Teaching Simple Constructive Proofs with Haskell Programs

TL;DR

This paper explores using Haskell programming exercises to teach constructive proofs in logic and formal languages, aiming to replace traditional written proofs with interactive digital assessments.

Contribution

It demonstrates how Haskell-based exercises can effectively teach constructive proofs and discusses design considerations and student responses in this digital learning approach.

Findings

Haskell exercises can target skills similar to written proofs.

Students engage actively with digital proof exercises.

The approach supports formative and summative assessment.

Abstract

In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on these mathematical topics. We have found it possible to offer almost all formative and summative assessment through an interactive learning platform, using Haskell as a lingua franca for digital exercises across our broad syllabus. One of the hardest exercises to convert into this format are traditional written proofs conveying constructive arguments. In this paper we reflect on the digitisation of this kind of exercise. We share many examples of Haskell exercises designed to target similar skills to written proof exercises across topics in propositional logic and formal languages, discussing various aspects of the design of such exercises. We also catalogue a sample of student responses to such exercises. This discussion contributes to our broader exploration of programming problems as a flexible digital medium for learning and assessment.