Interaction trees: representing recursive and impure programs in Coq

Xia, Li-yao; Zakowski, Yannick; He, Paul; Hur, Chung-Kil; Malecha, Gregory; Pierce, Benjamin C.; Zdancewic, Steve

doi:10.1145/3371119

Cited by 61 publications

(23 citation statements)

References 61 publications

(50 reference statements)

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“…By supporting field update, Hofmann and Pierce's theory addresses shortcomings of purely functional object models, but its support for object aggregates or complex ownership structures appears limited and not much studied. A twolevel encoding could likely also be developed for concurrency-inspired object models [33,32,31], perhaps by adapting the theory of interaction trees [68,39]. However, VST's partial-correctness interpretation of triples limits the end-to-end usefulness of coinductive reasoning.…”

Section: Discussionmentioning

confidence: 99%

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Beringer

2021

Programming Languages and Systems

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Modularity - the partitioning of software into units of functionality that interact with each other via interfaces - has been the mainstay of software development for half a century. In case of the C language, the main mechanism for modularity is the compilation unit / header file abstraction. This paper complements programmatic modularity for C with modularity idioms for specification and verification in the context of Verifiable C, an expressive separation logic for CompCert . Technical innovations include (i) abstract predicate declarations – existential packages that combine Parkinson & Bierman’s abstract predicates with their client-visible reasoning principles; (ii) residual predicates, which help enforcing data abstraction in callback-rich code; and (iii) an application to pure (Smalltalk-style) objects that connects code verification to model-level reasoning about features such as subtyping, self, inheritance, and late binding. We introduce our techniques using concrete example modules that have all been verified using the Coq proof assistant and combine to fully linked verified programs using a novel, abstraction-respecting component composition rule for Verifiable C.

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Section: Discussionmentioning

confidence: 99%

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Beringer

2021

Programming Languages and Systems

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“…We would like to explore temporal specification of general, effectful programs. To do so, we wish to develop the treatment of the coinductive resumptions monad [55], that provides a general framework to reason on effectful computations, as shown by interaction trees [70]. It would be interesting to study temporal specifications we could give to effectful programs encoded in this setting.…”

Section: Discussionmentioning

confidence: 99%

Temporal Refinements for Guarded Recursive Types

Jaber

Riba

2021

Programming Languages and Systems

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We propose a logic for temporal properties of higher-order programs that handle infinite objects like streams or infinite trees, represented via coinductive types. Specifications of programs use safety and liveness properties. Programs can then be proven to satisfy their 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 $$\lambda $$ λ -calculus, a $$\lambda $$ λ -calculus with guarded recursive types. The refinements are formulae of a modal $$\mu $$ μ -calculus which embeds usual temporal modal logics such as and . 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.

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“…For starters, we need to extend F ★ with concurrency. To do this, we follow the well-known approach of encoding computational effects as definitional interpreters over free monads (Hancock and Setzer 2000;Kiselyov and Ishii 2015;Swierstra 2008;Xia et al 2019). That is, we can represent computations as a datatype of (infinitely branching) trees of atomic actions.…”

Section: Steelcore: a Concurrent Separation Logic Embedded In F ★mentioning

confidence: 99%

SteelCore: an extensible concurrent separation logic for effectful dependently typed programs

Swamy

Rastogi

Fromherz

et al. 2020

Proc. ACM Program. Lang.

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Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and program logics, extending the reasoning principles that apply within the host effectful type theory itself. Concretely, our main contribution is a semantics for concurrent separation logic (CSL) within the F ★ proof assistant in a manner that enables dependently typed, effectful F ★ programs to make use of concurrency and to be specified and verified using a full-featured, extensible CSL. In contrast to prior approaches, we directly derive the partial-correctness Hoare rules for CSL from the denotation of computations in the effectful semantics of non-deterministically interleaved atomic actions. Demonstrating the flexibility of our semantics, we build generic, verified libraries that support various concurrency constructs, ranging from dynamically allocated, storable spin locks, to protocol-indexed channels. We conclude that our effectful semantics provides a simple yet expressive basis on which to layer domainspecific languages and logics for verified, concurrent programming.

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Interaction trees: representing recursive and impure programs in Coq

Cited by 61 publications

References 61 publications

Verified Software Units

Verified Software Units

Temporal Refinements for Guarded Recursive Types

SteelCore: an extensible concurrent separation logic for effectful dependently typed programs

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