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None of that was even the abstract stuff. It is all models of sizes, order, and inclusion (integers, cardinals, ordinals, sets). Not the nastier abstractions of
by jmount 1y ago
None of that was even the abstract stuff. It is all models of sizes, order, and inclusion (integers, cardinals, ordinals, sets). Not the nastier abstractions of partial orders, associativity, composition and so on (lattices, categories, ...).
- lambdasquirrel 1y agoAnd yet it all circles back. We used Peano arithmetic when doing C++ template metaprogramming anytime a for loop from 0..n was needed. It was fun and games as long as you didn't make a mistake because the compiler errors would be gnarly. The Haskell people still do stuff like this, and I wouldn't be surprised if someone were doing it in Scala's type system as well. Also, the PLT people are using lattices and categories to formalize their work.