debug-trace-var VS emmy

> Can you give me an example of a Haskell expression which isn't reverentially transparent (without unsafePerformIO)?

Yes: https://github.com/ncaq/debug-trace-var The trick, however, is not unsafePerformIO (destructive mutability has nothing to do with referential transparency in general) but with TemplateHaskell, as quoting has everything to do with referential transparency.

> But the bog standard FP definition is a real and useful concept.

Actually, it's rather tautological. It defines FP circularly (see my comment here: https://news.ycombinator.com/item?id=36152488). It says nothing more than the far more useful explanation: "the meaning of every expression is a value".

I'm a senior level programmer who recently became interested in furthering my math education.

I also just became aware of computational algebra systems like emmy: https://github.com/mentat-collective/emmy

My question is: is there an interactive math curriculum/textbook/etc that uses such a system to teach the math? I would find that a lot more engaging than learning math the old way!

This library bring these capabilities to Clojure:

https://github.com/mentat-collective/emmy

It's based on an older library for Scheme, by Sussman.

Of course! And referencing your other comment, during the ~2 year period I've been working on Emmy (on top of work by Colin Smith), I was keen to make the implementation more accessible and well-documented than the original.

There's still not a great map of the project (from primitives to general relativity), but many of the namespaces are written as literate programming explorations: https://emmy.mentat.org/#explore-the-project

Here's the automatic differentiation implementation/essay, for example: https://sritchie.github.io/emmy/src/emmy/differential.html

A rough sketch of the tower is:

- `emmy.value` and `emmy.generic` implement the extensible generic operations

- `emmy.ratio`, `emmy.complex` and `emmy.numbers` fleshes out the numeric tower

- `emmy.expression` and `emmy.abstract.number` add support for symbolic literals

Next we need an algebraic simplifier...

- `emmy.pattern.{match,rule,syntax} give us a pattern matching language

- `emmy.simplify.rules` adds a ton of simplification rules, out of which

- `emmy.simplify` builds a simplification engine

Actually the simplifier has three parts... the first two start in `emmy.rational-function` and `emmy.polynomial` and involve converting an expression into either a polynomial or a rational function and then back out, putting them into "canonical form" in the process. That will send you down the rabbit hole of polynomial GCD etc...

And on and on! I'm happy to facilitate any code reading journey you go on or chat about Emmy or the original scmutils, feel free to write at sam [at] mentat.org, or else visit the Discord I run for the project at https://discord.gg/hsRBqGEeQ4.

> You can get a feel for how unergonomic this is by avoiding the use of all arithmetic operators in your code and instead forcing yourself to use user defined plus(a,b), minus(a,b), assign(a,b), etc, or programming directly with the C blas api.

You've dramatically overstated your case, since that's true of every Lisp-like language.

Lisp is a perfectly suitable language for developing mathematics in, see SICM [0] for details.

If you want to see SICM in action, Emmy [1] is a Clojure project that ported SICM to both Clojure and Clerk notebooks (like Jupyter notebooks, but better for programmers).

[0] https://mitpress.mit.edu/9780262028967/structure-and-interpr...

[1] https://emmy.mentat.org/

Here's some Clojure code I wrote for the Emmy computer algebra system that implements polynomial interpolation with a few different algorithms described in Numerical Recipes:

https://github.com/mentat-collective/emmy/blob/main/src/emmy...

I discovered while writing this that I could express each of these algorithms as folds that consumed a stream of points, accumulating a progressively higher order polynomial.

Here's the same sort of thing but for rational function interpolation: https://github.com/mentat-collective/emmy/blob/main/src/emmy...