN QUERY list_accum_update_ex2(["person1","person5"])
GSQL > RUN QUERY list_accum_update_ex2(["person1","person5"])
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"S1": [
      {
        "v_id": "person1",
        "attributes": {
          "S1.@int_list": [
            1,
            2,
            -99
          ],
          "S1.skill_list": [
            1,
            2,
            3
          ],
          "S1.interest_list": [
            "management",
            "financial"
          ],
          "S1.@string_list": [
            "management",
            "fizz"
          ]
        },
        "v_type": "Person"
      },
      {
        "v_id": "person5",
        "attributes": {
          "S1.@int_list": [
            8,
            2,
            -99
          ],
          "S1.skill_list": [
            8,
            2,
            5
          ],
          "S1.interest_list": [
            "sport",
            "financial",
            "engineering"
          ],
          "S1.@string_list": [
            "sport",
            "financial",
            "fizz"
          ]
        },
        "v_type": "Person"
      }
    ]},
    {
      "@@int_fails": [],
      "@@str_fails": []
    }
  ]
}

SetAccum

The SetAccum type maintains a collection of unique elements.The output of a SetAccum is a list of elements in arbitrary order. A SetAccum instance can contain values of one type. The element type can be any base type, tuple, or STRING COMPRESS.

For SetAccum, the += arg operation adds a non-duplicate element or set of elements to the set. If an element is already represented in the set, then the SetAccum state does not change.

SetAccum also can be used with the three canonical set operators: UNION, INTERSECT, and MINUS (see the Set/Bag Expression and Operators section for more details).

SetAccum also supports the following class functions.

Functions that modify the SetAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function (T is the element type) Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the number of elements in the set.

contains( T value )

BOOL

Accessor

Returns true if the set contains value. Returns false if the set doesn’t contain value.

remove( T value )

VOID

Mutator

Removes value from the set.

clear()

VOID

Mutator

Clears the set so it becomes empty with size 0.

Example

  • Query

  • Results

SetAccum Example
# SetAccum Example
CREATE QUERY setAccumEx() FOR GRAPH Minimal_Net {

  SetAccum<INT> @@intSetAccum;
  SetAccum<STRING> @@stringSetAccum;

  @@intSetAccum += 5;
  @@intSetAccum.clear();

  @@intSetAccum += 4;
  @@intSetAccum += 11;
  @@intSetAccum += 1;
  @@intSetAccum += 11; # Sets do not store duplicates

  @@intSetAccum += (1,2,3,4); # Can create simple sets this way
  PRINT @@intSetAccum;
  @@intSetAccum.remove(2);
  PRINT @@intSetAccum AS RemovedVal2; # Demostrate remove.

  PRINT @@intSetAccum.contains(3);

  @@stringSetAccum += "Hello";
  @@stringSetAccum += "Hello";
  @@stringSetAccum += "There";
  @@stringSetAccum += "World";
  PRINT @@stringSetAccum;

  PRINT @@stringSetAccum.contains("Hello");
  PRINT @@stringSetAccum.size();
}
setAccumEx.json Result
GSQL > RUN QUERY set_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "edition": "developer",
    "schema": 0,
    "api": "v2"
  },
  "results": [ {"@@intSetAccum": [ 3, 2, 1, 11, 4 ]},
    {"@@intSetAccum.contains(3)": true},
    {"@@stringSetAccum": [ "World", "There", "Hello" ]},
    {"@@stringSetAccum.contains(Hello)": true},
    {"@@stringSetAccum.size()": 3}
  ]
}

BagAccum

The BagAccum type maintains a collection of elements with duplicated elements allowed. The output of a BagAccum is a list of elements in arbitrary order. A BagAccum instance can contain values of one type. The element type can be any base type, tuple, or STRING COMPRESS.

For BagAccum, the += arg operation adds an element or bag of elements to the bag.

BagAccum also supports the + operator:

  • @bag1 + @bag2 creates a new BagAccum, which contains the elements of @bag1 and the elements of @bag2. The two BagAccums must have identical data types.

BagAccum also supports the following class functions.

Functions which modify the BagAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function (T is the element type) Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the number of elements in the bag.

contains( T value )

BOOL

Accessor

Returns true/false if the bag does/doesn’t contain value .

clear()

VOID

Mutator

Clears the bag so it becomes empty with size 0.

remove( T value )

VOID

Mutator

Removes one instance of value from the bag.

removeAll( T value )

VOID

Mutator

Removes all instances of the given value from the bag.

Example

  • Query

  • Results

BagAccum Example
CREATE QUERY bag_accum_ex() FOR GRAPH Minimal_Net {

    //Unordered collection
    BagAccum<INT>        @@int_bag_accum;
    BagAccum<STRING> @@string_bag_accum;

    @@int_bag_accum += 5;
    @@int_bag_accum.clear();

    @@int_bag_accum += 4;
    @@int_bag_accum += 11;
    @@int_bag_accum += 1;
    @@int_bag_accum += 11;         //Bag accums can store duplicates
    @@int_bag_accum += (1,2,3,4);
    PRINT @@int_bag_accum;

    PRINT @@int_bag_accum.size();
    PRINT @@int_bag_accum.contains(4);

    @@string_bag_accum += "Hello";
    @@string_bag_accum += "Hello";
    @@string_bag_accum += "There";
    @@string_bag_accum += "World";
    PRINT @@string_bag_accum.contains("Hello");
    @@string_bag_accum.remove("Hello");        //Remove one matching element
    @@string_bag_accum.removeAll("There"); //Remove all matching elements
    PRINT @@string_bag_accum;
}
GSQL > RUN QUERY bag_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@int_bag_accum": [
      2,
      3,
      1,
      1,
      11,
      11,
      4,
      4
    ]},
    {"@@int_bag_accum.size()": 8},
    {"@@int_bag_accum.contains(4)": true},
    {"@@string_bag_accum.contains(\"Hello\")": true},
    {"@@string_bag_accum": [
      "World",
      "Hello"
    ]}
  ]
}

MapAccum

The MapAccum type maintains a collection of (key → value) pairs. The output of a MapAccum is a set of key and value pairs in which the keys are unique.

The key type of a MapAccum can be all base types or tuples. If the key type is VERTEX, then only the vertex’s id is stored and displayed.

The value type of a MapAccum can be all base types, tuples, or any type of accumulator, except for HeapAccum.

For MapAccum, the += (key→val) operation adds a key-value element to the collection if key is not yet used in the MapAccum. If the MapAccum already contains key , then val is accumulated to the current value, where the accumulation operation depends on the data type of val. (Strings would get concatenated, lists would be appended, numerical values would be added, etc.)

MapAccum also supports the + operator:

  • @map1 + @map2 creates a new MapAccum, which contains the key-value pairs of @map2 added to the key-value pairs of @map1. The two MapAccums must have identical data types.

MapAccum also supports the following class functions.

Functions that modify the MapAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function (KEY is the key type) Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the number of elements in the map.

containsKey( KEY key )

BOOL

Accessor

Returns true if the map does contain key and false if it doesn’t.

get( KEY key )

value type

Accessor

Returns the value which the map associates with key. If the map doesn’t contain key, then the return value is undefined.

clear()

VOID

Mutator

Clears the map so it becomes empty with size 0.

.remove( KEY key )

VOID

Mutator

Removes the key-value pair with the specified key. If there is no matching key, then the function will do nothing.

Example

  • Query

  • Results

MapAccum Example
CREATE QUERY map_accum_ex() FOR GRAPH Minimal_Net {

    // Map(Key, Value)
    // Keys can be INT or STRING only
    MapAccum<STRING, INT> @@int_map_accum;
    MapAccum<INT, STRING> @@string_map_accum;
    MapAccum<INT, MapAccum<STRING, STRING>> @@nested_map_accum;

    @@int_map_accum += ("foo" -> 1);
    @@int_map_accum.clear();

    @@int_map_accum += ("foo" -> 3);
    @@int_map_accum += ("bar" -> 2);
    @@int_map_accum += ("baz" -> 2);
    @@int_map_accum += ("baz" -> 1); //add 1 to existing value

    PRINT @@int_map_accum.containsKey("baz");
    PRINT @@int_map_accum.get("bar");
    PRINT @@int_map_accum.get("root");

    @@string_map_accum += (1 -> "apple");
    @@string_map_accum += (2 -> "pear");
    @@string_map_accum += (3 -> "banana");
    @@string_map_accum += (4 -> "a");
    @@string_map_accum += (4 -> "b"); //append "b" to existing value
    @@string_map_accum += (4 -> "c"); //append "c" to existing value

    PRINT @@int_map_accum;
    PRINT @@string_map_accum;

    //Checking and getting keys
    if @@string_map_accum.containsKey(1) THEN
        PRINT @@string_map_accum.get(1);
    END;

    //Map nesting
    @@nested_map_accum += ( 1 -> ("foo"  -> "bar") );
    @@nested_map_accum += ( 1 -> ("flip" -> "top") );
    @@nested_map_accum += ( 2 -> ("fizz" -> "pop") );
    @@nested_map_accum += ( 1 -> ("foo"  -> "s") );

    PRINT @@nested_map_accum;

    IF @@nested_map_accum.containsKey(1) THEN
        IF @@nested_map_accum.get(1).containsKey("foo") THEN
             PRINT @@nested_map_accum.get(1).get("foo");
        END;
    END;
}
GSQL > RUN QUERY map_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@int_map_accum.containsKey(\"baz\")": true},
    {"@@int_map_accum.get(\"bar\")": 2},
    {"@@int_map_accum.get(\"root\")": 0},
    {"@@int_map_accum": {
      "bar": 2,
      "foo": 3,
      "baz": 3
    }},
    {"@@string_map_accum": {
      "1": "apple",
      "2": "pear",
      "3": "banana",
      "4": "abc"
    }},
    {"@@string_map_accum.get(1)": "apple"},
    {"@@nested_map_accum": {
      "1": {
        "foo": "bars",
        "flip": "top"
      },
      "2": {"fizz": "pop"}
    }},
    {"@@nested_map_accum.get(1).get(\"foo\")": "bars"}
  ]
}

ArrayAccum

The ArrayAccum type maintains an array of accumulators. An array is a fixed-length sequence of elements, with direct access to elements by position. The ArrayAccum has these particular characteristics:

  • The elements are accumulators, not primitive or base data types. All accumulators, except HeapAccum, MapAccum, and GroupByAccum, can be used.

  • An ArrayAccum instance can be multidimensional. There is no limit to the number of dimensions.

  • The size can be set at run-time (dynamically).

  • There are operators which update the entire array efficiently.

When an ArrayAccum is declared, the instance name should be followed by a pair of brackets for each dimension. The brackets may either contain an integer constant to set the size of the array, or they may be empty. In that case, the size must be set with the reallocate function before the ArrayAccum can be used.

ArrayAccum declaration example
ArrayAccum<SetAccum<STRING>> @@names[10];
ArrayAccum<SetAccum<INT>> @@ids[][];  // 2-dimensional, size to be determined

Because each element of an ArrayAccum itself is an accumulator, the operators =, +=, and + can be used in two contexts: accumulator-level and element-level.

Element-level operations

If @A is an ArrayAccum of length 6, then @A[0] and @A[5] refer to its first and last elements, respectively. Referring to an ArrayAccum element is like referring to an accumulator of that type. For example, given the following definitions:

ArrayAccum<SumAccum<INT>> @@Sums[3];
ArrayAccum<ListAccum<STRING>> @@Lists[2];

then @@Sums[0], @@Sums[1], and @@Sums[2] each refer to an individual SumAccum<INT>, and @@Lists[0] and @@Lists[1] each refer to a ListAccum<STRING>, supporting all the operations for those accumulator and data types.

@@Sums[1] = 1;
@@Sums[1] += 2;  // value is now 3
@@Lists[0] = "cat";
@@Lists[0] += "egory";  // value is now "category"

Accumulator-level operations

The operators =, +=, and + have special meanings when applied to an ArrayAccum as a whole. There operations efficiently update an entire ArrayAccum. All ArrayAccums must have the same element type.

Operator Description Example

=

Sets the ArrayAccum on the left equal to the ArrayAccum on the right. The two ArrayAccums must have the same element type, but the left-side ArrayAccum will change its size and dimensions to match the one on the right side.

@A = @B;

+

Performs element-by-element addition of two ArrayAccums of the same type and size. The result is a new ArrayAccum of the same size.

@C = @A + @B; // @A and @B must be the same size

+=

Performs element-by-element accumulation (+=) from the right-side ArrayAccum to the left-side ArrayAccum. They must be the same type and size.

@A += @B; // @A and @B must be the same size

ArrayAccum also supports the following class functions.

Functions that modify the ArrayAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the total number of elements in the (multidimensional) array. For example, the size of an ArrayAccum declared as @A[3][4] is 12.

reallocate( INT, …​ )

VOID

Mutator

Discards the previous ArrayAccum instance and creates a new ArrayAccum, with the size(s) given. An N-dimensional ArrayAccum requires N integer parameters. The reallocate function cannot be used to change the number of dimensions.

Example

  • Query

  • Results

Example of ArrayAccum Element-level Operations
CREATE QUERY array_accum_elem() FOR GRAPH Minimal_Net {

	ArrayAccum<SumAccum<DOUBLE>> @@aa_sumD[2][2];  // 2D Sum Double
	ArrayAccum<SumAccum<STRING>> @@aa_sumS[2][2];  // 2D Sum String
	ArrayAccum<MaxAccum<INT>> @@aa_max[2];
	ArrayAccum<MinAccum<UINT>> @@aa_min[2];
	ArrayAccum<AvgAccum> @@aa_avg[2];
	ArrayAccum<AndAccum<BOOL>> @@aa_and[2];
	ArrayAccum<OrAccum<BOOL>> @@aa_or[2];
	ArrayAccum<BitwiseAndAccum> @@aa_bit_and[2];
	ArrayAccum<BitwiseOrAccum> @@aa_bit_or[2];
	ArrayAccum<ListAccum<INT>> @@aa_list[2][2];    // 2D List
	ArrayAccum<SetAccum<FLOAT>> @@aa_setF[2];
	ArrayAccum<BagAccum<DATETIME>> @@aa_bagT[2];

	// for test data
	ListAccum<STRING> @@words;
	BOOL toggle = false;
	@@words += "1st"; @@words += "2nd"; @@words += "3rd"; @@words += "4th";

	// Int:  a[0] += 1, 2;   a[1] += 3, 4
	// Bool: alternate true/false
	// Float: a[0] += 1.111, 2.222;  a[1] += 3.333, 4.444
	// 2D Double: a[0][0] += 1.111, 2.222;   a[0][1] += 5.555, 6.666;
	//          a[1][0] += 3.333, 4.444;   a[0][1] += 7.777, 8.888;

	FOREACH i IN RANGE [0,1] DO
		FOREACH n IN RANGE [1, 2] DO
			toggle = NOT toggle;
			@@aa_max[i] += i*2 + n;
			@@aa_min[i] += i*2 + n;
			@@aa_avg[i] += i*2 + n;
			@@aa_and[i] += toggle;
			@@aa_or[i] += toggle;
			@@aa_bit_and[i] += i*2 + n;
			@@aa_bit_or[i] += i*2 + n;
			@@aa_setF[i] += (i*2 + n)/0.9;
			@@aa_bagT[i] += epoch_to_datetime(i*2 + n);

			FOREACH j IN RANGE [0,1] DO
				@@aa_sumD[i][j] += (j*4 + i*2 + n)/0.9;
				@@aa_sumS[i][j] += @@words.get((j*2 + i + n)%4);
				@@aa_list[i][j] += j*4 +i*2 + n ;
			END;
		END;
	END;

	PRINT @@aa_sumD;		PRINT @@aa_sumS;
	PRINT @@aa_max;		PRINT @@aa_min;		PRINT @@aa_avg;
	PRINT @@aa_and;		PRINT @@aa_or;
	PRINT @@aa_bit_and;	PRINT @@aa_bit_or;
	PRINT @@aa_list;		PRINT @@aa_setF;		PRINT @@aa_bagT;
}
GSQL > RUN QUERY array_accum_elem()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@aa_sumD": [
      [
        3.33333,
        12.22222
      ],
      [
        7.77778,
        16.66667
      ]
    ]},
    {"@@aa_sumS": [
      [
        "2nd3rd",
        "4th1st"
      ],
      [
        "3rd4th",
        "1st2nd"
      ]
    ]},
    {"@@aa_max": [
      2,
      4
    ]},
    {"@@aa_min": [
      1,
      3
    ]},
    {"@@aa_avg": [
      1.5,
      3.5
    ]},
    {"@@aa_and": [
      false,
      false
    ]},
    {"@@aa_or": [
      true,
      true
    ]},
    {"@@aa_bit_and": [
      "0000000000000000000000000000000000000000000000000000000000000000",
      "0000000000000000000000000000000000000000000000000000000000000000"
    ]},
    {"@@aa_bit_or": [
      "0000000000000000000000000000000000000000000000000000000000000011",
      "0000000000000000000000000000000000000000000000000000000000000111"
    ]},
    {"@@aa_list": [
      [
        [
          1,
          2
        ],
        [
          5,
          6
        ]
      ],
      [
        [
          3,
          4
        ],
        [
          7,
          8
        ]
      ]
    ]},
    {"@@aa_setF": [
      [
        2.22222,
        1.11111
      ],
      [
        4.44444,
        3.33333
      ]
    ]},
    {"@@aa_bagT": [
      [
        2,
        1
      ],
      [
        4,
        3
      ]
    ]}
  ]
}

  • Query

  • Results

CREATE QUERY array_accum_op3(INT lenA) FOR GRAPH Minimal_Net {

	ArrayAccum<SumAccum<INT>> @@arrayA[5]; // Original size
	ArrayAccum<SumAccum<INT>> @@arrayB[2];
	ArrayAccum<SumAccum<INT>> @@arrayC[][]; // No size
	STRING msg;
	@@arrayA.reallocate(lenA);  // Set/Change size dynamically
	@@arrayB.reallocate(lenA+1);
	@@arrayC.reallocate(lenA, lenA+1);

	// Initialize arrays
	FOREACH i IN RANGE[0,lenA-1] DO
		@@arrayA[i] += i*i;
		FOREACH j IN RANGE[0,lenA] DO
			@@arrayC[i][j] += j*10 + i;
		END;
	END;
	FOREACH i IN RANGE[0,lenA] DO
		@@arrayB[i] += 100-i;
	END;
	msg = "Initial Values";
	PRINT msg, @@arrayA, @@arrayB, @@arrayC;

    msg = "Test 1: A = C, C = B";	// = operator
    @@arrayA = @@arrayC;		// change dimensions: 1D <- 2D
    @@arrayC = @@arrayB;		// change dimensions: 2D <- 1D
    PRINT msg, @@arrayA, @@arrayC;

    msg = "Test 2: B += C"; 		// += operator
    @@arrayB += @@arrayC; 		// B and C must have same size & dim
    PRINT msg, @@arrayB, @@arrayC;

    msg = "Test 3: A = B + C"; 		// + operator
    @@arrayA = @@arrayB + @@arrayC; // B & C must have same size & dim
    PRINT msg, @@arrayA; 			// A changes size & dim
}
RUN QUERY ArrayAccumOp3(3)
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {
      "msg": "Initial Values",
      "@@arrayC": [
        [
          0,
          10,
          20,
          30
        ],
        [
          1,
          11,
          21,
          31
        ],
        [
          2,
          12,
          22,
          32
        ]
      ],
      "@@arrayB": [
        100,
        99,
        98,
        97
      ],
      "@@arrayA": [
        0,
        1,
        4
      ]
    },
    {
      "msg": "Test 1: A = C, C = B",
      "@@arrayC": [
        100,
        99,
        98,
        97
      ],
      "@@arrayA": [
        [
          0,
          10,
          20,
          30
        ],
        [
          1,
          11,
          21,
          31
        ],
        [
          2,
          12,
          22,
          32
        ]
      ]
    },
    {
      "msg": "Test 2: B += C",
      "@@arrayC": [
        100,
        99,
        98,
        97
      ],
      "@@arrayB": [
        200,
        198,
        196,
        194
      ]
    },
    {
      "msg": "Test 3: A = B + C",
      "@@arrayA": [
        300,
        297,
        294,
        291
      ]
    }
  ]
}

  • Query

  • Results

CREATE QUERY array_accum_local() FOR GRAPH Social_Net API("v2") {
	// Count each person's edges by type
	// friend/liked/posted edges are type 0/1/2, respectively
	ArrayAccum<SumAccum<INT>> @edges_by_type[3];
	persons = {Person.*};

	persons = SELECT s
		FROM persons:s -(:e)- :t
		ACCUM CASE e.type
			WHEN "Friend" THEN s.@edges_by_type[0] += 1
			WHEN "Liked"  THEN s.@edges_by_type[1] += 1
			WHEN "Posted" THEN s.@edges_by_type[2] += 1
			END
		ORDER BY s.id;

	//PRINT persons.@edges_by_type; // api v1
    PRINT persons[persons.@edges_by_type]; // api v2
}
GSQL > RUN QUERY array_accum_local()
{
  "error": false,
  "message": "",
  "version": {
    "edition": "developer",
    "schema": 0,
    "api": "v2"
  },
  "results": [{"Persons": [
    {
      "v_id": "person1",
      "attributes": {"Persons.@edgesByType": [ 2, 1, 1 ]},
      "v_type": "person"
    },
    {
      "v_id": "person2",
      "attributes": {"Persons.@edgesByType": [ 2, 2, 1 ]},
      "v_type": "person"
    },
    {
      "v_id": "person3",
      "attributes": {"Persons.@edgesByType": [ 2, 1, 1 ]},
      "v_type": "person"
    },
    {
      "v_id": "person4",
      "attributes": {"Persons.@edgesByType": [ 3, 1, 1 ]},
      "v_type": "person"
    },
    {
      "v_id": "person5",
      "attributes": {"Persons.@edgesByType": [ 2, 1, 2 ]},
      "v_type": "person"
    },
    {
      "v_id": "person6",
      "attributes": {"Persons.@edgesByType": [ 2, 1, 2 ]},
      "v_type": "person"
    },
    {
      "v_id": "person7",
      "attributes": {"Persons.@edgesByType": [ 2, 1, 2 ]},
      "v_type": "person"
    },
    {
      "v_id": "person8",
      "attributes": {"Persons.@edgesByType": [ 3, 1, 2 ]},
      "v_type": "person"
    }
  ]}]
}

HeapAccum

The HeapAccum type maintains a sorted collection of tuples and enforces a maximum number of tuples in the collection. The output of a HeapAccum is a sorted collection of tuple elements. The =` operation adds a tuple to the collection in sorted order. If the HeapAccum is already at maximum capacity when the `= operator is applied, then the tuple which is last in the sorted order is dropped from the HeapAccum. Sorting of tuples is performed on one or more defined tuple fields ordered either ascending or descending. Sorting precedence is performed based on defined tuple fields from left to right.

You must have defined a custom tuple type to declare a HeapAccum, and one of the fields in the tuple must be a data type that can be sorted.

The declaration syntax is outlined in the figure below:

HeapAccum declaration syntax
HeapAccum<tupleType>( [capacity,] field_a [ASC|DESC],... , field_z [ASC|DESC]);

In the declaration of the HeapAccum, the keyword HeapAccum is followed by the tuple type in angle brackets < >. This is followed by a parenthesized list of two or more parameters.

  • If the first parameter is a positive integer, it sets the maximum number of tuples that the HeapAccum may store.

  • The subsequent parameters are a subset of the tuple’s field, which are used as sort keys. The sort key hierarchy is from left to right, with the leftmost key being the primary sort key. The keywords ASC and DESC indicate Ascending (lowest value first) or Descending (highest value first) sort order. Ascending order is the default.

Functions

HeapAccum also supports the following class functions.

Functions that modify the HeapAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the number of elements in the heap.

top()

tupleType

Accessor

Returns the top tuple. If this heap is empty, returns a tuple with each element equal to the default value.

pop()

tupleType

Mutator

Returns the top tuple and removes it from the heap. If this heap is empty, returns a tuple with each element equal to the default value.

resize( INT newSize)

VOID

Mutator

Changes the maximum capacity of the heap.

clear()

VOID

Mutator

Clears the heap so it becomes empty with size 0.

Example

  • Query

  • Results

CREATE QUERY heap_accum_ex() FOR GRAPH Minimal_Net {
    TYPEDEF tuple<STRING first_name, STRING last_name, INT score> Test_Results;

    //Heap with max size of 4 sorted descending by score then ascending last name
    HeapAccum<Test_Results>(4, score DESC, last_name ASC) @@top_test_results;

    PRINT @@top_test_results.top();

    @@top_test_results += Test_Results("Bruce", "Wayne", 80);
    @@top_test_results += Test_Results("Peter", "Parker", 80);
    @@top_test_results += Test_Results("Tony", "Stark", 100);
    @@top_test_results += Test_Results("Bruce", "Banner", 95);
    @@top_test_results += Test_Results("Jean", "Summers", 95);
    @@top_test_results += Test_Results("Clark", "Kent", 80);

    //Show element with the highest sorted position
    PRINT @@top_test_results.top();
    PRINT @@top_test_results.top().first_name, @@top_test_results.top().last_name, @@top_test_results.top().score;

    PRINT @@top_test_results;

    //Increase the size of the heap to add more elements
    @@top_test_results.resize(5);

    //Find the size of the current heap
    PRINT @@top_test_results.size();

    @@top_test_results += Test_Results("Bruce", "Wayne", 80);
    @@top_test_results += Test_Results("Peter", "Parker", 80);

    PRINT @@top_test_results;

    //Resizing smaller WILL REMOVE excess elements from the HeapAccum
    @@top_test_results.resize(3);
    PRINT @@top_test_results;

    //Increasing capacity will not restore dropped elements
    @@top_test_results.resize(5);
    PRINT @@top_test_results;

    //Removes all elements from the Heap_accum
    @@top_test_results.clear();
    PRINT @@top_test_results.size();
}
GSQL > RUN QUERY heap_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@top_test_results.top()": {
      "score": 0,
      "last_name": "",
      "first_name": ""
    }},
    {"@@top_test_results.top()": {
      "score": 100,
      "last_name": "Stark",
      "first_name": "Tony"
    }},
    {
      "@@top_test_results.top().first_name": "Tony",
      "@@top_test_results.top().last_name": "Stark",
      "@@top_test_results.top().score": 100
    },
    {"@@top_test_results": [
      {
        "score": 100,
        "last_name": "Stark",
        "first_name": "Tony"
      },
      {
        "score": 95,
        "last_name": "Banner",
        "first_name": "Bruce"
      },
      {
        "score": 95,
        "last_name": "Summers",
        "first_name": "Jean"
      },
      {
        "score": 80,
        "last_name": "Kent",
        "first_name": "Clark"
      }
    ]},
    {"@@top_test_results.size()": 4},
    {"@@top_test_results": [
      {
        "score": 100,
        "last_name": "Stark",
        "first_name": "Tony"
      },
      {
        "score": 95,
        "last_name": "Banner",
        "first_name": "Bruce"
      },
      {
        "score": 95,
        "last_name": "Summers",
        "first_name": "Jean"
      },
      {
        "score": 80,
        "last_name": "Kent",
        "first_name": "Clark"
      },
      {
        "score": 80,
        "last_name": "Parker",
        "first_name": "Peter"
      }
    ]},
    {"@@top_test_results": [
      {
        "score": 100,
        "last_name": "Stark",
        "first_name": "Tony"
      },
      {
        "score": 95,
        "last_name": "Banner",
        "first_name": "Bruce"
      },
      {
        "score": 95,
        "last_name": "Summers",
        "first_name": "Jean"
      }
    ]},
    {"@@top_test_results": [
      {
        "score": 100,
        "last_name": "Stark",
        "first_name": "Tony"
      },
      {
        "score": 95,
        "last_name": "Banner",
        "first_name": "Bruce"
      },
      {
        "score": 95,
        "last_name": "Summers",
        "first_name": "Jean"
      }
    ]},
    {"@@top_test_results.size()": 0}
  ]
}

GroupByAccum

The GroupByAccum is a compound accumulator, an accumulator of accumulators. At the top level, it is a MapAccum where both the key and the value can have multiple fields, each of them an accumulator type.

GroupByAccum syntax
GroupByAccum<type [, type]* , accumType [, accumType]* >

In the EBNF above, the type terms form the key set, and the accumType terms form the map’s value. Since they are accumulators, they perform a grouping. Like a MapAccum, if we try to store a (key→value) whose key has already been used, then the new value will accumulate to the data which is already stored. In this case, each field of the multiple-field value has its own accumulation function. One way to think about GroupByAccum is that each unique key is a group ID.

In GroupByAccum, the key types can be base type, tuple, or STRING COMPRESS. The accumulators are used for aggregating group values. Each accumulator type can be any type including HeapAccum. Each base type and each accumulator type must be followed an alias. Below is an example declaration.

TYPEDEF TUPLE <id INT, name STRING, age INT> My_Tuple;
TYPEDEF HeapAccum <My_Tuple> (2, name desc, age desc, id asc) My_Heap;
GroupByAccum<INT a, STRING b,
             MaxAccum<INT> maxa,
             ListAccum<ListAccum<INT>> lists,
             My_Heap h> @@group;

To add new data to this GroupByAccum, the data should be formatted as (key1, key2 → value1, value2) .

GroupByAccum also supports the following class functions.

Functions that modify the GroupByAccum (mutator functions) can be used only under the following conditions:

  • Mutator functions of global accumulators may only be used at the query-body level.

  • Mutator functions of vertex-attached accumulators may only be used in a POST-ACCUM clause.
Function (KEY1..KEYn are the key types) Return type Accessor / Mutator Description

size()

INT

Accessor

Returns the number of elements in the heap.

get( KEY1 key_value1 , KEY2 key_value2 …​ )

element type(s) of the accumulator(s)

Accessor

Returns the values from each accumulator in the group associating with the given key(s). If the key(s) doesn’t exist, return the default value(s) of the accumulator type(s).

containsKey( KEY1 key_value1 , KEY2 key_value2…​ )

BOOL

Accessor

Returns true/false if the accumulator contains the key(s)

clear()

VOID

Mutator

Clears the heap so it becomes empty with size 0.

remove ( KEY1 key_value1 , KEY2 key_value2 …​ )

VOID

Mutator

Removes the group associating with the key(s)

Example

  • Query

  • Results

GroupByAccum Example
CREATE QUERY group_by_accum_ex () FOR GRAPH Social_Net {
    // declare HeapAccum type and tuple used in the HeapAccum
    TYPEDEF TUPLE <id INT, name STRING, age INT> My_Tuple;
    TYPEDEF HeapAccum <My_Tuple> (2, name DESC, age DESC, id asc) My_Heap;
    // declaration, first two primitive type are group by keys; the rest accumulator type are aggregates
    GroupByAccum<INT a, STRING b, MaxAccum<INT> maxa, ListAccum<ListAccum<INT>> lists> @@group;
    GroupByAccum<STRING gender, MapAccum<VERTEX<Person>, DATETIME> m> @@group2;
    GroupByAccum<INT age, My_Heap h> @@group4;
    // nested GroupByAccum
    GroupByAccum<INT a, MaxAccum<INT> maxa, GroupByAccum<INT a, MaxAccum<INT> maxa> heap> @@group3;
    Start = { Person.* };

    // usage of global GroupByAccum
    @@group += (1, "a" -> 1, [1]);
    @@group += (1, "a" -> 2, [2]);
    @@group += (2, "b" -> 1, [4]);

    @@group3 += (2 -> 1, (2 -> 0) );
    @@group3 += (2 -> 1, (2 -> 5) );
    @@group3 += (2 -> 5, (3 -> 3) );
    PRINT @@group, @@group.get(1, "a"), @@group.get(1, "a").lists,  @@group.containsKey(1, "c"), @@group3;

    // HeapAccum inside GroupByAccum
    @@group4 += (29->My_Tuple(1,"aaa", 18));
    @@group4 += (29->My_Tuple(2,"bbb", 19));
    @@group4 += (29->My_Tuple(3,"ccc", 20));
    PRINT @@group4;

    // two kinds of foreach
    FOREACH g IN @@group DO
        PRINT g.a, g.b, g.maxa, g.lists;
    END;
    FOREACH (g1,g2,g3,g4) IN @@group DO
        PRINT g1,g2,g3,g4;
    END;

    S = SELECT v
      FROM Start:v - (Liked:e) - Post:t
      ACCUM @@group2 += (v.gender -> (v -> e.action_time));

    PRINT @@group2, @@group2.get("Male").m, @@group2.get("Female").m;
}
GSQL > RUN QUERY group_by_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "edition": "developer",
    "schema": 0,
    "api": "v2"
  },
  "results": [
    {
      "@@group.get(1,a).lists": [
        [1],
        [2]
      ],
      "@@group3": [{
        "a": 2,
        "heap": [
          {
            "a": 3,
            "maxa": 3
          },
          {
            "a": 2,
            "maxa": 5
          }
        ],
        "maxa": 5
      }],
      "@@group.containsKey(1,c)": false,
      "@@group.get(1,a)": {
        "lists": [
          [1],
          [2]
        ],
        "maxa": 2
      },
      "@@group": [
        {
          "a": 2,
          "b": "b",
          "lists": [[4]],
          "maxa": 1
        },
        {
          "a": 1,
          "b": "a",
          "lists": [
            [1],
            [2]
          ],
          "maxa": 2
        }
      ]
    },
    {
      "g.b": "b",
      "g.maxa": 1,
      "g.lists": [[4]],
      "g.a": 2
    },
    {
      "g.b": "a",
      "g.maxa": 2,
      "g.lists": [
        [1],
        [2]
      ],
      "g.a": 1
    },
    {
      "g1": 2,
      "g2": "b",
      "g3": 1,
      "g4": [[4]]
    },
    {
      "g1": 1,
      "g2": "a",
      "g3": 2,
      "g4": [
        [1],
        [2]
      ]
    },
    {
      "@@group2.get(Male).m": {
        "person3": 1263618953,
        "person1": 1263209520,
        "person8": 1263180365,
        "person7": 1263295325,
        "person6": 1263468185
      },
      "@@group2": [
        {
          "gender": "Male",
          "m": {
            "person3": 1263618953,
            "person1": 1263209520,
            "person8": 1263180365,
            "person7": 1263295325,
            "person6": 1263468185
          }
        },
        {
          "gender": "Female",
          "m": {
            "person4": 1263352565,
            "person2": 2526519281,
            "person5": 1263330725
          }
        }
      ],
      "@@group2.get(Female).m": {
        "person4": 1263352565,
        "person2": 2526519281,
        "person5": 1263330725
      }
    }
  ]
}

Nested Accumulators

Certain collection accumulators may be nested. That is, an accumulator may contain a collection of elements where the elements themselves are accumulators. For example:

ListAccum<ListAccum<INT>> @@matrix; // a 2-dimensional jagged array of integers.  Each inner list has its own unique size.

Only ListAccum, ArrayAccum, MapAccum, and GroupByAccum can contain other accumulators. However, not all combinations of collection accumulators are allowed. The following constraints apply:

  1. ListAccum: ListAccum is the only accumulator type that can be nested within ListAccum, up to a depth of 3:

    ListAccum<ListAccum<INT>>
ListAccum<ListAccum<ListAccum<INT>>>
ListAccum<SetAccum<INT>> // illegal

  2. MapAccum: All accumulator types, except for HeapAccum, can be nested within MapAccum as the value type. For example,

    MapAccum<STRING, ListAccum<INT>>
MapAccum<INT, MapAccum<INT, STRING>>
MapAccum<VERTEX, SumAccum<INT>>
MapAccum<STRING, SetAccum<VERTEX>>
MapAccum<STRING, GroupByAccum<VERTEX a, MaxAccum<INT> maxs>>
MapAccum<SetAccum<INT>, INT> # illegal

  3. GroupByAccum: All accumulator types, except for HeapAccum, can be nested within GroupByAccum as the accumulator type. For example:

    GroupByAccum<INT a, STRING b, MaxAccum<INT> maxs, ListAccum<ListAccum<INT>> lists>

  4. ArrayAccum: Unlike the other accumulators in this list, where nesting is optional, nesting is mandatory for ArrayAccum. See the ArrayAccum section.

It is legal to define nested ListAccums to form a multidimensional array. Note the declaration statements and the nested [ bracket ] notation in the example below:

  • Query

  • Results

CREATE QUERY nested_accum_ex() FOR GRAPH Minimal_Net {
    ListAccum<ListAccum<INT>> @@_2d_list;
    ListAccum<ListAccum<ListAccum<INT>>> @@_3d_list;
    ListAccum<INT> @@_1d_list;
    SumAccum <INT> @@sum = 4;

    @@_1d_list += 1;
    @@_1d_list += 2;
    // add 1D-list to 2D-list as element
    @@_2d_list += @@_1d_list;

    // add 1D-enum-list to 2D-list as element
    @@_2d_list += [@@sum, 5, 6];
    // combine 2D-enum-list and 2d-list
    @@_2d_list += [[7, 8, 9], [10, 11], [12]];

    // add an empty 1D-list
    @@_1d_list.clear();
    @@_2d_list += @@_1d_list;

    // combine two 2D-list
    @@_2d_list += @@_2d_list;

    PRINT @@_2d_list;

    // test 3D-list
    @@_3d_list += @@_2d_list;
    @@_3d_list += [[7, 8, 9], [10, 11], [12]];
    PRINT @@_3d_list;
}
GSQL > RUN QUERY nested_accum_ex()
{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [
    {"@@_2d_list": [
      [
        1,
        2
      ],
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