Right, domain theory and denotational semantics let you talk about ⊥ in an order-theoretic setting, and I think it's also rich in connections between topology a

Right, domain theory and denotational semantics let you talk about ⊥ in an order-theoretic setting, and I think it's also rich in connections between topology and lambda calculus. Though it might be the case that if functors already pose a pedagogical conundrum for programmers, Scott-continuity might be even harder to get across. A quote from Bauer's post is particularly relevant: > [I am arguing against] the fact that some people find it acceptable to defend broken mathematics on the grounds that it is useful. Non-broken mathematics is also useful, as well as correct. Good engineers do not rationalize broken math by saying “life is tough”.