Infix

Infix is a form of notation in which an operator is placed between its operands. In mathematics and many programming languages, the familiar expression 3 + 4 uses the plus operator between the operands 3 and 4. Infix notation is the dominant form for expressing binary operations.

By contrast, prefix notation (Polish) places the operator before its operands, as in + 3 4, while postfix notation (Reverse Polish) places the operator after its operands, as in 3 4 +. Infix is generally preferred for readability, especially in complex expressions, but prefix and postfix forms are often used in computer science contexts such as parsing and evaluation.

Infix expressions require rules of precedence and associativity to determine evaluation order. Parentheses can override these rules, clarifying the intended grouping. Common operators include addition, subtraction, multiplication, division, and comparison; exponentiation may be written as ^ or ** depending on the language. Some languages also support infix assignment operators, such as a = b + c, and augmented assignments like a += b.

Parsing infix notation is more intricate than parsing prefix or postfix forms because of operator precedence and associativity. Techniques such as the Shunting-yard algorithm or construction of expression trees are used to convert infix expressions into a form suitable for evaluation.

In mathematics and logic, infix notation aligns with conventional reading and human intuition, making it the standard choice for expressing most arithmetic and logical operations.