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.
Teaching Simple Constructive Proofs with Haskell Programs [link]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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