How Operators: Infix, Prefix, Postfix, or Mixfix (Distfix)

How Operators: Infix, Prefix, Postfix, or Mixfix (Distfix)
Infix, prefix, postfix and Mixfix operators are different ways to write expressions equally.

Infix Notation

Operators are written in the middle of the operands

Examples

• (6-5)*7
• A*B + C/D

Prefix Notation

Also knowns as Polish notion. Operators are placed in the left of the operands

Examples

• *(- 6 5) 7 or * - 6 5 7
• + * A B / C D

Postfix Notation

Also knowns as Reverse Polish notion. Operators are placed in the right of the operands

Examples

• 6 5 - 7 *
• A B * C D / +

Outfix Notation

Operators are placed out of the operands

Examples

• |_| in Maude, e.g. | 1 0 1 1 0 | is 5

Mixfix Notation

Have several name parts and can be infix, postfix, prefix, and closed (a).

References

• Mixfix Part1
• Mixfix Part2
• Mixfix Part2a
• Mixfix parser

Examples

• if n + n == n ! then n else (n + n - n) in Agda: several name parts, mixed fixity (prefix, infix, postfix)
• L ? S : T in Maude: comination of outfix and infix

Definition

• Holes: denoted by _ in _[_]
• Precedence
• Infix _ + _: two holes and one name part +
• Prefix if _ then _ else _: three name parts (if, then, else), and three holes.