Correct looping arrows from cyclic terms

Authors:
Makoto Hamana
Affiliations:
Department of Computer Science, Gunma University, Japan
Venue:
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
Year:
2012

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Abstract

Arrows involving a loop operator provide an interesting programming methodology for looping computation. On the other hand, Haskell can define cyclic data structures by recursive definitions. This paper shows that there exists a common principle underlying both cyclic data and cyclic computations of arrow programs. We examine three concrete examples of constructing looping arrows from a syntactic structure called cyclic terms. Then we present a general pattern of constructing correct looping arrows, that is based on categorical semantics of loops and arrows, i.e. traced and Freyd categories.