# Definition:Replacement Operation

## Contents

## Definition

The **replacement operation** on two variables $a$ and $b$ is denoted:

- $a \gets b$

and is interpreted as:

- the value of variable $a$ is to be replaced by the current value of variable $b$, while leaving the value of variable $b$ the same.

## Examples

### Exchange Operation as Replacement Operations

Let $x$ and $y$ be variables whose values are to be exchanged.

The exchange operation on $x$ and $y$ can be implemented using replacement operations.

Let $t$ be a third variable which has been established for this purpose.

Then the sequence of replacement operations:

- $t \gets x$
- $x \gets y$
- $y \gets t$

performs the task.

### Rearrangement Operation as Replacement Operations

Let $\left({a, b, c, d}\right)$ be an ordered quadruple consisting of four variables whose values are to be rearranged into the order $\left({b, c, d, a}\right)$.

This can be implemented using replacement operations.

Let $t$ be a new variable which has been established for this purpose.

Then the sequence of replacement operations:

- $t \gets a$
- $a \gets b$
- $b \gets c$
- $c \gets d$
- $d \gets t$

performs the task.

## Also known as

The operation of **replacement** is also known as **assignment** or **substitution**.

## Also see

Do not confuse with the left operation, which has the same notation but is interpreted in exactly the opposite manner.

## Sources

- 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.1$: Algorithms