Axioms for Recursion in Call-by-Value

Abstract

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 controls, provided that we define the uniformity principle on such an iterator via a notion of effect-freeness (centrality). We also investigate how these two results are related in terms of the underlying categorical models.

Combining algebraic effects with continuations

“…and one can also give versions of the uniformity and stability axioms of [16] (the authors there employ a slightly different version of the call-by-value recursion operator). The operator can be interpreted in the standard least fixedpoint way provided that the locally continuous monad T is pointed, meaning here that every T (P) contains a least element; the three axioms then hold.…”

“…We give an account of this calculus in Appendix A, extended with type variables in order to get a smoother treatment of the relation between conditions on the interpretation of the calculus and semantic properties, such as the truth of equations. See [16] for another account of this calculus and [33] for the original source.…”

Order-enriched categorical models of the classical sequent calculus

“…This terminology was introduced by [22] and also used in [21,7,12]. (However, those publications deal with the semantics of functional programming languages and natural-deduction calculi, and the premonoidal categories they use differ significantly from linearly distributive categories.)…”

“…Dually, we define what it means for a symmetric monoidal category C=(C, ⊗, 1) to have co-monoids, and the notions co-copyable, co-discardable, co-focal, and co-focus. (Caution: the notions "copyable", "discardable", and "focal", in [22,5,12] correspond to our notions "co-copyable", "co-discardable", and "co-focal". However, our terminology agrees with [21].)…”

Linearly Used Effects: Monadic and CPS Transformations into the Linear Lambda Calculus

“…Following the results in [12], we can enrich our transformations with recursion while keeping the type-soundness and equational soundness valid. For interpreting a call-by-value fixpoint operator on function types…”