Agda

Verified Functional Programming in Agda

Agda is an advanced programming language based on Type Theory. Agda's type system is expressive enough to support full functional verification of programs, in two styles. In external verification, we write pure functional programs and then write proofs of properties about them. The proofs are separate external artifacts, typically using structural induction. In internal verification, we specify properties of programs through rich types for the programs themselves. This often necessitates including proofs inside code, to show the type checker that the specified properties hold. The power to prove properties of programs in these two styles is a profound addition to the practice of programming, giving programmers the power to guarantee the absence of bugs, and thus improve the quality of software more than previously possible. Verified Functional Programming in Agda is the first book to provide a systematic exposition of external and internal verification in Agda, suitable for undergraduate students of Computer Science. No familiarity with functional programming or computer-checked proofs is presupposed. The book begins with an introduction to functional programming through familiar examples like booleans, natural numbers, and lists, and techniques for external verification. Internal verification is considered through the examples of vectors, binary search trees, and Braun trees. More advanced material on type-level computation, explicit reasoning about termination, and normalization by evaluation is also included. The book also includes a medium-sized case study on Huffman encoding and decoding.

Mastering Agda

"Mastering Agda: A Practical Guide to Dependently Typed Programming and Formal Verification" serves as an essential resource for developers and researchers looking to harness the full potential of Agda's advanced type system. This book meticulously covers the foundations of dependently typed programming, introducing readers to Agda's unique capabilities as both a programming language and a proof assistant. Through detailed chapters, it guides learners from basic installations to crafting complex, verified programs, emphasizing Agda’s strength in providing robust guarantees about code correctness. With a structured approach, the book delves into the core components of Agda, including inductive types, pattern matching, and dependent types, while also exploring interfacing with other languages for broader applicability. Practical examples and case studies demonstrate Agda's application in fields like cryptography, formal algorithm verification, and industrial software development. By combining theoretical insights with real-world applications, "Mastering Agda" equips readers with the knowledge and skills to improve software reliability and explore innovative programming paradigms through formal methods.

40 Pieces Selected by Agda Skjerne