Imperative Functional Programming with Isabelle/HOL

Bulwahn, Lukas; Krauß, Alexander; Haftmann, Florian; Erkök, Levent; Matthews, John

doi:10.1007/978-3-540-71067-7_14

Cited by 71 publications

(60 citation statements)

References 15 publications

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“…both types and constants. 10 This paper, which presents a clean syntactic argument for consistency, is a culmination of previous efforts by Wenzel [48], Obua [38], ourselves [26,28], and many other Isabelle designers and developers.…”

Section: Conclusion and Related Workmentioning

confidence: 98%

“…It is being used in major verification projects, such as the seL4 operating system kernel [24]. In addition, Isabelle/HOL is a framework for certified programming: functional programming (including lazy (co)programming [9]) is supported natively and imperative programming is supported via a monadic extension [10]. Programs can be written and verified in Isabelle/HOL, and efficient code for them (in Haskell, Standard ML, OCaml and Scala) can be produced using a code generator [19].…”

Section: Introductionmentioning

confidence: 99%

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Comprehending Isabelle/HOL’s Consistency

KunăźAr¹,

Popescu²

2017

Programming Languages and Systems

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Abstract. The proof assistant Isabelle/HOL is based on an extension of HigherOrder Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means-following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs.

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Section: Conclusion and Related Workmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Comprehending Isabelle/HOL’s Consistency

KunăźAr¹,

Popescu²

2017

Programming Languages and Systems

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“…The final step leads into the heap-monad of Imperative HOL [22], which supports imperative data structures. Here, the Sepref tool [6] replaces functional by imperative data structures and generates a refinement theorem automatically.…”

Section: Listing 11 Cyclicity Checkermentioning

confidence: 99%

Verified Model Checking of Timed Automata

Wimmer

Lammich

2018

Lecture Notes in Computer Science

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Abstract. We have constructed a mechanically verified prototype implementation of a model checker for timed automata, a popular formalism for modeling real-time systems. Our goal is two-fold: first, we want to provide a reference implementation that is fast enough to check other model checkers against it on reasonably sized benchmarks; second, we strive for maximal feature compatibility with the state-of-the-art tool Uppaal. The starting point of our work is an existing highly abstract formalization of reachability checking of timed automata. We reduce checking of Uppaal-style models to the problem of model checking a single automaton in this abstract formalization, while retaining the ability to perform on the fly model-checking. Using the Isabelle Refinement Framework, the abstract specification of the model checker is refined, via multiple intermediate steps, to an actual imperative implementation in Standard ML. The resulting tool is evaluated on a set of standard benchmarks to demonstrate its practical usability.

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“…ACL2 (Kaufmann and Moore 1997) does not support higher-order logic or higherorder functional programming. Bulwahn et al (2008) describe a system for encoding and verifying impure monadic programs in Isabelle/HOL. Their implementation does not support storing functions in the heap.…”

Section: Related Workmentioning

confidence: 99%

Effective interactive proofs for higher-order imperative programs

Chlipala

Malecha

Morrisett

et al. 2009

Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming

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We present a new approach for constructing and verifying higherorder, imperative programs using the Coq proof assistant. We build on the past work on the Ynot system, which is based on Hoare Type Theory. That original system was a proof of concept, where every program verification was accomplished via laborious manual proofs, with much code devoted to uninteresting low-level details. In this paper, we present a re-implementation of Ynot which makes it possible to implement fully-verified, higher-order imperative programs with reasonable proof burden. At the same time, our new system is implemented entirely in Coq source files, showcasing the versatility of that proof assistant as a platform for research on language design and verification.Both versions of the system have been evaluated with case studies in the verification of imperative data structures, such as hash tables with higher-order iterators. The verification burden in our new system is reduced by at least an order of magnitude compared to the old system, by replacing manual proof with automation. The core of the automation is a simplification procedure for implications in higher-order separation logic, with hooks that allow programmers to add domain-specific simplification rules.We argue for the effectiveness of our infrastructure by verifying a number of data structures and a packrat parser, and we compare to similar efforts within other projects. Compared to competing approaches to data structure verification, our system includes much less code that must be trusted; namely, about a hundred lines of Coq code defining a program logic. All of our theorems and decision procedures have or build machine-checkable correctness proofs from first principles, removing opportunities for tool bugs to create faulty verifications.

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Imperative Functional Programming with Isabelle/HOL

Cited by 71 publications

References 15 publications

Comprehending Isabelle/HOL’s Consistency

Comprehending Isabelle/HOL’s Consistency

Verified Model Checking of Timed Automata

Effective interactive proofs for higher-order imperative programs

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