infixl

Infixl is a fixity declaration used in some functional programming languages to designate that an operator is left-associative and to assign it a precedence level. With a left-associative operator, chains of the same operator are grouped from the left, so a op b op c is parsed as (a op b) op c. The precedence level also influences how operators with different binding strengths are grouped when parentheses are not used.

Syntax commonly appears as infixl n op, where n is an integer from 0 to 9 and op is the operator symbol or name. The number indicates the operator’s precedence, with higher numbers binding stronger. For example, infixl 7 * declares * to be left-associative with a precedence of 7. A separate declaration such as infixl 6 + would assign + to precedence 6.

Examples help illustrate the effect. If you declare infixl 7 * and infixl 6 +, then an expression like a + b * c is parsed as a + (b * c) because * has higher precedence than +. An expression like a - b - c is parsed as (a - b) - c due to left associativity. If two operators share the same precedence and associativity, chaining is evaluated from the left.

Related forms include infixr for right-associative operators and infix for non-associative operators. The choice of fixity affects parsing order but not the underlying runtime semantics, so fixity declarations are mainly a tool for ensuring expressions are read unambiguously when introducing new operators. In languages such as Haskell, fixity declarations help control how complex expressions are interpreted without excessive parentheses.