Verified Textbook Algorithms

Nipkow, Tobias; Eberl, Manuel; Haslbeck, Maximilian P. L.

doi:10.1007/978-3-030-59152-6_2

Cited by 13 publications

(7 citation statements)

References 139 publications

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“…There is a large panel of work on the verification of data structures and algorithms. Nipkow et al [2020] present a survey that focuses on verified textbook algorithms. Here, we highlight a few results, so as to give an idea of the kind of data structures that state-ofthe-art program verification tools can handle.…”

Section: Verification Of Data Structuresmentioning

confidence: 99%

Specification and verification of a transient stack

Moine

Charguéraud

Pottier

2022

Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs

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A transient data structure is a package of an ephemeral data structure, a persistent data structure, and fast conversions between them. We describe the specification and proof of a transient stack and its iterators. This data structure is a scaleddown version of the general-purpose transient sequence data structure implemented in the OCaml library Sek. Internally, it relies on fixed-capacity arrays, or chunks, which can be shared between several ephemeral and persistent stacks. Dynamic tests are used to determine whether a chunk can be updated in place or must be copied: a chunk can be updated if it is uniquely owned or if the update is monotonic. Using CFML, which implements Separation Logic with Time Credits inside Coq, we verify the functional correctness and the amortized time complexity of this data structure. Our verification effort covers iterators, which involve direct pointers to internal chunks. The specification of iterators describes what the operations on iterators do, how much they cost, and under what circumstances an iterator is invalidated.

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Section: Verification Of Data Structuresmentioning

confidence: 99%

Specification and verification of a transient stack

Moine

Charguéraud

Pottier

2022

Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs

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“…We are not aware of any textbooks for teaching logic using the Isabelle proof assistant, but textbooks on formalizing a number of other computer science topics exist, like the book on programming language semantics [24,29] or functional algorithms [26][27][28]. These books show that the proof assistant Isabelle/HOL can be used for teaching semantics, algorithms and data structures.…”

Section: Related Workmentioning

confidence: 99%

Using Isabelle in Two Courses on Logic and Automated Reasoning

Villadsen¹,

Jacobsen²

2021

Formal Methods Teaching

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We present our experiences teaching two courses on formal methods and detail the contents of the courses and their positioning in the curriculum. The first course is a bachelor course on logical systems and logic programming, with a focus on classical first-order logic and automatic theorem proving. The second course is a master course on automated reasoning, with a focus on classical higher-order logic and interactive theorem proving. The proof assistant Isabelle is used in both courses, using Isabelle/Pure as well as Isabelle/HOL. We describe our online tools to be used with Isabelle/HOL, in particular the Sequent Calculus Verifier (SeCaV) and the Natural Deduction Assistant (NaDeA). We also describe our innovative Students' Proof Assistant which is formally verified in Isabelle/HOL and integrated in Isabelle/jEdit using Isabelle/ML.

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“…A methodology with notable success in developing provably correct software involves the use of interactive theorem provers (ITPs). Success stories of the use of ITPs to develop trustworthy software include a formally verified OS kernel (Klein et al 2009), a verified compiler for C (Leroy 2009), and verified implementations of a multitude of algorithms (Nipkow, Eberl, and Haslbeck 2020).…”

Section: Introductionmentioning

confidence: 99%

Formally Verified Solution Methods for Markov Decision Processes

Schäffeler,

Abdulaziz

2023

AAAI

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We formally verify executable algorithms for solving Markov decision processes (MDPs) in the interactive theorem prover Isabelle/HOL. We build on existing formalizations of probability theory to analyze the expected total reward criterion on finite and infinite-horizon problems. Our developments formalize the Bellman equation and give conditions under which optimal policies exist. Based on this analysis, we verify dynamic programming algorithms to solve tabular MDPs. We evaluate the formally verified implementations experimentally on standard problems, compare them with state-of-the-art systems, and show that they are practical.

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Verified Textbook Algorithms

Cited by 13 publications

References 139 publications

Specification and verification of a transient stack

Specification and verification of a transient stack

Using Isabelle in Two Courses on Logic and Automated Reasoning

Formally Verified Solution Methods for Markov Decision Processes

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