Changing a table’s shape
The six verbs work down a table. Sometimes the table is the wrong shape to begin with: a year in four columns when you wanted a year in four rows, or the reverse.
Two verbs turn a table one way and back. lengthen makes it taller and widen makes it wider, and the names say which, because nobody could remember which of melt and cast did what.
This is the part where a reader arriving from tidyr will recognize the job and not the argument list. There is a table in the first chapter comparing the two.