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Is it feasible (yet?) to support a (say) sophomore-level introduction to mathematical proof with an automated proof assistant such as HOL (or one of its variants), Isabelle, or Coq?

Can I find publications, pre-publications or lecture notes that introduce one or more proof assistants at a lower-division undergraduate level?

Of the many proof assistants out there, famous or not, which would promise the best experience for complete beginners?

David Feldman
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    Complete beginner, probably one of the super simple fitch / natural deduction clients. You won't be proving anything major like the integrity of a piece of software, but it will get you started. "Beginner" can mean a lot of things, how much type theory do you know? – DanielV Nov 27 '17 at 17:09
  • how much type theory do you know? Enough...but my students will know none. Mathematics department, so not directly interested in software integrity, just in establishing an objective standard about proof correctness/adequacy lest beginners find the standards too arbitrary. – David Feldman Nov 27 '17 at 22:37
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    You may find Logitext interesting, but it's probably not comprehensive enough for your purposes. – Derek Elkins left SE Nov 28 '17 at 01:42
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    Then I strongly recommend just using one of the Fitch / Natural deduction clients, other people on the site have used them. I think it is called opencourseware or something. Especially since natural deduction is practically a prerequisite for type theory. – DanielV Nov 28 '17 at 04:43

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It's definitely possible. Jeremy Avigad and two of his PhD students, Floris van Doorn and Rob Lewis, taught such a course at Carnegie Mellon aimed at freshman- and sophomore-level undergraduates. The course was an introduction to logic and proof, using the Lean proof assistant.

The lecture notes they wrote for the course can be downloaded here (HTML version here).

See also Jeremy's page, Resources for Teaching with Formal Methods, which contains lots of other resources relevant to what you're looking for.

Lean is designed with accessibility in mind. It has very readable and relatively intuitive syntax, so would be a good choice for beginners.

Clive Newstead
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