Abstract
We propose an axiomatization of fixpoint operators in typed call-by-value programming languages, and give its justifications in two ways. First, it is shown to be sound and complete for the notion of uniform T-fixpoint operators of Simpson and Plotkin. Second, the axioms precisely account for Filinski's fixpoint operator derived from an iterator (infinite loop constructor) in the presence of first-class continuations, provided that we define the uniformity principle on such an iterator via a notion of effect-freeness (centrality). We then explain how these two results are related in terms of the underlying categorical structures.
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Hasegawa, M., Kakutani, Y. Axioms for Recursion in Call-by-Value. Higher-Order and Symbolic Computation 15, 235–264 (2002). https://doi.org/10.1023/A:1020895213317
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DOI: https://doi.org/10.1023/A:1020895213317