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Substructural Proofs as Automata

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Programming Languages and Systems (APLAS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10017))

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Abstract

We present subsingleton logic as a very small fragment of linear logic containing only \(\oplus \), \(\mathbf {1}\), least fixed points and allowing circular proofs. We show that cut-free proofs in this logic are in a Curry–Howard correspondence with subsequential finite state transducers. Constructions on finite state automata and transducers such as composition, complement, and inverse homomorphism can then be realized uniformly simply by cut and cut elimination. If we freely allow cuts in the proofs, they correspond to a well-typed class of machines we call linear communicating automata, which can also be seen as a generalization of Turing machines with multiple, concurrently operating read/write heads.

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Notes

  1. 1.

    Notice that the proposition \(\mathord {\mathbin {\oplus }}_{}\{k{:}A\}\) is distinct from A.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Henry DeYoung & Frank Pfenning

Authors
  1. Henry DeYoung
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  2. Frank Pfenning
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Correspondence to Frank Pfenning .

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Editors and Affiliations

  1. Kyoto University , Kyoto, Japan

    Atsushi Igarashi

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DeYoung, H., Pfenning, F. (2016). Substructural Proofs as Automata. In: Igarashi, A. (eds) Programming Languages and Systems. APLAS 2016. Lecture Notes in Computer Science(), vol 10017. Springer, Cham. https://doi.org/10.1007/978-3-319-47958-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-47958-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47957-6

  • Online ISBN: 978-3-319-47958-3

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