  This paper presents a study of the metaphorism pattern of relational
specification, showing how it can be refined into recursive programs.
Metaphorisms express input-output relationships which preserve relevant
information while at the same time some intended optimization takes place. Text
processing, sorting, representation changers, etc., are examples of
metaphorisms. The kind of metaphorism refinement studied in this paper is a
strategy known as change of virtual data structure. By framing metaphorisms in
the class of (inductive) regular relations, sufficient conditions are given for
such implementations to be calculated using relation algebra. The strategy is
illustrated with examples including the derivation of the quicksort and
mergesort algorithms, showing what they have in common and what makes them
different from the very start of development.
