souffle VS mathlib

> In fact, we could have used Datalog to achieve our data goals — but that would mean we have to build our own Datalog implementation, backing data store, etc. We don’t want to do that.

Surprising that creating a whole new language made more sense then a backend. I wonder if they did a proof of concept with an existing logic system like Souffle¹ or Rel² first.

¹ https://github.com/souffle-lang/souffle

² https://relational.ai/blog/rel

Consider using Datalog (the incredible subset of Prolog) for this perfect use case. Compared to Prolog, you get:

1. Free de-duplication. No more debugging why a predicate is returning the same result more than once.

2. Commutativity. Order of predicates does not change the result. Finally, true logic programming!

3. Easy static analysis. There are many papers that describe how to do points-to analysis (and other similar techniques) with Datalog rules that fit on a single page :O

Souffle[0] is a mature Datalog that is highly performant and has many nice features. I highly recommend playing with it!

[0] https://souffle-lang.github.io

Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.

It's true that this SPARQL-inspired view of Datalog as a triplestore query language is quite a narrow interpretation compared to something closer to the academic Prolog roots like https://souffle-lang.github.io/ - what do you feel are the most important differences?

Very cool! I love the sqlite install everywhere model.

Could you compare use case with Souffle? https://souffle-lang.github.io/

I'd suggest putting the link to the docs more prominently on the github page

Is the "traditional" datalog `path(x,z) :- edge(x,y), path(y,z).` syntax not pleasant to the modern eye? I've grown to rather like it. Or is there something that syntax can't do?

I've been building a Datalog shim layer in python to bridge across a couple different datalog systems https://github.com/philzook58/snakelog (including a datalog built on top of the python sqlite bindings), so I should look into including yours

TerminusDB CTO here.

Echoing what triska said, CLP(ℤ) and friends are some of the most under-appreciated aspects of prolog implementations.

I'm amazed that programmers still don't have access to CLP when trying to do scheduling and planning solutions.

As an example in practice, what if you want to know about a transaction in which a number of entities transitively had holdings in one of the beneficiaries of the transaction at that particular time. The date window is not known, and the date windows are important in the ownership chain as well as the transactions that are being undertaken.

With CLP(FD) you can ask for a window of time, and the solution will zoom in on an appropriate time window which exists for the entire chain and match the time of the transaction.

Now try to do this query in SQL. It's almost impossibly hard.

I can't wait until I have the time to implement constraint variables for TerminusDB, but at the minute we are still working on more prosaic features.

Aside from that there are very interesting program correctness and optimisation systems which are based on prolog (usually a datalog). For instance Soufflé: https://souffle-lang.github.io

No problem :) What do you mean by voice control systems? Prolog has a bit of a learning curve and it's very difficult to write efficient code in. Although it did inspire Erlang, which is used in telecom and has some pretty interesting advantages not offered by other languages (reliance, multithreading, and updating without shutting down) Prolog is also pretty procedural, (the order you declare clauses in really really matters). There are other languages that use a much more pure for of logic Datalog: https://en.wikipedia.org/wiki/Datalog https://souffle-lang.github.io/

It's been on my mind lately as well. I was trying out `symbolics.jl` (a CAS written in Julia), and it turned out that it didn't support symbolic integration beyond simple linear functions or polynomials (at least back then, things have changed now it seems). Implementing a generic algorithm for finding integrals is hard, but I was expecting more from that CAS since this seems to be implemented in most other CASs. The thing is that every single CAS that covers general maths knowledge will have to implement the same algorithm, while it's hard to do it even once!

I feel like at least a large part of the functionality of a general purpose CAS can be written down once, and every CAS out there could benefit from it, similar to what the Language Server Protocol did for programming tools. They also had to rewrite the same tool for some language multiple times because there are lots of editors out there, and the LSP cut the time investment down a lot. They did have to invest a large amount of time to get LSP up and running, and it'll have to be maintained, but I think it's orders of magnitudes more efficient than having every tool developed and maintained for every single (programming language, editor) pair out there.

Main problem is like you said how to write down mathematical knowledge in a way that all CASs can understand it. I've been learning about Mathlib lately [0], which seems like a great starting point for this. It is as far as I know one of the first machine readable libraries of mathematical knowledge; it has a large community which has been pushing it continuously forward for years into research-level mathematics and covering the entire undergraduate maths curriculum and it's still accelerating. If some kind of protocol can be designed to read from libraries like this and turn it into CAS code, that would be a major step towards making the CAS ecosystem more sustainable I think.

It's not exactly what you were talking about, as in, this would allow multiple CASs to co-exist and benefit from each other, but I think that's better than having one massive CAS that has a monopoly. No software is perfect, but having a diverse set of choices that are open source would be more than enough to satisfy everyone.

(I have posted about this before on the Lean Zulip forum, it's open to everyone to read without an account [1])

[0] https://leanprover-community.github.io/

Kinda agree but Mathlib and its documentation makes for a big corpus to learn by example from. Not ideal but it helps.

https://github.com/leanprover-community/mathlib

https://github.com/leanprover-community/mathlib

https://1lab.dev/

You can watch the next generation, or participate, right now.

Still, there are many useful tools based on these ideas, used by programmers and mathematicians alike. What you describe sounds rather like Datalog (e.g. Soufflé Datalog), where you supply some rules and an initial fact, and the system repeatedly expands out the set of facts until nothing new can be derived. (This has to be finite, if you want to get anywhere.) In Prolog (e.g. SWI Prolog) you also supply a set of rules and facts, but instead of a fact as your starting point, you give a query containing some unknown variables, and the system tries to find an assignment of the variables that proves the query. And finally there is a rich array of theorem provers and proof assistants such as Agda, Coq, Lean, and Twelf, which can all be used to help check your reasoning or explore new ideas.

For the math that you mention, I would suggest looking at mathlib (https://github.com/leanprover-community/mathlib). I agree that the foundations of Coq are somewhat distanced from the foundations most mathematicians are trained in. Lean/mathlib might be a bit more familiar, not sure. That said, I don't see any obstacles to developing classical real analysis or linear algebra in Coq, once you've gotten used to writing proofs in it.

At this point I would go with Lean because of mathlib. Mathlib's goal is to formalize modern mathematics, so many of the theorems you would need for analysis should already be there for you.

I think about that every day. Lean's mathlib is a gigantic (with respect to this kind of project) code base and each function, each definition has a precise and rigorous natural language counterpart (in a maths book, somewhere).

It's been around since 2013, although there are LLM that interact with Lean to do automated theorem proving. Anyway, you can learn more about Lean here. I enjoyed their natural numbers game (which reminds, me I should finish the last two levels)