Generalizing the AUGMENT

Neil Ghani, Tarmo Uustalu, Varmo Vene

To appear at Symposium on Trends in Functional Programming (TFP04), Munich, Germany, 25-26 November, 2004


The usual initial algebra semantics of inductive types provides a clear and uniform explanation the FOLD combinator. In our recent work [1], we de- scribed an alternative equivalent semantics of inductive types as limits of algeb ra structure forgetting functors to obtain an elegant account in terms of a universa l property of the BUILD and AUGMENT combinators which form the core of the shortcut deforestation program transformation method by Gill et al. [2, 3]. Here we present further evidence for the flexibility of our approach by showing that a useful AUGMENT-like combinator is definable for a far more wide class of param- eterized inductive types than free monads, namely for all monads arising from a parameterized monad via an initial algebra construction.

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