Multi types and reasonable space
Programming Languages
2026-03-24 v2 Logic in Computer Science
Abstract
Accattoli, Dal Lago, and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the lambda-calculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system.
Cite
@article{arxiv.2207.08795,
title = {Multi types and reasonable space},
author = {Beniamino Accattoli and Ugo Dal Lago and Gabriele Vanoni},
journal= {arXiv preprint arXiv:2207.08795},
year = {2026}
}