I would say recursion (but I come from programming background so I have no idea what a proof theorist would think about my analogy).
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yes, but recursion is also for loops ;-)
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I actually introduced induction as “recursion, but for proofs” in a lecture I gave in a discrete math class last semester lmao
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how'd it work?
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When I studied PL theory and learned about structural induction I realized it was a very clean generalization of both: * induction and case analysis proofs I learned in math classes and * reasoning about functions, esp. those involving sum+product types
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yeah, esp as the natural structural induction is just a commonly useful scheme, similar to `foldl`, particularized to that algebraic type. Of course, there are myriad other induction schemes you could use, too!
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Except it's usually infinite!
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