Boolean Expression Rules
Overview
A predicate expression outputs a boolean value. Milvus conducts scalar filtering by searching with predicates. A predicate expression, when evaluated, returns either TRUE or FALSE. View Python SDK API Reference for instruction on using predicate expressions.
EBNF grammar rules describe boolean expressions rules:
Expr = LogicalExpr  NIL
LogicalExpr = LogicalExpr BinaryLogicalOp LogicalExpr
 UnaryLogicalOp LogicalExpr
 "(" LogicalExpr ")"
 SingleExpr;
BinaryLogicalOp = "&&"  "and"  ""  "or";
UnaryLogicalOp = "not";
SingleExpr = TermExpr  CompareExpr;
TermExpr = IDENTIFIER "in" ConstantArray;
Constant = INTEGER  FLOAT
ConstantExpr = Constant
 ConstantExpr BinaryArithOp ConstantExpr
 UnaryArithOp ConstantExpr;
ConstantArray = "[" ConstantExpr { "," ConstantExpr } "]";
UnaryArithOp = "+"  ""
BinaryArithOp = "+"  ""  "*"  "/"  "%"  "**";
CompareExpr = IDENTIFIER CmpOp IDENTIFIER
 IDENTIFIER CmpOp ConstantExpr
 ConstantExpr CmpOp IDENTIFIER
 ConstantExpr CmpOpRestricted IDENTIFIER CmpOpRestricted ConstantExpr;
CmpOpRestricted = "<"  "<=";
CmpOp = ">"  ">="  "<"  "<="  "==" "!=";
MatchOp = "like"  "LIKE";
JsonArrayOps = JsonDefs "(" IDENTIFIER "," JsonExpr  JsonArray ")";
JsonArrayDefs = "json_contains"  "JSON_CONTAINS"
 "json_contains_all"  "JSON_CONTAINS_ALL"
 "json_contains_any"  "JSON_CONTAINS_ANY";
JsonExpr = Constant  ConstantArray  STRING  BOOLEAN;
JsonArray = "[" JsonExpr { "," JsonExpr } "]";
The following table lists the description of each symbol mentioned in the above Boolean expression rules.
Notation  Description 

=  Definition. 
,  Concatenation. 
;  Termination. 
  Alternation. 
{...}  Repetition. 
(...)  Grouping. 
NIL  Empty. The expression can be an empty string. 
INTEGER  Integers such as 1, 2, 3. 
FLOAT  Float numbers such as 1.0, 2.0. 
CONST  Integers or float numbers. 
IDENTIFIER  Identifier. In Milvus, the IDENTIFIER represents the field name. 
LogicalOp  A LogicalOp is a logical operator that supports combining more than one relational operation in one comparison. Returned value of a LogicalOp is either TRUE (1) or FALSE (0). There are two types of LogicalOps, including BinaryLogicalOps and UnaryLogicalOps. 
UnaryLogicalOp  UnaryLogicalOp refers to the unary logical operator "not". 
BinaryLogicalOp  Binary logical operators that perform actions on two operands. In a complex expression with two or more operands, the order of evaluation depends on precedence rules. 
ArithmeticOp  An ArithmeticOp, namely an arithmetic operator, performs mathematical operations such as addition and subtraction on operands. 
UnaryArithOp  A UnaryArithOp is an arithmetic operator that performs an operation on a single operand. The negative UnaryArithOp changes a positive expression into a negative one, or the other way round. 
BinaryArithOp  A BinaryArithOp, namely a binary operator, performs operations on two operands. In a complex expression with two or more operands, the order of evaluation depends on precedence rules. 
CmpOp  CmpOp is a relational operator that perform actions on two operands. 
CmpOpRestricted  CmpOpRestricted is restricted to "Less than" and "Equal". 
ConstantExpr  ConstantExpr can be a Constant or a BinaryArithOp on two ConstExprs or a UnaryArithOp on a single ConstantExpr. It is defined recursively. 
ConstantArray  ConstantArray is wrapped by square brackets, and ConstantExpr can be repeated in the square brackets. ConstArray must include at least one ConstantExpr. 
TermExpr  TermExpr is used to check whether the value of an IDENTIFIER appears in a ConstantArray. TermExpr is represented by "in". 
CompareExpr  A CompareExpr, namely comparison expression can be relational operations on two IDENTIFIERs, or relational operations on one IDENTIFIER and one ConstantExpr, or ternary operation on two ConstantExprs and one IDENTIFIER. 
SingleExpr  SingleExpr, namely single expression, can be either a TermExpr or a CompareExpr. 
LogicalExpr  A LogicalExpr can be a BinaryLogicalOp on two LogicalExprs, or a UnaryLogicalOp on a single LogicalExpr, or a LogicalExpr grouped within parentheses, or a SingleExpr. The LogicalExpr is defined recursively. 
Expr  Expr, an abbreviation meaning expression, can be LogicalExpr or NIL. 
MatchOp  A MatchOp, namely a match operator, compares a string to a string constant or a string prefix constant. 
JsonArrayOp  A JsonOp, namely a JSON operator, checks whether the specified identifier contains the specified elements. 
Operators
Logical operators
Logical operators perform a comparison between two expressions.
Symbol  Operation  Example  Description 

'and' &&  and  expr1 && expr2  True if both expr1 and expr2 are true. 
'or'   or  expr1  expr2  True if either expr1 or expr2 are true. 
Binary arithmetic operators
Binary arithmetic operators contain two operands and can perform basic arithmetic operations and return the corresponding result.
Symbol  Operation  Example  Description 

+  Addition  a + b  Add the two operands. 
  Subtraction  a  b  Subtract the second operand from the first operand. 
*  Multiplication  a * b  Multiply the two operands. 
/  Division  a / b  Divide the first operand by the second operand. 
**  Power  a ** b  Raise the first operand to the power of the second operand. 
%  Modulo  a % b  Divide the first operand by the second operand and yield the remainder portion. 
Relational operators
Relational operators use symbols to check for equality, inequality, or relative order between two expressions.
Symbol  Operation  Example  Description 

<  Less than  a < b  True if a is less than b. 
>  Greater than  a > b  True if a is greater than b. 
==  Equal  a == b  True if a is equal to b. 
!=  Not equal  a != b  True if a is not equal to b. 
<=  Less than or equal  a <= b  True if a is less than or equal to b. 
>=  Greater than or equal  a >= b  True if a is greater than or equal to b. 
Operator precedence and associativity
The following table lists the precedence and associativity of operators. Operators are listed top to bottom, in descending precedence.
Precedence  Operator  Description  Associativity 

1  +   UnaryArithOp  Lefttoright 
2  not  UnaryLogicOp  Righttoleft 
3  **  BinaryArithOp  Lefttoright 
4  * / %  BinaryArithOp  Lefttoright 
5  +   BinaryArithOp  Lefttoright 
6  < <= > >=  CmpOp  Lefttoright 
7  == !=  CmpOp  Lefttoright 
8  like LIKE  MatchOp  Lefttoright 
9  json_contains JSON_CONTAINS  JsonArrayOp  Lefttoright 
10  json_contains_all JSON_CONTAINS_ALL  JsonArrayOp  Lefttoright 
11  json_contains_any JSON_CONTAINS_ANY  JsonArrayOp  Lefttoright 
12  && and  BinaryLogicOp  Lefttoright 
13   or  BinaryLogicOp  Lefttoright 
Expressions are normally evaluated from left to right. Complex expressions are evaluated one at a time. The order in which the expressions are evaluated is determined by the precedence of the operators used.
If an expression contains two or more operators with the same precedence, the operator to the left is evaluated first.
For example, 10 / 2 * 5 will be evaluated as (10 / 2) and the result multiplied by 5.
When a lower precedence operation should be processed first, it should be enclosed within parentheses.
For example, 30 / 2 + 8. This is normally evaluated as 30 divided by 2 then 8 added to the result. If you want to divide by 2 + 8, it should be written as 30 / (2 + 8).
Parentheses can be nested within expressions. Innermost parenthetical expressions are evaluated first.
Usage
Samples of all available boolean expression usage in Milvus are listed as follows (int64
represents the scalar field that contains data of INT64 type, float
represents the scalar field that contains data of floatingpoint type, and VARCHAR
represents the scalar field that contains data of VARCHAR type):
 CmpOp
"int64 > 0"
"0 < int64 < 400"
"500 <= int64 < 1000"
VARCHAR > "str1"
 BinaryLogicalOp and parentheses
"(int64 > 0 && int64 < 400) or (int64 > 500 && int64 < 1000)"
 TermExpr and UnaryLogicOp
Milvus only supports deleting entities with clearly specified primary keys, which can be achieved merely with the term expression in
.
"int64 not in [1, 2, 3]"
VARCHAR not in ["str1", "str2"]
 TermExpr, BinaryLogicalOp, and CmpOp (on different fields)
"int64 in [1, 2, 3] and float != 2"
 BinaryLogicalOp and CmpOp
"int64 == 0  int64 == 1  int64 == 2"
 CmpOp and UnaryArithOp or BinaryArithOp
"200+300 < int64 <= 500+500"
 MatchOp (prefix matching)
VARCHAR like "prefix%"
 JsonArrayOp

JSON_CONTAINS(identifier, JsonExpr)
If the JSON expression of a
JSON_CONTAINS
(the second argument) statement is a list, the identifier (the first argument) should be list of list. Otherwise, the statement always evaluates to False.# {"x": [1,2,3]} json_contains(x, 1) # ==> true json_contains(x, "a") # ==> false # {"x": [[1,2,3], [4,5,6], [7,8,9]]} json_contains(x, [1,2,3]) # ==> true json_contains(x, [3,2,1]) # ==> false

JSON_CONTAINS_ALL(identifier, JsonExpr)
The JSON expression in a
JSON_CONTAINS_ALL
statement should always be a list.# {"x": [1,2,3,4,5,7,8]} json_contains_all(x, [1,2,8]) # ==> true json_contains_all(x, [4,5,6]) # ==> false 6 is not exists

JSON_CONTAINS_ANY(identifier, JsonExpr)
The JSON expression in a
JSON_CONTAINS_ANY
statement should always be a list. Otherwise, it acts the same asJSON_CONTAINS
.# {"x": [1,2,3,4,5,7,8]} json_contains_any(x, [1,2,8]) # ==> true json_contains_any(x, [4,5,6]) # ==> true json_contains_any(x, [6,9]) # ==> false
What's next
Now that you know how bitsets work in Milvus, you might also want to:
 Learn how to conduct a Hybrid Search.
 Learn how to use strings to filter your search results.
 Learn how to use dynamic fields in building boolean expressions.