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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 programming languages, 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 Agda script---and also explains the role Agda is playing in IOHK's new cryptocurrency.
The textbook can be found here.
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Philip Wadler has contributed to the designs of Haskell, Java, and XQuery, and is a co-author of XQuery from the Experts (Addison Wesley, 2004) and Generics and Collections in Java (O'Reilly, 2006).