An Infinite Pebble Game and Applications

We generalize the well-known pebble game to infinite dag's, and we use this generalization to give new and shorter proofs of results in different areas of computer science (as diverse as "logic of programs" and "formal language theory"). Our applications here include a proof of a theorem due to Salomaa, asserting the existence of a context-free language with infinite index, and a proof of a theorem due to Tiuryn and Erimbetov, asserting that unbounded memory increases the power of logics of programs. The original proofs by Salomaa, Tiuryn, and Erimbetov, are fairly technical. The proofs by Tiuryn and Erimbetov also involve advanced techniques of model theory, namely, back-and-forth constructions based on a variant of Ehrenfeucht-Fraisse games. By contrast, our proofs are not only shorter, but also elementary. All we need is essentially finite induction and, in the case of the Tiuryn-Erimbetov result, the compactness and completeness of first-order logic.

Faithful Translations between Polyvariant Flows and Polymorphic Types

Recent work has shown equivalences between various type systems and flow logics. Ideally, the translations upon which such equivalences are based should be faithful in the sense that information is not lost in round-trip translations from flows to types and back or from types to flows and back. Building on the work of Nielson & Nielson and of Palsberg & Pavlopoulou, we present the first faithful translations between a class of finitary polyvariant flow analyses and a type system supporting polymorphism in the form of intersection and union types. Additionally, our flow/type correspondence solves several open problems posed by Palsberg & Pavlopoulou: (1) it expresses call-string based polyvariance (such as k-CFA) as well as argument based polyvariance; (2) it enjoys a subject reduction property for flows as well as for types; and (3) it supports a flow-oriented perspective rather than a type-oriented one.