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Communication Dans Un Congrès Année : 2024

Liveness Properties in Geometric Logic for Domain-Theoretic Streams

Résumé

We devise a version of Linear Temporal Logic (LTL) on a denotational domain of streams. We investigate this logic in terms of domain theory, (point-free) topology and geometric logic. This yields the first steps toward an extension of the "Domain Theory in Logical Form" paradigm to temporal liveness properties. We show that the negation-free formulae of LTL induce sober subspaces of streams, but that this is in general not the case in presence of negation. We propose a direct, inductive, translation of negation-free LTL to geometric logic. This translation reflects the approximations used to compute the usual fixpoint representations of LTL modalities. As a motivating example, we handle a natural input-output specification for the usual filter function on streams.
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Dates et versions

hal-04406332 , version 1 (19-01-2024)

Identifiants

  • HAL Id : hal-04406332 , version 1

Citer

Colin Riba, Solal Stern. Liveness Properties in Geometric Logic for Domain-Theoretic Streams. 35es Journées Francophones des Langages Applicatifs (JFLA 2024), Jan 2024, Saint-Jacut-de-la-Mer, France. ⟨hal-04406332⟩
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