Abstract

Many problems call for a mixture of generic and specific programming techniques. We propose a polytypic programming approach based on generalised (monadic) folds where a separation is made between basic fold algebras that model generic behaviour and updates on these algebras that model specific behaviour. We identify particular basic algebras as well as some algebra combinators, and we show how these facilitate structured programming with updatable fold algebras. This blend of genericity and specificity allows programming with folds to scale up to applications involving large systems of mutually recursive datatypes. Finally, we address the possibility of providing generic definitions for the functions, algebras, and combinators that we propose.