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Temporal Refinements for Guarded Recursive Types

Abstract : We propose a logic to reason on temporal properties of higher-order programs that handle infinite objects like streams or infinite trees, represented via coinductive types. Specifications of programs are defined using safety and liveness properties. A given program can then be proven to satisfy its specification, in a compositional way, our logic being based on a type system. The logic is presented as a refinement type system over the guarded lambda-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.
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https://hal.archives-ouvertes.fr/hal-02512655
Contributor : Colin Riba <>
Submitted on : Thursday, July 16, 2020 - 12:53:44 PM
Last modification on : Tuesday, February 2, 2021 - 4:47:28 PM

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  • HAL Id : hal-02512655, version 2

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Guilhem Jaber, Colin Riba. Temporal Refinements for Guarded Recursive Types. 2020. ⟨hal-02512655v2⟩

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