This paper introduces a pattern for almost compositional functions
over recursive data types, and over families of mutually recursive
data types. Here "almost compositional" means that for a number of
the constructors in the type(s), the result of the function depends
only on the constructor and the results of calling the function on the
constructor's arguments. The pattern consists of a generic part
constructed once for each data type or family of data types, and a
task-specific part. The generic part contains the code for the
predictable compositional cases, leaving the interesting work to the
task-specific part. Examples of the pattern implemented in dependent
type theory with inductive families, in Haskell with generalized
algebraic data types and rank-2 polymorphism, and in Java using a
variant of the Visitor design pattern are given. The relationship to
the "Scrap Your Boilerplate" approach to generic programming, and to
general tree types in dependent type theory are also investigated.