This presentation was recorded at YOW! 2019. #GOTOcon #YOW https://yowcon.com

Philip Wadler - Professor at University of Edinburgh ‪@philipwadler‬

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ABSTRACT The most profound connection between logic and computation is a pun. The doctrine of Propositions as Types asserts that propositions correspond to types, proofs to programs, and simplification of proofs to evaluation of programs. The proof of a conjunction is a pair, the proof of a disjunction is a case expression, and the proof of an implication is a lambda expression. Proof by induction is just programming by #recursion.

Dependently-typed #ProgrammingLanguages, such as #Agda, exploit this pun. To prove properties of programming languages in Agda, all we need do is program a description of those languages Agda. Finding an abstruse mathematical proof becomes as simple and as fun as hacking a program. This talk introduces Programming Language Foundations in Agda, a new textbook that is also an executable #AgdaScript---and also explains the role Agda is playing in #IOHK's new cryptocurrency. [...]

RECOMMENDED BOOKS Rebecca Skinner • Effective Haskell • https://amzn.to/3SxTpwY Vitaly Bragilevsky • Haskell in Depth • https://amzn.to/3EXpmbe

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