Church encodings

Church encoding is a way to represent data and functions using only pure functions in the lambda calculus. It encodes basic data types like numbers and booleans as functions that operate on other functions, allowing computation without built-in data types. For example, numbers (like zero, one, two) are represented by functions that apply other functions a specific number of times, and booleans (true, false) are functions selecting between options. This approach demonstrates that all data and operations can be constructed solely through function application, highlighting the expressive power of functions in computing systems.