# Definition:Concatenation of URM Programs

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## Definition

Let $P$ and $Q$ be URM programs.

The **concatenation of $P$ and $Q$** is denoted $P * Q$.

It consists of program $P$ followed immediately by program $Q$.

If $P$ and $Q$ compute particular functions, then it is usually necessary to make modifications to either $P$ or $Q$, or both, to make sure that the concatenated program continues to compute a function.

The simplest concatenation is illustrated in Composition of One-Variable URM Computable Functions.

## Linguistic Note

The word **concatenation** derives from the Latin **com-** for **with/together** and the Latin word **catena** for **chain**.

However, the end result of such an operation is not to be confused with a (set theoretical) chain.