Building Blocks for Reasoning on the BEAM

14 pages•Published: October 24, 2026

Johannes Schuster and Christoph Benzmüller

Abstract

We report on automated reasoning infrastructure for the Elixir ecosystem and the BEAM virtual machine. Four packages supply the components a higher-order reasoning tool on this platform would otherwise write from scratch: data structures for higher-order terms and proof problems, parsing of the TPTP THF dialects, higher-order unification, a decidable term ordering, and uniform access to external provers. On top of them sits a fifth, Shot, a higher-order free-variable tableau prover organised around the actor model, and an interactive environment for teaching automated reasoning. The platform choice also carried the hypothesis that concurrency would repay the constant factor a managed runtime costs on the symbolic inner loop. We report that our current procedure for computing simultaneous closure bottlenecks concurrency. On the TPTP TH0 and TH1 problems a worker pool multiplies inference by a factor of 3.27 over a single worker, the rate of global closure attempts does not follow, and coverage is unchanged. The cause lies in the component that reconciles closure across branches. The libraries are early and under revision, and we present them as such.

Keyphrases: automated theorem proving, concurrency, elixir, higher order logic, tableaux

In: Stephan Schulz, Konstantin Korovin and Michael Rawson (editors). Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers), vol 23, pages 98-111.

Links:	https://easychair.org/publications/paper/SDCR
	https://doi.org/10.29007/z6j1

BibTeX entry

@inproceedings{IWIL-2026:Building_Blocks_Reasoning_BEAM,
  author    = {Johannes Schuster and Christoph Benzmüller},
  title     = {Building Blocks for Reasoning on the BEAM},
  booktitle = {Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers)},
  editor    = {Stephan Schulz and Konstantin Korovin and Michael Rawson},
  series    = {Kalpa Publications in Computing},
  volume    = {23},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/SDCR},
  doi       = {10.29007/z6j1},
  pages     = {98-111},
  year      = {2026}}

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