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Documents authored by Nawrocki, Wojciech

Document
DOI: 10.4230/LIPIcs.SAT.2023.6
Certified Knowledge Compilation with Application to Verified Model Counting

Authors: Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value. We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF). We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting.
Cite as

Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule. Certified Knowledge Compilation with Application to Verified Model Counting. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bryant_et_al:LIPIcs.SAT.2023.6,
  author =	{Bryant, Randal E. and Nawrocki, Wojciech and Avigad, Jeremy and Heule, Marijn J. H.},
  title =	{{Certified Knowledge Compilation with Application to Verified Model Counting}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.6},
  URN =		{urn:nbn:de:0030-drops-184685},
  doi =		{10.4230/LIPIcs.SAT.2023.6},
  annote =	{Keywords: Propositional model counting, Proof checking}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.24
An Extensible User Interface for Lean 4

Authors: Wojciech Nawrocki, Edward W. Ayers, and Gabriel Ebner

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
Contemporary proof assistants rely on complex automation and process libraries with millions of lines of code. At these scales, understanding the emergent interactions between components can be a serious challenge. One way of managing complexity, long established in informal practice, is through varying external representations. For instance, algebraic notation facilitates term-based reasoning whereas geometric diagrams invoke spatial intuition. Objects viewed one way become much simpler than when viewed differently. In contrast, modern general-purpose ITP systems usually only support limited, textual representations. Treating this as a problem of human-computer interaction, we aim to demonstrate that presentations - UI elements that store references to the objects they are displaying - are a fruitful way of thinking about ITP interface design. They allow us to make headway on two fronts - introspection of prover internals and support for diagrammatic reasoning. To this end we have built an extensible user interface for the Lean 4 prover with an associated ProofWidgets 4 library of presentation-based UI components. We demonstrate the system with several examples including type information popups, structured traces, contextual suggestions, a display for algebraic reasoning, and visualizations of red-black trees. Our interface is already part of the core Lean distribution.
Cite as

Wojciech Nawrocki, Edward W. Ayers, and Gabriel Ebner. An Extensible User Interface for Lean 4. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nawrocki_et_al:LIPIcs.ITP.2023.24,
  author =	{Nawrocki, Wojciech and Ayers, Edward W. and Ebner, Gabriel},
  title =	{{An Extensible User Interface for Lean 4}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{24:1--24:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.24},
  URN =		{urn:nbn:de:0030-drops-183991},
  doi =		{10.4230/LIPIcs.ITP.2023.24},
  annote =	{Keywords: user interfaces, human-computer interaction, Lean}
}
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