emmy VS tigerbeetle

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...

I'm waiting for someone to implement the Redis API by swapping out the state machine in TigerBeetle (which was built modularly such that the state machine can be swapped out).

https://tigerbeetle.com/

I fully agree with what Prime says at the end - Joran has really set a new bar here for all future database presentations.

Hearing that the entire TigerBeetle domain logic lives in a single file [0] (and is intended to be pluggable for other OLTP use cases!) makes it 1000% more tempting to spend the weekend getting up to speed with Zig.

[0] https://github.com/tigerbeetle/tigerbeetle/blob/main/src/sta...

Why would you want to build your own accounting ledger from scratch? Accounting is a completely new domain for most engineers, and TigerBeetle (https://tigerbeetle.com/) already solves this problem.

Maelstrom [1], a workbench for learning distributed systems from the creator of Jepsen, includes a simple (model-checked) implementation of Raft and an excellent tutorial on implementing it.

Raft is a simple algorithm, but as others have noted, the original paper includes many correctness details often brushed over in toy implementations. Furthermore, the fallibility of real-world hardware (handling memory/disk corruption and grey failures), the requirements of real-world systems with tight latency SLAs, and a need for things like flexible quorum/dynamic cluster membership make implementing it for production a long and daunting task. The commit history of etcd and hashicorp/raft, likely the two most battle-tested open source implementations of raft that still surface correctness bugs on the regular tell you all you need to know.

The tigerbeetle team talks in detail about the real-world aspects of distributed systems on imperfect hardware/non-abstracted system models, and why they chose viewstamp replication, which predates Paxos but looks more like Raft.

[1]: https://github.com/jepsen-io/maelstrom/

[2]: https://github.com/tigerbeetle/tigerbeetle/blob/main/docs/DE...

> There is no reason to use a memory unsafe language anymore, except legacy codebases, and that is also slowly but surely diminishing. I'm still yet to hear this amazingly compelling reason that you just need memory unsafe languages. In terms of cost/benefits analysis, memory unsafety is literally all costs.

Tell that to the authors of new memory unsafe languages (like Zig) and creators of new project in those languages (like https://tigerbeetle.com) :(