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Explore how types can guide and automate software implementation through pure logical reasoning in this 23-minute conference talk from Lambda Days 2025. Discover how type signatures can provide sufficient information to automatically derive fully verified code using the Curry-Howard correspondence, without relying on machine learning approaches. Learn about the logical process through recursion schemes, where proof search spaces unfold from initial proof sequents and term extraction emerges from folding over proof trees. Understand how hylomorphisms provide brute-force algorithms for finite search spaces, while specialized traversals handle other algorithmic requirements. Gain insights into practical implementation using Scala 3 macros and the tagless-final approach to bring these coalgebraic techniques into real-world development workflows.
