Explore advanced functional programming techniques in this conference talk from YOW! 2017. Delve into alternative approaches to domain-specific embedded languages (DSELs) for operations like root-finding, optimization, and differentiation. Learn how to give new interpretations to existing functional programs using a GHC plugin, translating code to a more generalizable form. Discover implementations for hardware circuits, automatic differentiation, incremental evaluation, and interval analysis. Follow along as the speaker demonstrates computation graphs, Haskell-to-hardware conversion, and constraint solving. Gain insights into composing interpretations and applying these concepts to various examples, enhancing your understanding of denotational design and software architecture in Haskell.