For those who like proof assistants, this is cool: https://nextjournal.com/zampino/latte-cantor
Proving Cantor's Theorem in Clojure Using LaTTe *LaTTe* <https://github.com/latte-central/LaTTe>* is a Lisp proof assistant based on the typed lambda calculus **System-F* <https://en.wikipedia.org/wiki/System_F>*. It is written in Clojure and exposes a powerful DSL for expressing the basic terms of mathematical reasoning: definitions, axioms, theorems, and proofs. In this short article we're showing how LaTTe can prove — ad absurdum of course — the well known Cantor inequality using the diagonal method. In words, given a type T, there have to be strictly more sets (predicates) over T than inhabitants of T itself. This not hard to prove on paper, indeed **just three lines* <https://en.wikipedia.org/wiki/Cantor%27s_theorem#Proof>*, but it's awesome to see how LaTTe verifies the natural logical steps to obtain the very same proof.* - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
