Algebraic solutions to recursion schemes

Reducing Recursion to Iteration by Algebraic Extension

Recursion-Closed Algebraic Theories

A class of algebraic theories called “recursion-closed,” which generalize the rational theories studied by J. A. Goguen, J. W. Thatcher, E.G. Wagner and J. B. Wright in [in “Proceedings, 17th IEEE Symposium on Foundations of Computer Science, Houston, Texas, October 1976,” pp. 147-158; in “Mathematical Foundations of Computer Science, 1978,” Lecture Notes in Computer Science, Vol. 64, Springer-...

Unifying Recursion Schemes

Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such unifications are the ‘recursion schemes from comonads’ of Uustalu, Vene and Pardo, and our own ‘a...

Recursion Schemes From

Within the setting of the categorical approach to total functional programming, we introduce a \many-in-one" recursion scheme that neatly uniies a variety of seemingly diverging strengthenings of the basic recursion scheme of iteration. The new scheme is doubly generic: in addition to being parametric in a functor capturing the signature of an inductive type, it is also parametric in a comonad ...

Program Schemes, Recursion Schemes, and Formal Languages

This paper presents general methods for studying the problems of translatability between classes of schemes and equivalence of schemes in a given class. There are four methods: applying the theory of formal languages, programming, measuring the complexity of a computation, and "cutting and pasting." These methods are used to answer several questions of translatability and equivalence for classe...