SeCaV: A Sequent Calculus Verifier in Isabelle/HOL

Self Cite

We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems and understanding of proofs in the higher-order logic of Isabelle/HOL in particular. The use of Isabelle enables almost automatic grading of large parts of the exam. We explain our approach through a number of example problems, and explain why we believe that each of the kinds of problems we have selected are adequate measures of our intended learning outcomes. Finally, we discuss our experiences using the approach for the exam of a course on automated reasoning and suggest potential future work.

Section: Natural Deduction and Sequent Calculus Proofsmentioning

confidence: 99%

On Exams with the Isabelle Proof Assistant

Jacobsen

Villadsen

2023

Self Cite

“…Many purpose-built proof assistants designed for learning specific topics have been developed, including Jape [37,38], ProofWeb [17], SPA [31], SeCaV [15] and NaDeA [40][41][42].…”

Section: Using Proof Assistants In Educationmentioning

confidence: 99%

“…• Proof assistants are useful for teaching mathematics [2,4,10,11,17] • Proof assistants are useful for teaching functional programming [4,5,17,18,21,26] • Proof assistants are useful for teaching logic [2,4,5,8,15,17,18,21,26,34,36,41] • Proof assistants are useful for teaching abstract thinking [4,11,34,36] • Proof assistants make the rules of formal reasoning clear [2,4,11] • Proof assistants help students learn how to structure proofs [4,5,8,10,11,17,19,21,31] • Students are helped by instant feedback on their proofs [2, 4, 8, 10-12, 15, 21, 26] • Proof competence gained using a proof assistant transfers to pen-and-paper [2,12,26,34] • Proof assistants help students fix their proof errors as early as possible [4,11] • Proof assistants make it easier for stude...…”

Section: Claimed Benefits and Drawbacks Of Using Proof Assistants In ...mentioning

confidence: 99%

ProofBuddy: A Proof Assistant for Learning and Monitoring

Karsten,

Jacobsen,

Eiken

et al. 2023

Self Cite

Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and the ascertainment of whether proofs, especially the students' own, are complete and correct. Many authors have suggested using proof assistants to assist in teaching proof competence, but the efficacy of the approach is unclear. To improve the state of affairs, we introduce PROOFBUDDY: a web-based tool using the Isabelle proof assistant which enables researchers to conduct studies of the efficacy of approaches to using proof assistants in education by collecting fine-grained data about the way students interact with proof assistants. We have performed a preliminary usability study of PROOFBUDDY at the Technical University of Denmark. Related WorkThis section covers work related to PROOFBUDDY, by which we mean not only descriptions of superficially similar tools, but also the articles and studies that have motivated the development of PROOFBUDDY, and the tools from similar fields that have inspired its design. We will cover a selection of reports on

“…That formalization is here expanded to higher-order logic, and thereby also first-order logic. In contrast to some other Isabelle formalizations of proof systems [6,14], which are developed in the complex Isabelle/HOL, we give a theory built directly on the fundamental Isabelle/Pure theory. Our formalization can therefore be viewed as an alternative (though very minimal) logical foundation to Isabelle/HOL.…”

Section: Introductionmentioning

confidence: 99%

Teaching Higher-Order Logic Using Isabelle

Lund,

Villadsen

2024

Self Cite

We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good introduction for someone looking into learning about higherorder logic and proof assistants, without having to study the much more complex Isabelle/HOL with heavier automation. To showcase our development and approach we explain a sample proof, describe the axioms and rules of our higher-order logic, and discuss our experience with teaching the subject in a classroom setting.