Pat Hanrahan · A reading guide
How the way we write changes
the way we think.
Follow the talk into the classroom: lecture slides, domain-specific languages, and the ideas behind expressive, executable mathematics.
sum [1, 3 .. 2*n - 1] == n*nStart with the ideas.
Representations and cognition, SETL, Iverson’s APL/K, mathematical notation, Haskell, and Agda.
Open lecture slidesThe talk that prompted this collection. Explore the relationship between mathematical notation and programming languages.
Watch on YouTubeAn earlier version of the lecture, from representation effects and number scrabble to executable mathematics.
Open lecture slidesHanrahan on macros, staged programming with Terra, functors, and dependent types. The companion lecture on building languages.
Open lecture slidesThe classroom reference begins at 5:11 in the talk . Video source: the RacketCon 2026 program.
The wider context.
Programming models for scientific computing, data science, and machine learning. Topics include dense and sparse computation, the separation of algorithms from schedules, and compiler construction.
An earlier DSL course taught by Pat Hanrahan, Jonathan Ragan-Kelley, and Zach DeVito, with Gilbert Bernstein as TA. Public materials include slides, example code, readings, and assignment descriptions covering Lua, Terra, Halide, intermediate representations, and macros.
Some assignment repositories and reference solutions require course access.
Two readings assigned with “Notation.”
The case for combining the strengths of mathematical notation with executable programming languages.
A history of mathematical notation and a discussion of its possibilities in computational systems.
Iverson’s paper: free HTML edition at Jsoftware · ACM publication record .