Teaching Simple Constructive Proofs with Haskell Programs. Farrugia-Roberts, M., Jeffries, B., & Søndergaard, H. In Achten, P. & Machkasova, E., editors, Trends in Functional Programming in Education (TFPIE), volume 363, of Electronic Proceedings in Theoretical Computer Science, pages 54–73, 2022.
Paper doi abstract bibtex 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.
@InProceedings{Far-Jef-Son_TFPIE21,
author = {Matthew Farrugia-Roberts and
Bryn Jeffries and
Harald S{\o}ndergaard},
title = {Teaching Simple Constructive Proofs with {Haskell} Programs},
editor = {P. Achten and E. Machkasova},
booktitle = {Trends in Functional Programming in Education (TFPIE)},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {363},
pages = {54--73},
year = {2022},
url_Paper = {https://arxiv.org/abs/2208.04699v1},
doi = {10.4204/EPTCS.363.4},
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.},
keywords = {Education, Web-based learning, Haskell},
}
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