A Functional Algorithm for Exact Real Integration with Invariant Measures

Authors:
Adam Scriven
Affiliations:
School of Computer Science, University of Birmingham, Birmingham, England
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2008

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Abstract

We develop an algorithm for exact real integration over a class of self-similar spaces and measures defined by Hutchinson. We construct the algorithm in an idealised lazy functional programming language and prove its correctness using domain theory. The work generalises an algorithm developed by Alex Simpson for exact Riemann integration over the real line. We implement the algorithm in the functional language Haskell and give some preliminary results.