Expression grammars need to decide how operators group. A Pratt parser handles this by assigning operators binding strengths and letting the parser decide how far an expression extends from those strengths.

Prefix and infix roles

A token can define how it starts an expression, such as unary -, and separately how it continues one, such as binary -.

Binding power

When parsing an infix operator, the parser compares its binding power with the surrounding context. Higher-binding operators are consumed inside the current expression before lower-binding operators.

This naturally parses

2 + 3 * 4

as

2 + (3 * 4)

without creating one grammar rule for every precedence level.

Associativity can be expressed by choosing slightly different left and right binding powers.

Pratt parsing is therefore a compact technique for expression languages with many prefix, postfix and infix operators.