[2203.00362] Reasonable Space for the $λ$-Calculus, Logarithmically
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arXiv:2203.00362 (cs)
[Submitted on 1 Mar 2022 (v1), last revised 19 Nov 2024 (this version, v6)]

Title:Reasonable Space for the $λ$-Calculus, Logarithmically

Authors:Beniamino Accattoli, Ugo Dal Lago, Gabriele Vanoni
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Abstract:Can the $\lambda$-calculus be considered a reasonable computational model? Can we use it for measuring the time $\textit{and}$ space consumption of algorithms? While the literature contains positive answers about time, much less is known about space. This paper presents a new reasonable space cost model for the $\lambda$-calculus, based on a variant over the Krivine abstract machine. For the first time, this cost model is able to accommodate logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value $\lambda$-calculus.
Subjects: Logic in Computer Science (cs.LO); Computational Complexity (cs.CC); Programming Languages (cs.PL)
Cite as: arXiv:2203.00362 [cs.LO]
  (or arXiv:2203.00362v6 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2203.00362
Journal reference: Logical Methods in Computer Science, Volume 20, Issue 4 (November 20, 2024) lmcs:10883
Related DOI: https://doi.org/10.46298/lmcs-20%284%3A15%292024

Submission history

From: Gabriele Vanoni [view email] [via Logical Methods In Computer Science as proxy]
[v1] Tue, 1 Mar 2022 11:20:49 UTC (125 KB)
[v2] Mon, 18 Jul 2022 17:38:13 UTC (124 KB)
[v3] Tue, 31 Jan 2023 17:33:19 UTC (96 KB)
[v4] Wed, 8 May 2024 14:08:38 UTC (109 KB)
[v5] Thu, 7 Nov 2024 15:48:26 UTC (139 KB)
[v6] Tue, 19 Nov 2024 10:41:03 UTC (141 KB)
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