Transfinite Step-Indexing: Decoupling Concrete and Logical Steps

Kasper Svendsen 1 Filip Sieczkowski 2 Lars Birkedal 3
1 CAM - University of Cambridge [UK]
2 GALLIUM - Langages de programmation, types, compilation et preuves
Inria de Paris
3 Aarhus University [Aarhus]
Abstract : Step-indexing has proven to be a powerful technique for defining logical relations for languages with advanced type systems and models of expressive program logics. In both cases, the model is stratified using natural numbers to solve a recursive equation that has no naive solutions. As a result of this stratification, current models require that each unfolding of the recursive equation – each logical step – must coincide with a concrete reduction step. This tight coupling is problematic for applications where the number of logical steps cannot be statically bounded. In this paper we demonstrate that this tight coupling between logical and concrete steps is artificial and show how to loosen it using transfinite step-indexing. We present a logical relation that supports an arbitrary but finite number of logical steps for each concrete step.
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Kasper Svendsen, Filip Sieczkowski, Lars Birkedal. Transfinite Step-Indexing: Decoupling Concrete and Logical Steps. 25th European Symposium on Programming Languages and Systems, Dec 2016, Eindhoven, Netherlands. pp.727 - 751, ⟨10.1007/978-3-662-49498-1_28⟩. ⟨hal-01408649⟩

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