Programming Languages in Agda - Propositions as Types

Explore the profound connection between logic and computation in this conference talk from YOW! 2019. Delve into the Propositions as Types doctrine, which asserts that propositions correspond to types, proofs to programs, and simplification of proofs to evaluation of programs. Learn how dependently-typed programming languages like Agda exploit this concept, allowing programmers to prove properties of programming languages by simply programming their descriptions in Agda. Discover how finding complex mathematical proofs can become as straightforward and enjoyable as writing code. Get introduced to "Programming Language Foundations in Agda," a new textbook that doubles as an executable Agda script, and understand Agda's role in IOHK's cryptocurrency development. Gain insights from Philip Wadler, a professor at the University of Edinburgh, as he demonstrates how proof by induction relates to programming by recursion and explains the correspondence between logical constructs and programming concepts.