Programming Language Fundamentals in Agda
Quick read
An online book that teaches programming language theory using the Agda proof assistant. It guides readers through logical foundations, operational and denotational semantics, and includes exercises and code in a GitHub repository.
- Step-by-step chapters from naturals to denotational semantics
- Includes Agda code and encourages GitHub pull requests
- Lists courses and alternative formalizations (Arend, Lean 4)
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A closer look at Programming Language Fundamentals in Agda
What this book is
Programming Language Fundamentals in Agda is a textbook that introduces programming language theory while using the proof assistant Agda. The site presents the book split into three parts: Logical Foundations, Programming Language Foundations, and Denotational Semantics.
Each part is broken into focused chapters such as natural numbers and induction, lambda calculus and typing properties, and denotational semantics with soundness and adequacy results.
What you can do on the site
Read a structured textbook that mixes programming-language theory with machine-checked Agda developments. The table of contents lists chapters and topics you can navigate to, including proofs and code snippets.
Find pointers to related projects: a version with code rewritten in Arend and a Lean 4 reimplementation covering parts of the book. The repository for the book is on GitHub and the authors welcome comments and pull requests; there is also a private repository of answers to selected questions available on request from the authors.
Who will find it useful
Students and teachers of programming languages who want a treatment that uses Agda for formal development. The site lists many instructors and courses that have used the textbook, indicating it is suitable as a course text.
Researchers or readers interested in machine-checked proofs of standard PL results (progress, preservation, confluence, denotational soundness and adequacy) and in seeing code worked out in a proof assistant.
Questions people ask about Programming Language Fundamentals in Agda
- Can I contribute or report errors?
- Yes - the authors ask for comments on organisation, missing material, explanations, exercises, errors and typos, and they encourage pull requests via the book repository on GitHub.
- Is there worked-out solution material?
- There is a private repository of answers to selected questions; you need to contact one of the authors to request access.
- Are there versions in other proof assistants?
- Yes - the site mentions PLFArend, with code rewritten in Arend, and PLFaLean, with proofs implemented in Lean 4 covering parts of the book.
Programming Language Fundamentals in Agda was shared on NexURLs by Nexis on October 20, 2026, in Tech & AI.
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Quick answers
What is Programming Language Fundamentals in Agda?
Programming Language Fundamentals in Agda (plfa.github.io): An online book that teaches programming language theory using the Agda proof assistant. It guides readers through logical foundations, operational and denotational semantics, and includes exercises and code in a GitHub repository.
Who shared Programming Language Fundamentals in Agda on NexURLs?
It was shared by Nexis in October 2026. Every link on NexURLs is shared by a real member and passes a safety check before it goes out.
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