PostgreSQL 7.1.3 Documentation
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# 1.4. Lexical Precedence

The precedence and associativity of the operators is hard-wired into the parser. Most operators have the same precedence and are left-associative. This may lead to non-intuitive behavior; for example the Boolean operators "<" and ">" have a different precedence than the Boolean operators "<=" and ">=". Also, you will sometimes need to add parentheses when using combinations of binary and unary operators. For instance

    SELECT 5 ! - 6;

will be parsed as

    SELECT 5 ! (- 6);

because the parser has no idea -- until it is too late -- that ! is defined as a postfix operator, not an infix one. To get the desired behavior in this case, you must write

    SELECT (5 !) - 6;

This is the price one pays for extensibility.

Table 1-1. Operator Precedence (decreasing)

Operator/Element | Associativity | Description
--- | --- | ---
:: | left | Postgres-style typecast
[ ] | left | array element selection
. | left | table/column name separator
- | right | unary minus
^ | left | exponentiation
* / % | left | multiplication, division, modulo
+ - | left | addition, subtraction
IS |  | test for TRUE, FALSE, NULL
ISNULL |  | test for NULL
NOTNULL |  | test for NOT NULL
(any other) | left | all other native and user-defined operators
IN |  | set membership
BETWEEN |  | containment
OVERLAPS |  | time interval overlap
LIKE ILIKE |  | string pattern matching
< > |  | less than, greater than
= | right | equality, assignment
NOT | right | logical negation
AND | left | logical conjunction
OR | left | logical disjunction

Note that the operator precedence rules also apply to user-defined operators that have the same names as the built-in operators mentioned above. For example, if you define a "+" operator for some custom data type it will have the same precedence as the built-in "+" operator, no matter what yours does.

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