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$Research paper thumbnail of Another iteration on \A synthesis of several sorting algorithms$

In \A synthesis of several sorting algorithms", Darlington showed how to use program transfo... more In \A synthesis of several sorting algorithms", Darlington showed how to use program transformation techniques to develop versions of six well-known sorting algorithms. We provide more evidence for the naturalness of the resulting taxonomy of algorithms by showing how it follows almost immediately from a consideration of the types of the objects involved. By exploiting the natural operations of iteration and coiteration over recursively dened data types, we may automatically derive the structure of each algorithm.

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this paper was presented at California State University, Northridge. This work was partially supp... more this paper was presented at California State University, Northridge. This work was partially supported by a grant from the Office of Naval Research. References

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An extension of the simply-typed lambda calculus is presented which contains both well- structure... more An extension of the simply-typed lambda calculus is presented which contains both well- structured inductive and coinductive types, and which also identifies a class of types for which general recursion is possible. The motivations for this work are certain natural constructions in category theory, in particular the notion of an algebraically bounded functor, due to Freyd. We propose that this is a particularly elegant language in which to work with recursive objects, since the potential for general recursion is contained in a single operator which interacts well with the facilities for bounded iteration and coiteration.

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