Abstract
In this paper we formally state and prove theorems characterizing when a function can be constructively reformulated using the recursion operators fold and unfold, i.e. given a function h, when can a function g be constructed such that h = fold g or h = unfold g? These results are refinements of the classical characterization of fold and unfold given by Gibbons, Hutton and Altenkirch in [6]. The proofs presented here have been formalized in Nuprl’s constructive type theory [5] and thereby yield program transformations which map a function h (accompanied by the evidence that h satisfies the required conditions), to a function g such that h = fold g or, as the case may be, h = unfold g.
This work was supported by NSF grant CCR-9985239, a DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under grant N00014-01-1-0765, and by the PhD program Logic in Computer Science of the German Research Foundation.
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Weber, T., Caldwell, J. (2004). Constructively Characterizing Fold and Unfold. In: Bruynooghe, M. (eds) Logic Based Program Synthesis and Transformation. LOPSTR 2003. Lecture Notes in Computer Science, vol 3018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25938-1_11
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DOI: https://doi.org/10.1007/978-3-540-25938-1_11
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