Related papers: Easyprove: a tool for teaching precise reasoning
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
Often user interfaces of theorem proving systems focus on assisting particularly trained and skilled users, i.e., proof experts. As a result, the systems are difficult to use for non-expert users. This paper describes a paper and pencil HCI…
This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE…
We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…
Formal verification tools are often developed by experts for experts; as a result, their usability by programmers with little formal methods experience may be severely limited. In this paper, we discuss this general phenomenon with…
With the widespread consumption of AI-generated content, there has been an increased focus on developing automated tools to verify the factual accuracy of such content. However, prior research and tools developed for fact verification treat…
Formal methods yet advantageous, face challenges towards wide acceptance and adoption in software development practices. The major reason being presumed complexity. The issue can be addressed by academia with a thoughtful plan of teaching…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
We discuss the idea that computers might soon help mathematicians to prove theorems in areas where they have not previously been useful. Furthermore we argue that these same computer tools will also help us in the communication and teaching…
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…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
In AI-rich higher education, polished written mathematics has become easier to produce than trustworthy evidence of understanding. This article develops a human-scale methodology for service mathematics, with informatics as its main running…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have…
Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…
Proof Blocks is a software tool which enables students to write proofs by dragging and dropping prewritten proof lines into the correct order. These proofs can be graded completely automatically, enabling students to receive rapid feedback…
"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
PyLog is a minimal experimental proof assistant based on linearised natural deduction for intuitionistic and classical first-order logic extended with a comprehension operator. PyLog is interesting as a tool to be used in conjunction with…