Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.Comment: 26 page

Deep Understanding of Technical Documents : Automated Generation of Pseudocode from Digital Diagrams & Analysis/Synthesis of Mathematical Formulas

The technical document is an entity that consists of several essential and interconnected parts, often referred to as modalities. Despite the extensive attention that certain parts have already received, per say the textual information, there are several aspects that severely under researched. Two such modalities are the utility of diagram images and the deep automated understanding of mathematical formulas. Inspired by existing holistic approaches to the deep understanding of technical documents, we develop a novel formal scheme for the modelling of digital diagram images. This extends to a generative framework that allows for the creation of artificial images and their annotation. We contribute on the field with the creation of a novel synthetic dataset and its generation mechanism. We propose the conversion of the pseudocode generation problem to an image captioning task and provide a family of techniques based on adaptive image partitioning. We address the mathematical formulas’ semantic understanding by conducting an evaluating survey on the field, published in May 2021. We then propose a formal synthesis framework that utilized formula graphs as metadata, reaching for novel valuable formulas. The synthesis framework is validated by a deep geometric learning mechanism, that outsources formula data to simulate the missing a priori knowledge. We close with the proof of concept, the description of the overall pipeline and our future aims

On the Effect of Semantically Enriched Context Models on Software Modularization

Many of the existing approaches for program comprehension rely on the linguistic information found in source code, such as identifier names and comments. Semantic clustering is one such technique for modularization of the system that relies on the informal semantics of the program, encoded in the vocabulary used in the source code. Treating the source code as a collection of tokens loses the semantic information embedded within the identifiers. We try to overcome this problem by introducing context models for source code identifiers to obtain a semantic kernel, which can be used for both deriving the topics that run through the system as well as their clustering. In the first model, we abstract an identifier to its type representation and build on this notion of context to construct contextual vector representation of the source code. The second notion of context is defined based on the flow of data between identifiers to represent a module as a dependency graph where the nodes correspond to identifiers and the edges represent the data dependencies between pairs of identifiers. We have applied our approach to 10 medium-sized open source Java projects, and show that by introducing contexts for identifiers, the quality of the modularization of the software systems is improved. Both of the context models give results that are superior to the plain vector representation of documents. In some cases, the authoritativeness of decompositions is improved by 67%. Furthermore, a more detailed evaluation of our approach on JEdit, an open source editor, demonstrates that inferred topics through performing topic analysis on the contextual representations are more meaningful compared to the plain representation of the documents. The proposed approach in introducing a context model for source code identifiers paves the way for building tools that support developers in program comprehension tasks such as application and domain concept location, software modularization and topic analysis