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Type-Based Termination for Futures

Authors Siva Somayyajula , Frank Pfenning

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Author Details

Siva Somayyajula
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Frank Pfenning
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

Funding

This material is based upon work supported by the United States Air Force and DARPA under Contract No. FA8750-18-C-0092.
  • Somayyajula, Siva: Partially supported by the Sansom Graduate Fellowship in Computer Science.

Acknowledgements

We would like to thank Farzaneh Derakhshan, Klaas Pruiksma, Henry DeYoung, Ankush Das, and the anonymous reviewers for helpful discussion and suggestions regarding the contents of this paper.

Cite AsGet BibTex

Siva Somayyajula and Frank Pfenning. Type-Based Termination for Futures. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FSCD.2022.12

Abstract

In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the concurrent setting. We extend the semi-axiomatic sequent calculus, a subsuming paradigm for futures-based functional concurrency, and its underlying operational semantics with recursion and arithmetic refinements. The latter enables a new and highly general sized type scheme we call sized type refinements. As a widely applicable technical device, we type recursive programs with infinitely deep typing derivations that unfold all recursive calls. Then, we observe that certain such derivations can be made infinitely wide but finitely deep. The resulting trees serve as the induction target of our strong normalization result, which we develop via a novel logical relations argument.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Computing methodologies → Concurrent programming languages
Keywords
  • type-based termination
  • sized types
  • futures
  • concurrency
  • infinite proofs

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