Temporal Refinements for Guarded Recursive Types

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• Colin Riba (ENS Lyon)
• Friday 04 November 2022, 13:30-14:20
• LG23, SoCS and Zoom (see abstract for link).

If you have a question about this talk, please contact George Kaye.

Zoom details

• Link: https://bham-ac-uk.zoom.us/j/81873335084?pwd=T1NaUFg2U1l6d0RLL2RlTzFBam1IUT09
• Meeting ID: 818 7333 5084
• Passcode: 217

Abstract

We propose a logic for temporal properties of higher-order programs that handle infinite objects like streams or infinite trees, rep- resented via coinductive types. Specifications of programs use safety and liveness properties. Programs can then be proven to satisfy their specifi- cation in a compositional way, our logic being based on a type system. The logic is presented as a refinement type system over the guarded λ-calculus, a λ-calculus with guarded recursive types. The refinements are formulae of a modal μ-calculus which embeds usual temporal modal logics such as LTL and CTL . The semantics of our system is given within a rich structure, the topos of trees, in which we build a realizability model of the temporal refinement type system. We use in a crucial way the connection with set-theoretic semantics to handle liveness properties.

j.w.w. Guilhem Jaber.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• LG23, SoCS and Zoom (see abstract for link)
• Theoretical computer science seminar
• computer sience

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