infixr

Infixr is a fixity declaration used in Haskell (and related languages) to specify that an operator is right-associative and to assign its precedence level. The declaration takes the form infixr n op, where n is an integer from 0 to 9. Higher numbers bind more tightly, and right associativity determines how consecutive occurrences of the operator group in expressions.

The primary purpose of infixr is to influence parsing, not to define the operator’s behavior. The operator must already be defined as a function; the fixity declaration only affects how sequences like a op b op c are parenthesized if they involve the operator op. Right-associative means a op (b op c) for a chain of three occurrences.

Example:

infixr 5 ++

a ++ b ++ c

With this declaration, a ++ b ++ c is parsed as a ++ (b ++ c). If the operator were declared infixl instead, the grouping would be (a ++ b) ++ c. An un-declared operator has a default fixity, which may differ from the intended behavior, so explicit fixity declarations help ensure predictable parsing across modules.

Notes:

- Fixity declarations apply at the module level and can be overridden by qualified imports or re-declarations in other modules.

- The specified precedence only affects parsing order relative to other operators; it does not change the operator’s implementation.

In fixity management, there are three forms: infixl (left-associative), infixr (right-associative), and infix (non-associative), each with a 0–9 precedence scale. This system helps developers control how complex expressions are interpreted without changing the underlying definitions of operators.