infixcentered

Infixcentered is a term used in discussions of syntax representation to describe a design principle whereby the infix operator is treated as the central element of an expression, situated between its operands. The concept is not tied to a single standard definition and has been used in varying ways across programming language design, formal grammar descriptions, and linguistic theory. In many contexts it refers to the familiar infix notation in which an operator appears between two operands, as opposed to prefix or postfix forms, and which often carries implications for precedence, associativity, and readability.

In parser theory and grammar design, infixcentered representations can be encoded with productions of the form Expr -> Expr op Expr, with the operator symbol visually or structurally centered between subexpressions. This framing supports readability and symmetric binding of binary operators, but care is needed to manage associativity and precedence to avoid ambiguity. Some grammar tools and pretty-printers use the notion to guide layout and display rather than to imply a distinct syntactic class.

In linguistics and education, infixcentered approaches may emphasize the central role of infixes in a language’s morphology or in teaching expression syntax, highlighting how the infix sits within a word or phrase rather than at a boundary position. The term is sometimes used descriptively rather than as a formal category.

See also: infix notation, prefix notation, postfix notation, operator precedence, parse tree, context-free grammar.