The Science of Functional Programming (draft version)

This book is a pedagogical in-depth tutorial and reference on the functional programming paradigm. Starting from issues found in practical coding, the book builds up the theoretical intuition, knowledge, and techniques that functional programmers use for for rigorous reasoning about types and code. The book's topics include working with collections; recursive functions and types; the Curry-Howard correspondence; laws, structural analysis, and code for functors, monads, and other typeclasses; techniques of symbolic derivation and proof; parametricity theorems; and free typeclass constructions. Detailed explanations and derivations are accompanied by solved examples tested in the Scala interpreter, as well as exercises and discussions that further build upon each chapter's material. The difficulty of this book's mathematical material is at the level of high-school calculus.