Explore the mathematical foundations of promises in C++ and their practical implementation in this comprehensive conference talk from C++Now 2017. Delve into the algebraic basis of promises and learn how to apply these concepts to develop a robust promise library. Discover the process of functional design in creating practical libraries, addressing key questions about fundamental operations for types and adapting mathematical designs to fit programming language constraints. Gain insights into purity, denotational semantics, monads, laziness, and pragmatism, with all abstract concepts thoroughly explained for audiences without a mathematical background. Walk away with a solid understanding of functional design in practice and inspiration to apply these principles in future projects. The talk covers topics such as promise operations, mathematical promise operations, promise implementation, syntax, and interfaces, as well as addressing challenges like mono state and empty promises.