Recursion and Sequentiality in Categories of Sheaves

Authors Cristina Matache, Sean Moss, Sam Staton

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Cristina Matache
  • University of Oxford, UK
Sean Moss
  • University of Oxford, UK
Sam Staton
  • University of Oxford, UK

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Cristina Matache, Sean Moss, and Sam Staton. Recursion and Sequentiality in Categories of Sheaves. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We present a fully abstract model of a call-by-value language with higher-order functions, recursion and natural numbers, as an exponential ideal in a topos. Our model is inspired by the fully abstract models of O'Hearn, Riecke and Sandholm, and Marz and Streicher. In contrast with semantics based on cpo’s, we treat recursion as just one feature in a model built by combining a choice of modular components.

Subject Classification

ACM Subject Classification
  • Theory of computation → Denotational semantics
  • Theory of computation → Categorical semantics
  • Denotational semantics
  • Full abstraction
  • Recursion
  • Sheaf toposes
  • CPOs


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