emmy VS papers-we-love

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...

Papers We Love (PWL) is a community built around reading, discussing and learning more about academic computer science papers. This repository serves as a directory of some of the best papers the community can find, bringing together documents scattered across the web. You can also visit the Papers We Love site for more info.

You might find the paper Out of the Tar Pit interesting if you haven't already read it: https://github.com/papers-we-love/papers-we-love/blob/main/d...

The ideas and approaches you talk about evoked some of the concepts from that paper for me. It talks a lot about separating accidental complexity and infrastructure so you can focus only on what is essential to define your solutions.

Sure he was expecting a practical language and was designing one. Lisp was from day zero a project to implement a real programming language for a computer.

Earlier he experimented with IPL and also list processing programming on Fortran. The plan was to implement a Lisp compiler. At first the Lisp code McCarthy was experimenting with, was manually translated to machine code.

Then came up the idea to use EVAL as a base for an interpreter, which was implemented by manually translating the Lisp code to machine language. Around 1962 then a compiler followed.

https://github.com/papers-we-love/papers-we-love/blob/main/c...

I'm in a 4th camp: we should be writing our applications against a relational data model and _not_ marshaling query results into and out of Objects at all.

Elaborations on this approach:

- https://github.com/papers-we-love/papers-we-love/blob/main/d...

- https://riffle.systems/essays/prelude/

The short ask: Anyone know of any projects that bring incremental view maintenance to SQLite?

The why:

Applications are usually read heavy. It is a sad state of affairs that, for these kinds of apps, we don't put more work on the write path to allow reads to benefit.

Would the whole No-SQL movement ever even have been a thing if relational databases had great support for materialized views that updated incrementally? I'd like to think not.

And more context:

I'm working to push the state of "functional relational programming" [1], [2] further forward. Materialized views with incremental updates are key to this. Bringing them to SQLite so they can be leveraged one the frontend would solve this whole quagmire of "state management libraries." I've been solving the data-sync problem in SQLite (https://vlcn.io/) and this piece is one of the next logical steps.

If nobody knows of an existing solution, would love to collaborate with someone on creating it.

[1] - https://github.com/papers-we-love/papers-we-love/blob/main/design/out-of-the-tar-pit.pdf

Here is a great Repo on GitHub named paers-we-love. You will surely find some great papers there and also some good other resources. Hope this helps.

However, f and g are interchangeable anywhere else (this is not actually true because their addresses can be obtained and compared; showing that a C-like language retains its referential transparency despite the existence of so-called l-values was the point of what I think is the first paper to introduce the notion referential transparency to the study of programming languages: https://github.com/papers-we-love/papers-we-love/blob/main/l...)