GitHub repository for open source material related the book "Domain-Specific Languages of Mathematics" published in 2022 by College Publications.

The book and the repository are used in a BSc-level course at Chalmers and GU.

The main course homepage is in the Canvas LMS:

• Main course page including links to zoom lectures and other media
• Lecture media

Course codes: DAT326 / DIT982

• Tuesday 2022-01-18: First lecture of the 2022 course instance (zoom links, etc)
• 2022: book available from Amazon and from other sources. Bibtex entry.
• Lecture note snapshots with drafts of the full course book
• YouTube playlist with the recorded lectures from the 2021 course instance (most in Swedish, some in English)

• Main author, examiner, lecturer: Patrik Jansson (patrikj AT)
• First version (and continued support): Cezar Ionescu (cezar AT)
• Book co-author: Jean-Philippe Bernardy
• Teaching assistants:
  • 2022: Sólrún Einarsdóttir (slrn AT), David Wärn (warnd AT), and Felix Cherubini (felixche AT)
  • 2021: Maximilian Algehed (algehed AT) and Víctor López Juan (lopezv AT)
  • 2020: Sólrún Einarsdóttir (slrn AT) and Víctor López Juan (lopezv AT)
  • 2019: Maximilian Algehed (algehed AT) and Abhiroop Sarkar (sarkara AT)
  • 2018: Daniel Schoepe (schoepe AT)
  • 2017: Frederik Hanghøj Iversen (hanghj AT student) and Daniel Schoepe (schoepe AT)
  • 2016: Irene Lobo Valbuena (lobo AT)
• Project assistants: Daniel Heurlin, Sólrún Einarsdóttir, Adam Sandberg Ericsson (saadam AT)

where AT = @chalmers.se

This repository is mainly the home of the DSLsofMath book (originating from the course lecture notes), also available in print from Amazon.

Comments and contributions are always welcome – especially in the form of pull requests.

The main references are listed below.

The course presents classical mathematical topics from a computing science perspective: giving specifications of the concepts introduced, paying attention to syntax and types, and ultimately constructing DSLs of some mathematical areas mentioned below.

Learning outcomes as in the course syllabus.

• Knowledge and understanding
  • design and implement a DSL (Domain-Specific Language) for a new domain
  • organize areas of mathematics in DSL terms
  • explain main concepts of elementary real and complex analysis, algebra, and linear algebra
• Skills and abilities
  • develop adequate notation for mathematical concepts
  • perform calculational proofs
  • use power series for solving differential equations
  • use Laplace transforms for solving differential equations
• Judgement and approach
  • discuss and compare different software implementations of mathematical concepts

The course is elective for both computer science and mathematics students at both Chalmers and GU.

• Lectures
  • Introduction: Haskell, complex numbers, syntax, semantics, evaluation, approximation
  • Basic concepts of analysis: sequences, limits, convergence, ...
  • Types and mathematics: logic, quantifiers, proofs and programs, Curry–Howard, ...
    • Type classes, derivatives, differentiation, calculational proofs
  • Domain-Specific Languages and algebraic structures, algebras, homomorphisms
  • Polynomials, series, power series
  • Power series and differential equations, exp, sin, log, Taylor series, ...
  • Linear algebra: vectors, matrices, functions, bases, dynamical systems as matrices and graphs
  • Laplace transform: exp, powers series cont., solving PDEs with Laplace
• Weekly exercise sessions
  • Half time helping students solve problems in small groups
  • Half time joint problem solving at the whiteboard

The latest PDF snapshot of the book can be found in L/snapshots but please also consider buying the "real thing".

The "source code" for the chapters are in subdirectories of L/: L/01/, L/02/, etc. where chapter N is approximately course week N.

Most chapters end with weekly exercises.

(TODO: update the list to handle some reordering during 2021: In L/RecEx.md you will find a list of recommended exercises for each chapter of the lecture notes.)

Some important references:

• Thinking Functionally with Haskell, Richard Bird, Cambridge University Press, 2014 URL
• Introduction to Functional Programming Using Haskell, Richard Bird, Prentice Hall, 1998. A previous (but clearly different) version of the above.
• An Introduction to Functional Programming, Richard Bird and Phil Wadler, Prentice Hall, 1988. A previous (but clearly different) version of both of the above.

• Functional Programming for Domain-Specific Languages, Jeremy Gibbons. In Central European Functional Programming School 2015, LNCS 8606, 2015. URL

  This is currently the standard reference to DSLs for the functional programmer.

• Folding Domain-Specific Languages: Deep and Shallow Embeddings, Jeremy Gibbons and Nicolas Wu, ICFP 2014. URL

  Available at the same link: a highly recommended short version and the two videos of Jeremy presenting the most important ideas of DSLs in a very accessible way.

• Programming Languages, Mike Spivey. Lecture notes of a course given at the CS Department in Oxford. Useful material for understanding the design and implementation of embedded DSLs. URL

• Domain-Specific Languages, Martin Fowler, 2011. URL

  The view from the object-oriented programming perspective.

• Communicating Mathematics: Useful Ideas from Computer Science, Charles Wells, American Mathematical Monthly, May 1995. URL

  This article was one of the main triggers of this course.

  Short summary of the recommendations

• The Language of First-Order Logic, 3rd Edition, Jon Barwise and John Etchemendy, 1993. Out of print, but you can get it for one penny from Amazon UK. A vast improvement over its successors (as Tony Hoare said about Algol 60).

• Mathematics: Form and Function, Saunders Mac Lane, Springer 1986. An overview of the relationships between the many mathematical domains. Entertaining, challenging, rewarding. Fulltext from the library

• Functional Differential Geometry, Gerald Jay Sussman and Jack Wisdom, 2013, MIT. A book about using programming as a means of understanding differential geometry. Similar in spirit to the course, but more advanced and very different in form. An earlier version appeared as an AIM report.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.