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Open Higher-Order Logic

Authors Ugo Dal Lago , Francesco Gavazzo , Alexis Ghyselen

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  • 17 pages

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Author Details

Ugo Dal Lago
  • Department of Computer Science and Engineering, University of Bologna, Italy
Francesco Gavazzo
  • Department of Computer Science, University of Pisa, Italy
Alexis Ghyselen
  • Department of Computer Science and Engineering, University of Bologna, Italy

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Ugo Dal Lago, Francesco Gavazzo, and Alexis Ghyselen. Open Higher-Order Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 17:1-17:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We introduce a variation on Barthe et al.’s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity, differentiability, or monotonicity, can be expressed and reasoned about in a very natural way, following the structure of the underlying program. We give open higher-order logic in distinct flavors, and in particular in its relational and local versions, the latter being tailored for situations in which properties hold only in part of the underlying function’s domain of definition.

Subject Classification

ACM Subject Classification
  • Theory of computation → Higher order logic
  • Theory of computation → Logic and verification
  • Formal Verification
  • Relational Logic
  • First-Order Properties


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