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# 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";
``````

The following table lists the description of each symbol mentioned in the above Boolean expression rules.

NotationDescription
=Definition.
,Concatenation.
;Termination.
\Alternation.
{...}Repetition.
(...)Grouping.
NILEmpty. The expression can be an empty string.
INTEGERIntegers such as 1, 2, 3.
FLOATFloat numbers such as 1.0, 2.0.
CONSTIntegers or float numbers.
IDENTIFIERIdentifier. In Milvus, the IDENTIFIER represents the field name.
LogicalOpA 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.
UnaryLogicalOpUnaryLogicalOp refers to the unary logical operator "not".
BinaryLogicalOpBinary 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.
ArithmeticOpAn ArithmeticOp, namely an arithmetic operator, performs mathematical operations such as addition and subtraction on operands.
UnaryArithOpA 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.
BinaryArithOpA 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.
CmpOpCmpOp is a relational operator that perform actions on two operands.
CmpOpRestrictedCmpOpRestricted is restricted to "Less than" and "Equal".
ConstantExprConstantExpr can be a Constant or a BinaryArithOp on two ConstExprs or a UnaryArithOp on a single ConstantExpr. It is defined recursively.
ConstantArrayConstantArray is wrapped by square brackets, and ConstantExpr can be repeated in the square brackets. ConstArray must include at least one ConstantExpr.
TermExprTermExpr is used to check whether the value of an IDENTIFIER appears in a ConstantArray. TermExpr is represented by "in".
CompareExprA 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.
SingleExprSingleExpr, namely single expression, can be either a TermExpr or a CompareExpr.
LogicalExprA 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.
ExprExpr, an abbreviation meaning expression, can be LogicalExpr or NIL.
MatchOpA MatchOp, namely a match operator, compares a string to a string constant or a string prefix constant.

## Operators

### Logical operators:

Logical operators perform a comparison between two expressions.

SymbolOperationExampleDescription
'and' &&andexpr1 && expr2True if both expr1 and expr2 are true.
'or' \\orexpr1 \\expr2True 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.

SymbolOperationExampleDescription
-Subtractiona - bSubtract the second operand from the first operand.
*Multiplicationa * bMultiply the two operands.
/Divisiona / bDivide the first operand by the second operand.
**Powera ** bRaise the first operand to the power of the second operand.
%Moduloa % bDivide 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.

SymbolOperationExampleDescription
<Less thana < bTrue if a is less than b.
>Greater thana > bTrue if a is greater than b.
==Equala == bTrue if a is equal to b.
!=Not equala != bTrue if a is not equal to b.
<=Less than or equala <= bTrue if a is less than or equal to b.
>=Greater than or equala >= bTrue 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.

PrecedenceOperatorDescriptionAssociativity
1+ -UnaryArithOpLeft-to-right
2notUnaryLogicOpRight-to-left
3**BinaryArithOpLeft-to-right
4* / %BinaryArithOpLeft-to-right
5+ -BinaryArithOpLeft-to-right
6< <= > >=CmpOpLeft-to-right
7== !=CmpOpLeft-to-right
8like LIKEMatchOpLeft-to-right
9&& andBinaryLogicOpLeft-to-right
10\\orBinaryLogicOpLeft-to-right

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 floating-point type, and `VARCHAR` represents the scalar field that contains data of VARCHAR type):

1. CmpOp
``````"int64 > 0"
``````
``````"0 < int64 < 400"
``````
``````"500 <= int64 < 1000"
``````
``````VARCHAR > "str1"
``````
1. BinaryLogicalOp and parentheses
``````"(int64 > 0 && int64 < 400) or (int64 > 500 && int64 < 1000)"
``````
1. 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"]
``````
1. TermExpr, BinaryLogicalOp, and CmpOp (on different fields)
``````"int64 in [1, 2, 3] and float != 2"
``````
1. BinaryLogicalOp and CmpOp
``````"int64 == 0 || int64 == 1 || int64 == 2"
``````
1. CmpOp and UnaryArithOp or BinaryArithOp
``````"200+300 < int64 <= 500+500"
``````
1. MatchOp (prefix matching)
``````VARCHAR like "prefix%"
``````

## What's next

Now that you know how bitsets work in Milvus, you might also want to: