Hylomorphism (computer science)

In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism (which first builds a set of results; also known as 'unfolding') followed by a catamorphism (which then folds these results into a final return value). Fusion of these two recursive computations into a single recursive pattern then avoids building the intermediate data structure. This is an example of deforestation, a program optimization strategy. A related type of function is a metamorphism, which is a catamorphism followed by an anamorphism.

A hylomorphism ${\displaystyle h:A\rightarrow C}$ can be defined in terms of its separate anamorphic and catamorphic parts.

The anamorphic part can be defined in terms of a unary function ${\displaystyle g:A\rightarrow B\times A}$ defining the list of elements in ${\displaystyle B}$ by repeated application ("unfolding"), and a predicate ${\displaystyle p:A\rightarrow {\text{Boolean}}}$ providing the terminating condition.

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