The Basis is an exploration of pure declarative programming and reasoning in Swift. It by no means contains idiomatic code, but is instead intended to be a repository for structures and ideas grounded in theory and mathematics. Present in this repository are the necessary components to handle system interaction, control, data flow, and a number of extensions and improvements to the Swift Standard Library and its structures. Higher-level APIs and structures are generally excluded from the Basis to be implemented in other libraries. Swift provides an excellent opportunity to not just witness, but actually understand the formalization of many seemingly "complex" and abstract algebraic structures without having to learn Haskell or ML or any of the other famous FP languages. The documentation of types in this repository serves as a way to deserialize a lot of the complex terms and jargon you may come across in these languages. In this way, the Basis can be regarded as an encyclopedia of common techniques and practices rather than a simple tutorial. As such, if the documentation is too dense or unreadable, it means this library is failing one of its unit tests! Clarification or rewrites of documentation to serve the broader community are a priority and a promise.