Definition:Concatenation of URM Programs
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.
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.