12 Search Results for "Lammich, Peter"

Document
DOI: 10.4230/LIPIcs.ITP.2026.27
Fractional Separation Logic in Isabelle LLVM

Authors: Peter Lammich

Published in: LIPIcs, Volume 382, 17th International Conference on Interactive Theorem Proving (ITP 2026)

Abstract
We present a shallow embedding of fractional separation logic in Isabelle/HOL, based on fractional separation algebras with unbounded fractions. To support flexible ownership splitting and recombination, we use nominal labels that enable systematic distribution and collection of fractional permissions across separating conjunctions. The logic is integrated into a verification condition generator that automates substantial parts of fraction arithmetic and label reasoning, significantly reducing manual proof effort. As a backend, we connect the framework to Isabelle LLVM, enabling the verification of executable LLVM code. As a case study, we verify a parallel matrix-vector multiplication. The example illustrates recursive reasoning, parallel writes to disjoint segments of the result vector, and shared read access to the input vector via fractional permissions.
Cite as

Peter Lammich. Fractional Separation Logic in Isabelle LLVM. In 17th International Conference on Interactive Theorem Proving (ITP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 382, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lammich:LIPIcs.ITP.2026.27,
  author =	{Lammich, Peter},
  title =	{{Fractional Separation Logic in Isabelle LLVM}},
  booktitle =	{17th International Conference on Interactive Theorem Proving (ITP 2026)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-436-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{382},
  editor =	{Komendantskaya, Ekaterina and Nipkow, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2026.27},
  URN =		{urn:nbn:de:0030-drops-270016},
  doi =		{10.4230/LIPIcs.ITP.2026.27},
  annote =	{Keywords: Fractional Separation Logic, LLVM, verification, Isabelle}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.2
A Formal Analysis of Algorithms for Matroids and Greedoids

Authors: Mohammad Abdulaziz, Thomas Ammer, Shriya Meenakshisundaram, and Adem Rimpapa

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a formal analysis, in Isabelle/HOL, of optimisation algorithms for matroids, which are useful generalisations of combinatorial structures that occur in optimisation, and greedoids, which are a generalisation of matroids. Although some formalisation work has been done earlier on matroids, our work here presents the first formalisation of results on greedoids, and many results we formalise in relation to matroids are also formalised for the first time in this work. We formalise the analysis of a number of optimisation algorithms for matroids and greedoids. We also derive from those algorithms executable implementations of Kruskal’s algorithm for computing optimal spanning trees, an algorithm for maximum cardinality matching for bi-partite graphs, and Prim’s algorithm for computing minimum weight spanning trees.
Cite as

Mohammad Abdulaziz, Thomas Ammer, Shriya Meenakshisundaram, and Adem Rimpapa. A Formal Analysis of Algorithms for Matroids and Greedoids. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abdulaziz_et_al:LIPIcs.ITP.2025.2,
  author =	{Abdulaziz, Mohammad and Ammer, Thomas and Meenakshisundaram, Shriya and Rimpapa, Adem},
  title =	{{A Formal Analysis of Algorithms for Matroids and Greedoids}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{2:1--2:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.2},
  URN =		{urn:nbn:de:0030-drops-246012},
  doi =		{10.4230/LIPIcs.ITP.2025.2},
  annote =	{Keywords: Matroids, Greedoids, Combinatorial Optimisation, Graph Algorithms, Isabelle/HOL, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.35
Verifying an Efficient Algorithm for Computing Bernoulli Numbers

Authors: Manuel Eberl and Peter Lammich

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The Bernoulli numbers B_k are a sequence of rational numbers that is ubiquitous in mathematics, but difficult to compute efficiently (compared to e.g. approximating π). In 2008, Harvey gave the currently fastest known practical way for computing them: his algorithm computes B_k mod p in time O(p log^{1 + o(1)} p). By doing this for O(k) many small primes p in parallel and then combining the results with the Chinese Remainder Theorem, one recovers the value of B_k as a rational number in O(k² log^{2 + o(1)} k) time. One advantage of this approach is that the expensive part of the algorithm is highly parallelisable and has very low memory requirements. This algorithm still holds the world record with its computation of B_{10⁸}. We give a verified efficient LLVM implementation of this algorithm. This was achieved by formalising the necessary mathematical background theory in Isabelle/HOL, proving an abstract version of the algorithm correct, and refining this abstract version down to LLVM using Lammich’s Isabelle-LLVM framework, including many low-level optimisations. The performance of the resulting LLVM code is comparable with Harvey’s original unverified and hand-optimised C++ implementation.
Cite as

Manuel Eberl and Peter Lammich. Verifying an Efficient Algorithm for Computing Bernoulli Numbers. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eberl_et_al:LIPIcs.ITP.2025.35,
  author =	{Eberl, Manuel and Lammich, Peter},
  title =	{{Verifying an Efficient Algorithm for Computing Bernoulli Numbers}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.35},
  URN =		{urn:nbn:de:0030-drops-246331},
  doi =		{10.4230/LIPIcs.ITP.2025.35},
  annote =	{Keywords: Bernoulli numbers, LLVM, verification, Isabelle, Chinese remainder theorem, modular arithmetic, Montgomery arithmetic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.26
Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL

Authors: Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.
Cite as

Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli. Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lachnitt_et_al:LIPIcs.ITP.2025.26,
  author =	{Lachnitt, Hanna and Fleury, Mathias and Barbosa, Haniel and Jakpor, Jibiana and Andreotti, Bruno and Reynolds, Andrew and Schurr, Hans-J\"{o}rg and Barrett, Clark and Tinelli, Cesare},
  title =	{{Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.26},
  URN =		{urn:nbn:de:0030-drops-246243},
  doi =		{10.4230/LIPIcs.ITP.2025.26},
  annote =	{Keywords: interactive theorem proving, proof assistants, Isabelle/HOL, SMT, certification, proof certificates, proof reconstruction, proof automation}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.21
Practically Feasible Proof Logging for Pseudo-Boolean Optimization

Authors: Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Certifying solvers have long been standard for decision problems in Boolean satisfiability (SAT), allowing for proof logging and checking with very limited overhead, but developing similar tools for combinatorial optimization has remained a challenge. A recent promising approach covering a wide range of solving paradigms is pseudo-Boolean proof logging, but this has mostly consisted of proof-of-concept works far from delivering the performance required for real-world deployment. In this work, we present an efficient toolchain based on VeriPB and CakePB for formally verified pseudo-Boolean optimization. We implement proof logging for the full range of techniques in the state-of-the-art solvers RoundingSat and Sat4j, including core-guided search and linear programming integration with Farkas certificates and cut generation. Our experimental evaluation shows that proof logging and checking performance in this much more expressive paradigm is now quite close to the level of SAT solving, and hence is clearly practically feasible.
Cite as

Wietze Koops, Daniel Le Berre, Magnus O. Myreen, Jakob Nordström, Andy Oertel, Yong Kiam Tan, and Marc Vinyals. Practically Feasible Proof Logging for Pseudo-Boolean Optimization. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 21:1-21:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koops_et_al:LIPIcs.CP.2025.21,
  author =	{Koops, Wietze and Le Berre, Daniel and Myreen, Magnus O. and Nordstr\"{o}m, Jakob and Oertel, Andy and Tan, Yong Kiam and Vinyals, Marc},
  title =	{{Practically Feasible Proof Logging for Pseudo-Boolean Optimization}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{21:1--21:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.21},
  URN =		{urn:nbn:de:0030-drops-238825},
  doi =		{10.4230/LIPIcs.CP.2025.21},
  annote =	{Keywords: proof logging, certifying algorithms, combinatorial optimization, certification, pseudo-Boolean solving, 0-1 integer linear programming}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.32
Efficient Certified Reasoning for Binarized Neural Networks

Authors: Jiong Yang, Yong Kiam Tan, Mate Soos, Magnus O. Myreen, and Kuldeep S. Meel

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Neural networks have emerged as essential components in safety-critical applications - these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is constrained to a Boolean value; they are particularly well-suited for safety-critical tasks because they retain much of the computational capacities of full-scale (floating-point or quantized) deep neural networks, but remain compatible with satisfiability solvers for qualitative verification and with model counters for quantitative reasoning. However, existing methods for BNN analysis suffer from either limited scalability or susceptibility to soundness errors, which hinders their applicability in real-world scenarios. In this work, we present a scalable and trustworthy approach for both qualitative and quantitative verification of BNNs. Our approach introduces a native representation of BNN constraints in a custom-designed solver for qualitative reasoning, and in an approximate model counter for quantitative reasoning. We further develop specialized proof generation and checking pipelines with native support for BNN constraint reasoning, ensuring trustworthiness for all of our verification results. Empirical evaluations on a BNN robustness verification benchmark suite demonstrate that our certified solving approach achieves a 9× speedup over prior certified CNF and PB-based approaches, and our certified counting approach achieves a 218× speedup over the existing CNF-based baseline. In terms of coverage, our pipeline produces fully certified results for 99% and 86% of the qualitative and quantitative reasoning queries on BNNs, respectively. This is in sharp contrast to the best existing baselines which can fully certify only 62% and 4% of the queries, respectively.
Cite as

Jiong Yang, Yong Kiam Tan, Mate Soos, Magnus O. Myreen, and Kuldeep S. Meel. Efficient Certified Reasoning for Binarized Neural Networks. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 32:1-32:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{yang_et_al:LIPIcs.SAT.2025.32,
  author =	{Yang, Jiong and Tan, Yong Kiam and Soos, Mate and Myreen, Magnus O. and Meel, Kuldeep S.},
  title =	{{Efficient Certified Reasoning for Binarized Neural Networks}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{32:1--32:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.32},
  URN =		{urn:nbn:de:0030-drops-237665},
  doi =		{10.4230/LIPIcs.SAT.2025.32},
  annote =	{Keywords: Neural network verification, proof certification, SAT solving, approximate model counting}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.24
Refinement of Parallel Algorithms down to LLVM

Authors: Peter Lammich

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
We present a stepwise refinement approach to develop verified parallel algorithms, down to efficient LLVM code. The resulting algorithms' performance is competitive with their counterparts implemented in C/C++. Our approach is backwards compatible with the Isabelle Refinement Framework, such that existing sequential formalizations can easily be adapted or re-used. As case study, we verify a parallel quicksort algorithm, and show that it performs on par with its C++ implementation, and is competitive to state-of-the-art parallel sorting algorithms.
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Peter Lammich. Refinement of Parallel Algorithms down to LLVM. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lammich:LIPIcs.ITP.2022.24,
  author =	{Lammich, Peter},
  title =	{{Refinement of Parallel Algorithms down to LLVM}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.24},
  URN =		{urn:nbn:de:0030-drops-167333},
  doi =		{10.4230/LIPIcs.ITP.2022.24},
  annote =	{Keywords: Isabelle, Concurrent Separation Logic, Parallel Sorting, LLVM}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ITP.2021.3
Bounded-Deducibility Security (Invited Paper)

Authors: Andrei Popescu, Thomas Bauereiss, and Peter Lammich

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We describe Bounded-Deducibility (BD) security, an expressive framework for the specification and verification of information-flow security. The framework grew by confronting concrete challenges of specifying and verifying fine-grained confidentiality properties in some realistic web-based systems. The concepts and theorems that constitute this framework have an eventful history of such "confrontations", often involving trial and error, which are reported in previous papers. This paper is the first to focus on the framework itself rather than the case studies, gathering in one place all the abstract results about BD security.
Cite as

Andrei Popescu, Thomas Bauereiss, and Peter Lammich. Bounded-Deducibility Security (Invited Paper). In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{popescu_et_al:LIPIcs.ITP.2021.3,
  author =	{Popescu, Andrei and Bauereiss, Thomas and Lammich, Peter},
  title =	{{Bounded-Deducibility Security}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.3},
  URN =		{urn:nbn:de:0030-drops-138982},
  doi =		{10.4230/LIPIcs.ITP.2021.3},
  annote =	{Keywords: Information-flow security, Unwinding proof method, Compositionality, Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.11
A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

Authors: Julian Brunner, Benedikt Seidl, and Salomon Sickert

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We present a formalisation of the unified translation approach from linear temporal logic (LTL) to omega-automata from [Javier Esparza et al., 2018]. This approach decomposes LTL formulas into "simple" languages and allows a clear separation of concerns: first, we formalise the purely logical result yielding this decomposition; second, we develop a generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction for deterministic Rabin automata (DRA). We extract from this particular instantiation an executable tool translating LTL to DRAs. To the best of our knowledge this is the first verified translation of LTL to DRAs that is proven to be double-exponential in the worst case which asymptotically matches the known lower bound.
Cite as

Julian Brunner, Benedikt Seidl, and Salomon Sickert. A Verified and Compositional Translation of LTL to Deterministic Rabin Automata. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{brunner_et_al:LIPIcs.ITP.2019.11,
  author =	{Brunner, Julian and Seidl, Benedikt and Sickert, Salomon},
  title =	{{A Verified and Compositional Translation of LTL to Deterministic Rabin Automata}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.11},
  URN =		{urn:nbn:de:0030-drops-110664},
  doi =		{10.4230/LIPIcs.ITP.2019.11},
  annote =	{Keywords: Automata Theory, Automata over Infinite Words, Deterministic Automata, Linear Temporal Logic, Model Checking, Verified Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.20
Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL

Authors: Maximilian P. L. Haslbeck and Peter Lammich

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
Separation Logic with Time Credits is a well established method to formally verify the correctness and run-time of algorithms, which has been applied to various medium-sized use-cases. Refinement is a technique in program verification that makes software projects of larger scale manageable. Combining these two techniques for the first time, we present a methodology for verifying the functional correctness and the run-time analysis of algorithms in a modular way. We use it to verify Kruskal’s minimum spanning tree algorithm and the Edmonds - Karp algorithm for network flow. An adaptation of the Isabelle Refinement Framework [Lammich and Tuerk, 2012] enables us to specify the functional result and the run-time behaviour of abstract algorithms which can be refined to more concrete algorithms. From these, executable imperative code can be synthesized by an extension of the Sepref tool [Lammich, 2015], preserving correctness and the run-time bounds of the abstract algorithm.
Cite as

Maximilian P. L. Haslbeck and Peter Lammich. Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{haslbeck_et_al:LIPIcs.ITP.2019.20,
  author =	{Haslbeck, Maximilian P. L. and Lammich, Peter},
  title =	{{Refinement with Time - Refining the Run-Time of Algorithms in Isabelle/HOL}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.20},
  URN =		{urn:nbn:de:0030-drops-110754},
  doi =		{10.4230/LIPIcs.ITP.2019.20},
  annote =	{Keywords: Isabelle, Time Complexity Analysis, Separation Logic, Program Verification, Refinement, Run Time, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.22
Generating Verified LLVM from Isabelle/HOL

Authors: Peter Lammich

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We present a framework to generate verified LLVM programs from Isabelle/HOL. It is based on a code generator that generates LLVM text from a simplified fragment of LLVM, shallowly embedded into Isabelle/HOL. On top, we have developed a separation logic, a verification condition generator, and an LLVM backend to the Isabelle Refinement Framework. As case studies, we have produced verified LLVM implementations of binary search and the Knuth-Morris-Pratt string search algorithm. These are one order of magnitude faster than the Standard-ML implementations produced with the original Refinement Framework, and on par with unverified C implementations. Adoption of the original correctness proofs to the new LLVM backend was straightforward. The trusted code base of our approach is the shallow embedding of the LLVM fragment and the code generator, which is a pretty printer combined with some straightforward compilation steps.
Cite as

Peter Lammich. Generating Verified LLVM from Isabelle/HOL. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lammich:LIPIcs.ITP.2019.22,
  author =	{Lammich, Peter},
  title =	{{Generating Verified LLVM from Isabelle/HOL}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.22},
  URN =		{urn:nbn:de:0030-drops-110777},
  doi =		{10.4230/LIPIcs.ITP.2019.22},
  annote =	{Keywords: Isabelle/HOL, LLVM, Separation Logic, Verification Condition Generator, Code Generation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.23
Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra

Authors: Peter Lammich and Tobias Nipkow

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
The starting point of this paper is a new, purely functional, simple and efficient data structure combining a search tree and a priority queue, which we call a priority search tree. The salient feature of priority search trees is that they offer a decrease-key operation, something that is missing from other simple, purely functional priority queue implementations. As two applications of this data structure we verify purely functional, simple and efficient implementations of Prim’s and Dijkstra’s algorithms. This constitutes the first verification of an executable and even efficient version of Prim’s algorithm.
Cite as

Peter Lammich and Tobias Nipkow. Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lammich_et_al:LIPIcs.ITP.2019.23,
  author =	{Lammich, Peter and Nipkow, Tobias},
  title =	{{Proof Pearl: Purely Functional, Simple and Efficient Priority Search Trees and Applications to Prim and Dijkstra}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.23},
  URN =		{urn:nbn:de:0030-drops-110788},
  doi =		{10.4230/LIPIcs.ITP.2019.23},
  annote =	{Keywords: Priority queue, Dijkstra’s algorithm, Prim’s algorithm, verification, Isabelle}
}
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