Alignment-based Translations Across Formal Systems Using Interface Theories

Müller, Dennis; Rothgang, Colin; Liu, Yuanyuan; Rabe, Florian

doi:10.4204/eptcs.262.7

Cited by 4 publications

(4 citation statements)

References 19 publications

(14 reference statements)

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“…In [Kaliszyk and Pak, 2019], declarative proof outlines are exported from Mizar to Isabelle/Isar. The work in [Müller et al, 2017] share our motivation of contributing to building large libraries of mathematics.…”

Section: Discussionmentioning

confidence: 99%

Leveraging the Information Contained in Theory Presentations

Carette

Farmer

Sharoda

2020

Lecture Notes in Computer Science

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Building a large library of mathematical knowledge is a complex and labour-intensive task. By examining current libraries of mathematics, we see that the human effort put in building them is not entirely directed towards tasks that need human creativity.Instead, a non-trivial amount of work is spent on providing definitions that could have been mechanically derived.In this work, we propose a generative approach to library building, so definitions that can be automatically derived are computed by meta-programs. We focus our attention on libraries of algebraic structures, like monoids, groups, and rings. These structures are highly inter-related and their commonalities have been well-studied in universal algebra. We use theory presentation combinators to build a library of algebraic structures. Definitions from universal algebra and programming languages meta-theory are used to derive library definitions of constructions, like homomorphisms and term languages, from algebraic theory presentations. The result is an interpreter that, given 227 theory expressions, builds a library of over 5000 definitions. This library is, then, exported to Agda and Lean.iii To my family, You are my greatest blessing iv I would like to express my sincere thanks to my supervisors Dr. Jacques Carette and Dr. William Farmer for their continuous support to my learning journey. Your expertise and feedback were invaluable in shaping this research direction and throughout my studies. I learned from you a lot about how to do research and communicate it. I

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Section: Discussionmentioning

confidence: 99%

Leveraging the Information Contained in Theory Presentations

Carette

Farmer

Sharoda

2020

Lecture Notes in Computer Science

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“…In order to streamline the process of building the translations S → I and I → T , the concept of alignments was developed [KKMR16]. An alignment between two symbols c and c ′ in different libraries captures that translations should try to translate objects with c to objects with head d. Both exact manual efforts [MRLR17] and machine learning-based heuristic approaches were used to find alignments across formal libraries. The latter includes alignment from six proof assistants [GK19], showing that such alignments allow both conjecturing and more powerful automation [GK15].…”

Section: Interchange Librariesmentioning

confidence: 99%

A Survey of Languages for Formalizing Mathematics

Kaliszyk¹,

Rabe²

2020

Preprint

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In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce human-readable documents. These goals are challenging to combine and state-of-the-art tools typically have to make difficult compromises.In this paper we discuss languages that have been created for this purpose, including logical languages of proof assistants and other formal systems, semi-formal languages, intermediate languages for exchanging mathematical knowledge, and language frameworks that allow building customized languages.We evaluate their advantages based on our experience in designing and applying languages and tools for formalizing mathematics. We reach the conclusion that no existing language is truly good enough yet and derive ideas for possible future improvements.

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“…These alignments are currently produced and curated manually using the approach, repository, and syntax described in [Mül+17b;Mül+17a]. In the future, we will also consider automatically extracting alignments from the existing ad-hoc SageMath-to-X translations.…”

Section: Alignmentsmentioning

confidence: 99%

“…This two-step translation has been implemented in [Mül+17a] based on the MMT system [Rab13 ; MMT], which implements the OMDoc/MMT format along with logical and knowledge management algorithms.…”

Section: Mitm-based Distributed Computationmentioning

confidence: 99%

Knowledge-Based Interoperability for Mathematical Software Systems

Kohlhase¹,

Feo²,

Müller³

et al. 2017

Mathematical Aspects of Computer and Information Sciences

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Abstract. There is a large ecosystem of mathematical software systems. Individually, these are optimized for particular domains and functionalities, and together they cover many needs of practical and theoretical mathematics. However, each system specializes on one particular area, and it remains very difficult to solve problems that need to involve multiple systems. Some integrations exist, but the are ad-hoc and have scalability and maintainability issues. In particular, there is not yet an interoperability layer that combines the various systems into a virtual research environment (VRE) for mathematics. The OpenDreamKit project aims at building a toolkit for such VREs. It suggests using a central system-agnostic formalization of mathematics (Math-in-the-Middle, MitM) as the needed interoperability layer. In this paper, we report on a case study that instantiates the MitM paradigm the systems GAP, SageMath, and Singular to perform computation in group and ring theory. Our work involves massive practical efforts, including a novel formalization of computational group theory, improvements to the involved software systems, and a novel mediating system that sits at the center of a star-shaped integration layout between mathematical software systems.

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Alignment-based Translations Across Formal Systems Using Interface Theories

Cited by 4 publications

References 19 publications

Leveraging the Information Contained in Theory Presentations

Leveraging the Information Contained in Theory Presentations

A Survey of Languages for Formalizing Mathematics

Knowledge-Based Interoperability for Mathematical Software Systems

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