Domain-Specific Languages of Mathematics
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
News
- 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 collecting the 2022 lectures (all in English)
- Also available: the recorded lectures from the 2021 course instance (most in Swedish, some in English).
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Contributors
- 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
Course material
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.
Objectives
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.
Course setup
- 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
Lectures
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.
Exercises
Most chapters end with weekly exercises.
In L/RecEx.md you will find a list of recommended exercises for each chapter of the lecture notes.
Exams
The exams + solutions are available under the Exam/ subdirectory: for example 2016-Practice/, 2016-03/, 2016-08/, 2017-03/, 2017-08/, 2018-03/, 2018-08/, 2019-03/, 2019-08/, 2020-03/, 2020-08/, 2021-03/, 2021-08/.
References
Some important references:
Functional programming
- 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.
DSLs
-
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.
The computer science 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.
Mathematics
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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).
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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.
License: CC-BY-NC-SA 4.0
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
