Programming Language Theory

Learning about Programming Language Theory can be a tough journey, particularly for programming practitioners who haven't studied it formally. This resource is here to help. Please feel free to get in touch if you have ideas for improvement.

💡 Top Tips

For a quick course in Type Theory, Philip Wadler recommends: Types and Programming Languages, Proofs and Types, followed by Advanced Topics in Types and Programming Languages.

See also Daniel Gratzer's Learn Type Theory, and Darryl McAdams's So you want to learn type theory.

Type Theory

Books

• PLFA - Programming Language Foundations in Agda - Philip Wadler, Wen Kokke
• SF - Software Foundations - Benjamin C. Pierce et al. Available with jsCoq
• TAPL - Types and Programming Languages - Benjamin C. Pierce
• PROT Proofs and Types - Jean-Yves Girard, Yves Lafont and Paul Taylor - 1987-90 pdf
• PFPL - Practical Foundations for Programming Languages (Second Edition) - Robert Harper Online preview edition
• ATTAPL - Advanced Topics in Types and Programming Languages - Edited by Benjamin C. Pierce
• CPDT - Certified Programming with Dependent Types - Adam Chlipala
• SEwPR - Semantics Engineering with PLT Redex - Matthias Felleisen, Robby Findler, and Matthew Flatt. Redex
• HoTT - Homotopy Type Theory, Univalent Foundations of Mathematics
• Coq'Art Interactive Theorem Proving and Program Development, Coq'Art: The Calculus of Inductive Constructions - Yves Bertot, Pierre Castéran.
• TTFP - Type Theory and Functional Programming - Simon Thompson, 1991
• PiMLTT - Programming in Martin-Löf's Type Theory, An Introduction - Bengt Nordström, Kent Petersson, Jan M. Smith
• Using, Understanding, and Unravelling The OCaml Language — An introduction pdf
• Polymorphic typing of an algorithmic language (PhD Thesis) - Xavier Leroy pdf
• ATP - Handbook of Practical Logic and Automated Reasoning - John Harrison
• Basic Simple Type Theory - J. Roger Hindley pdf paperback@booko
• Lambda Calculus and Combinators pdf — J. Roger Hindley and Jonathan P. Seldin
• Semantics with Applications: An Appetizer — Hanne Riis Nielson, Flemming Nielson
• An Introduction to Lambda Calculi for Computer Scientists - Chris Hankin
• The Definition of Standard ML (1990) and Commentary on Standard ML (1991) definition (pdf) commentary (pdf)
• The Definition of Standard ML (Revised) - Milner, Fofte, Harper, and MacQueen
• Programs and Proofs — Ilya Sergey pdf
• Type Theory and Formal Proof: An Introduction — Rob Nederpelt, Herman Geuvers
• Lectures on the Curry-Howard Isomorphism (pdf)
• Program = Proof — Samuel Mimram pdf

Papers

• A Tutorial Implementation of a Dependently Typed Lambda Calculus — Andres Löh, Conor McBride and Wouter Swierstra pdf. Previously published as Simply Easy.
• ΠΣ: Dependent Types without the Sugar - Thorsten Altenkirch, Nils Anders Danielsson, Andres Löh, and Nicolas Oury
• Lambda Calculi with Types — Henk Barendregt
• Intuitionistic Type Theory
• Type Theory - Thierry Coquand

Videos

• OPLSS — Oregon Programming Language Summer School
  • OPLSS 2023 — Types, Semantics, and Logic
  • OPLSS 2022 — Types, Semantics, and Program Reasoning
  • OPLSS 2021 — Foundations of Programming and Security
  • OPLSS 2019 — Foundations of Probabilistic Programming and Security
  • OPLSS 2018 — Parallelism and Concurrency
  • OPLSS 2017 — A Spectrum of Types
  • OPLSS 2016 — Types, Logic, Semantics, and Verification
  • OPLSS 2015 — Types, Logic, Semantics, and Verification
  • OPLSS 2014 — Types, Logic, Semantics, and Verification
  • OPLSS 2013 — Types, Logic, and Verification
  • OPLSS 2012 — Logic, Languages, Compilation, and Verification
  • OPLSS 2011 — Types, Semantics and Verification
  • OPLSS 2010 — Logic, Languages, Compilation, and Verification
  • Complete archives 2002-Present
• HoTTEST — Homotopy Type Theory Summer School 2022
• ICFP 2012 Monday keynote. Conor McBride: Agda-curious?

Subtopics

• [Higher Type Theory]({{site.github.url | replace: 'http://', '//'}}/higher-type-theory/)
• [Module Systems]({{site.github.url | replace: 'http://', '//'}}/module-systems/)
• [Effect Systems]({{site.github.url | replace: 'http://', '//'}}/effect-systems/)

Programming Languages

Books

• DCPL - Design Concepts in Programming Languages – Franklyn Turbak and David Gifford, 2008. Course
• CTM - Concepts, Techniques, and Models of Computer Programming, Peter Van Roy and Seif Haridi
• EOPL - Essentials of Programming Languages, 3rd Edition - Daniel P. Friedman
• PLAI - Programming Languages: Application and Interpretation - Shriram Krishnamurthi
• PAIP Paradigms of Artificial Intelligence Programming: Case Studies in Common Lisp - Peter Norvig, 1992
• PLP Programming Language Pragmatics - Michael L. Scott
• FSPL The Formal Semantics of Programming Languages - Glynn Winskel
• PL:BPC Programming Languages: Build, Prove, and Compare - Norman Ramsey

Papers

• An argument against call/cc — Oleg Kiselyov

Compiler Construction

Books

• MinCaml - A Crash Course for the MinCaml Compiler
• MCIiML Modern Compiler Implementation in ML - Andrew W. Appel
• pj-lester-book Implementing functional languages: a tutorial - Simon Peyton Jones and David Lester, 1992
• slpj-book-1987 - The Implementation of Functional Programming Languages - Simon Peyton Jones - 1987
• MCD-2e Modern Compiler Design, Second Edition — Dick Grune et al.
• EaC-2e Engineering a Compiler, 2nd Edition, Cooper and Torczon
• Compiler Construction, Niklaus Wirth
• DragonBook - "The Dragon Book" Compilers: Principles, Techniques, and Tools
• LiSP - Lisp in Small Pieces - Christian Queinnec
• CwC Compiling with Continuations - Andrew W. Appel
• Static Program Analysis, Anders Møller and Michael I. Schwartzbach
• List of compiler books at the GCC Wiki

Papers

• An Incremental Approach to Compiler Construction, Abdulaziz Ghuloum
• A Nanopass Framework for Compiler Education, Dipanwita Sarkar, Oscar Waddell, R. Kent Dybvig
• A Nanopass Framework for Commercial Compiler Development, Andrew W. Keep
• ZINC - The ZINC experiment, an economical implementation of the ML language - Xavier Leroy (Technical Report) more OCaml papers

Videos

• Stanford - Compilers - Alex Aiken

Runtime systems

Books

• The Garbage Collection Handbook, The Art of Automatic Memory Management — Richard Jones, Antony Hosking, Eliot Moss, 2011.

Papers

• Debunking the 'Expensive Procedure Call' Myth, or, Procedure Call Implementations Considered Harmful, or, Lambda: The Ultimate GOTO — Guy Lewis Steele, Jr. (1977) pdf

Functional Programming

Books

• Bird and Wadler - Introduction to Functional Programming, 1st Edition - Bird and Wadler
• AoP - The Algebra of Programming - Richard Bird, Oege de Moor
• Programming in Haskell — Graham Hutton (2007)
• RWH - Real World Haskell - Bryan O'Sullivan, Don Stewart, and John Goerzen
• FPiS - Functional Programming in Scala - Paul Chiusano and Rúnar Bjarnason
• SICP, Structure and Interpretation of Computer Programs, by Abelson, Sussman, and Sussman
• PCPH - Parallel and Concurrent Programming in Haskell - Simon Marlow
• RWOC - Real World OCaml - Jason Hickey, Anil Madhavapeddy, and Yaron Minsky
• Developing Applications With OCaml — Emmanuel Chailloux, Pascal Manoury and Bruno Pagano (2000)
• BTLS - The Little Schemer - Daniel P. Friedman, Matthias Felleisen
• BTSS - The Seasoned Schemer - Daniel P. Friedman, Matthias Felleisen
• BTML - The Little MLer - Matthias Felleisen, Daniel P. Friedman
• The Reasoned Schemer and miniKanren
• HTDP - How to Design Programs - Matthias Felleisen, Robert Findler, Matthew Flatt, Shriram Krishnamurthi
• HR - The Haskell Road to Logic, Maths and Programming - 2nd Ed. - Kees Doets, Jan van Eijck pdf
• A Book of Abstract Algebra - 2nd Ed. - Charles C. Pinter booko
• Purely Functional Data Structures - Chris Okasaki phd-thesis in pdf paperback@booko More purely functional data structures

Papers

• Lambda Papers - Lambda: The Ultimate Imperative/Declarative/GOTO - Guy Steele and Gerald Sussman
• The Lambda Calculus - Jesse Alama and Johannes Korbacher
• A Tutorial Introduction to the Lambda Calculus - Raul Rojas
• Exploring Generic Haskell (PhD thesis) - Andres Löh. This an epic, accessible, book-length PhD on datatype generic programming.
• ICFP accepted papers
  • 2019
  • 2018, video playlist
  • 2017, video playlist
  • 2016, video playlist
  • 2015, by session, video playlist
  • 2014
  • 2013
  • 2012

Videos

• C9 Lectures: Dr. Erik Meijer - Functional Programming Fundamentals
• C9 Lectures: Dr. Ralf Lämmel - Going Bananas + Advanced Functional Programming
• Datatype-Generic Programming in Haskell - Andres Löh - slides in pdf

Category Theory

Philip Wadler's advice here is "read Pierce for motivation, Mac Lane for the presentation of the maths".

Books

• Cakes, Custard and Category Theory: Easy recipes for understanding complex maths — Eugenia Cheng
• Category Theory, Steve Awodey. pdf course
• Basic Category Theory for Computer Scientists - Benjamin C. Pierce. Previously available in a draft entitled A taste of category theory for computer scientists
• Categories for the Working Mathematician — Saunders Mac Lane
• Conceptual Mathematics A First Introduction to Categories, 2nd Edition - F. William Lawere and Stephen H. Schanuel
• Category Theory for the Sciences — David I. Spivak. Previously available in a draft entitled Category Theory for Scientists
• CTCS-2nd Category Theory for Computing Science - Michael Barr and Charles Wells CTCS-1st
• Categories, Types, and Structures: An Introduction to Category Theory for the Working Computer Scientist pdf
• Topoi, The Categorical Analysis of Logic, Robert Goldblatt Amazon
• TTT - Toposes, Triples and Theories - Michael Barr and Charles Wells
• Category Theory Lectures Notes for ESSLLI - Michael Barr and Charles Wells pdf
• Seven Sketches in Compositionality: An Invitation to Applied Category Theory - Brendan Fong, David I Spivak
• Applied Category Theory Course - online course conducted by John Baez forum
• CTFP - Category Theory for Programmers - Bartosz Milewski. The free PDF version was created by Igal Tabachnik. Video lectures based on this material: part 1, part 2, part 3.
• CT4P Category Theory for Programming — Benedikt Ahrens, Kobe Wullaert

Journals

• TAC - Theory and Applications of Categories

Subtopics

• [Recursion Schemes]({{site.github.url | replace: 'http://', '//'}}/category-theory/recursion-schemes.html)

Mathematics

Some related maths resources.

Mathematical Literacy/Thinking

It can be useful to have some background in mathematical thinking.

• Introduction to Mathematical Thinking — Keith Devlin
• How to prove it — Daniel J. Velleman

Algebra

• A Computational Introduction to Number Theory and Algebra — Victor Shoup
• Advanced Modern Algebra — Joseph J. Rotman pdf
• A Survey of Modern Algebra — Birkhoff and MacLane Scribd

Other collections

• Great Works in Programming Languages — Benjamin Piece
• Classic Papers in Programming Languages and Logic — Karl Crary
• The collected works of Per Martin-Löf — Michael Thompson and others
• PLT Texts Online — Frank Atanassow
• Functional programming books overview — Alex (Alexey) Ott
• TypeFunc — William Demeo
• Lambda the Ultimate — Ehud Lamm et al.
• Archives of Lambda the Ultimate (stale but includes "classic") — Chris Rathman
• Programming Language People — Chris Rathman
• PL Summer Schools forall — Aggelos Biboudis
• Summer Schools Interesting Conferences — Bengt Jonsson
• The Programming Language Zoo — Andrej Bauer