Prefix of a list

An initial segment of a list, including the empty segment and, for finite lists, the whole list. A proper prefix excludes the whole list. Fully materialising all prefixes of a length-$n$ list needs $\Theta (n^2)$ element constructors, although the outer list of prefixes has only $n+1$ entries.

An initial segment of a string, including the empty string or the whole string. Two strings share a prefix exactly when their initial characters agree up to its length. The longest common prefix is the longest such shared initial segment.