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Temporal Refinements for Guarded Recursive Types (full version)


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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Dates and versions

hal-02512655 , version 1 (19-03-2020)
hal-02512655 , version 2 (16-07-2020)
hal-02512655 , version 3 (07-01-2021)
hal-02512655 , version 4 (21-01-2021)
hal-02512655 , version 5 (14-03-2021)


  • HAL Id : hal-02512655 , version 5


Guilhem Jaber, Colin Riba. Temporal Refinements for Guarded Recursive Types (full version). 2021. ⟨hal-02512655v5⟩
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