An Extensible User Interface for Lean 4

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

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

User support for software development technologies

The adoption of software development technologies is very closely related to the topic of user support. This is especially true in early phases, when the users are not familiar with the modification or the build processes of the software that has to be developed nor with the technology used for software development. This work introduces an approach to improve the usability of software development technologies represented by the Combinatory Logic Synthesizer (CL)S Framework. (CL)S is based on a type inhabitation algorithm for the combinatory logic with intersection types and aims to automatically create software components from a domain-specified repository. The framework yields a complete enumeration of all inhabitants. The inhabitation results are computed in the form of tree grammars. Unfortunately, the underlying type system allows limited application of domain-specific knowledge. To compensate for this limit, this work provides a framework for debugging intersection type specifications and filtering inhabitation results using domain-specific constraints as main aspects. The aim of the debugger is to make potentially incomplete or erroneous input specifications and decisions of the inhabitation algorithm understandable for those who are not experts in the field of type theory. The combination of tree grammars and graph theory forms the foundation of a clear representation of the computed results that informs users about the search process of the algorithm. The graphical representations are based on hypergraphs that illustrate the inhabitation in a step-wise fashion. Within the scope of this work, three filtering algorithms were implemented and investigated. The filtering algorithm integrated into the framework for user support and used for the restriction of inhabitation results is practically feasible and represents a clear improvement compared to existing approaches. It is based on modifying the tree grammars resulting from the (CL)S Framework. Additionally, the usability of the (CL)S Framework is supported by eight perspectives included in a web-based integrated development environment (IDE) that provides detailed graphical and textual information about the synthesis

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing