Related papers: On Exams with the Isabelle Proof Assistant
Interactive theorem provers are complex systems that require sophisticated platform efforts - and hence systems programming environments - to manage effectively. The Isabelle platform exemplifies this with its Isabelle/Scala systems…
In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to…
Teaching assistants (TAs) are essential to grading and feedback provision in proof-based courses, yet these tasks are time-intensive and difficult to scale. Although Large Language Models (LLMs) have been studied for grading and feedback,…
A Forensic Lucid intensional programming language has been proposed for intensional cyberforensic analysis. In large part, the language is based on various predecessor and codecessor Lucid dialects bound by the higher-order intensional…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
In recent years, large language models have greatly improved in their ability to perform complex multi-step reasoning. However, even state-of-the-art models still regularly produce logical mistakes. To train more reliable models, we can…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Worked examples are step-by-step solutions to problems in a specific domain, offered to students to acquire domain-specific problem-solving skills. The effectiveness of worked examples could be enhanced by combining them with…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
We present a formalisation of finite Markov decision processes with rewards in the Isabelle theorem prover. We focus on the foundations required for dynamic programming and the use of reinforcement learning agents over such processes. In…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
In recent years the effectiveness of interactive theorem provers has increased to an extent that the bottleneck in the interactive process shifted to efficiency: while in principle large and complex theorems are provable (effectiveness), it…
Large language models (LLMs) can act as evaluators, a role studied by methods like LLM-as-a-Judge and fine-tuned judging LLMs. In the field of education, LLMs have been studied as assistant tools for students and teachers. Our research…
Grading exams is an important, labor-intensive, subjective, repetitive, and frequently challenging task. The feasibility of autograding textual responses has greatly increased thanks to the availability of large language models (LLMs) such…
We conducted a systematic literature review on automated grading and feedback tools for programming education. We analysed 121 research papers from 2017 to 2021 inclusive and categorised them based on skills assessed, approach, language…
In this paper, we investigate the potential of the Boyer-Moore waterfall model for the automation of inductive proofs within a modern proof assistant. We analyze the basic concepts and methodology underlying this 30-year-old model and…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
Analytical reasoning is an essential and challenging task that requires a system to analyze a scenario involving a set of particular circumstances and perform reasoning over it to make conclusions. In this paper, we study the challenge of…