Hello, as a compiler engineer I am interested in this area. Can you expand a little bit more? How would I be able to plug in my own language for example?

> So for example, you could write a program, then write an x86-specific optimization for one function which you can then prove correct with respect to the more abstract program specification.

So, what you are saying is that catgrad alllows me to write a program and then also plug in a compiler pass? I.e., the application author can also be the compiler developer?

One thing is that you can think of static analysis as building facts about the program. You can for example start by assuming nothing and then adding facts about the program. And you need to iteratively propagate these facts from one line of code to the next. But you can also start by assuming the universe and removing facts from this universe.

Some classes of program analysis are safe to stop early. For example, if I have a static analysis that tries to find the target of virtual calls (also known as a devirtualization), you can stop early after a time out. Not finding the target just implies a missed optimization.

There are some other classes of program analysis that are not safe until the algorithm finishes. For example, if you have to prove that two variables do not alias each other, you cannot stop until you have all possible points-to sets and verify that for each of those two variables, their points-to sets do not overlap.

So, given the above restriction, the first class (early termination) is perhaps more desirable and throwing more compute time would yield a better approximation. For the second one, it wouldn't.

Another thing to keep in mind is that most of these data flow frameworks are not easily parallelized. The only paper I've read (but I haven't kept up with these avenue of research) that implemented a control flow analysis in the GPU is the following:

* Prabhu, Tarun, et al. "EigenCFA: Accelerating flow analysis with GPUs." ACM SIGPLAN Notices 46.1 (2011): 511-522.

I'm sure people are working on it. (I should mention that there are some program analyses written in Datalog and Datalog can be parallelized, but I think this is a processor based parallelization and not a GPU one).

The third thing is that when you say whether we are limited by algorithms or compute, I think it is important to note that it is impossible to find all possible facts *precisely* about a program without running it. There is some relation between static program analysis and the halting problem. We want to be able to guarantee termination of our static program analysis and some facts are just unobtainable without running. However, there is not just static program analyses, but also dynamic program analyses which can analyze a program as it is running. An example of a dynamic program analysis can be value profiling. Imagine that you have a conditional and for 99% of the time, the conditional is false. With a virtual machine, you can add some instrumentation to find out the probability distribution of this conditional and then generate code without this condition, optimize the code, and only if the condition is false then run a less optimized version of the code with an additional penalty. Some virtual machines already do this for types and values. Type profiling and value profiling.

One last thing, when you say a meaningful performance boost, it depends on your code. If your code can be folded away completely at compile time, then yes, we could just generate the solution at compile time and that's it. But if it doesn't or parts of it cannot be folded away / the facts cannot be used to optimize the code, then no matter how much you search, you cannot optimize it statically.

Compilers are awesome :)

As an addendum, it might be desirable in the future to have a repository of analyzed code. Compilers right now are re-analyzing code on every single compile and not sharing their results across the web. It is a fantasy of mine to have a repository that maps some code with equivalent representations and every time one does a local compile it explores a new area and adds it to the repository. Essentially, each time you compile the code, it explores new potential optimizations and all of them get stored online.

  * Nandi, Chandrakana, et al. "Rewrite rule inference using equality saturation." Proceedings of the ACM on Programming Languages 5.OOPSLA (2021): 1-28.
  * Pal, Anjali, et al. "Equality Saturation Theory Exploration à la Carte." Proceedings of the ACM on Programming Languages 7.OOPSLA2 (2023): 1034-1062.

Thanks for sharing! Really exciting stuff!

  * Kam, John B., and Jeffrey D. Ullman. "Monotone data flow analysis frameworks." Acta informatica 7.3 (1977): 305-317.
  * Reps, Thomas, Susan Horwitz, and Mooly Sagiv. "Precise interprocedural dataflow analysis via graph reachability." Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages. 1995.
  * Sagiv, Mooly, Thomas Reps, and Susan Horwitz. "Precise interprocedural dataflow analysis with applications to constant propagation." TAPSOFT'95: Theory and Practice of Software Development: 6th International Joint Conference CAAP/FASE Aarhus, Denmark, May 22–26, 1995 Proceedings 20. Springer Berlin Heidelberg, 1995.
  * Reps, Thomas, et al. "Weighted pushdown systems and their application to interprocedural dataflow analysis." Science of Computer Programming 58.1-2 (2005): 206-263.
  * Späth, Johannes, Karim Ali, and Eric Bodden. "Context-, flow-, and field-sensitive data-flow analysis using synchronized pushdown systems." Proceedings of the ACM on Programming Languages 3.POPL (2019): 1-29.

  * Points-to Analysis
  * Abstract Interpretation
  * On demand dataflow analyses

Check his other research. Some of it is highly accessible via youtube videos. I recommend watching / reading:

  * Stabilizer
  * Mesh
  * Scalene

https://egg-smol-python.readthedocs.io/en/latest/

Native integration with Datalog.

Many times, I find myself working on a program and I realize that what I need is a database. But having a database, even sqlite3 or Berkely DB, would be an overkill. If I could just express my data and the relationships between them, then I would be able to query what I need in an efficient way.

I perhaps have not had a long professional life working with compilers (5+ years), but to me the definition of "compiles to binary" is too restrictive. The main things I care for in my work are:

1. To be able to perform some sort of static analysis on the program 2. To be able to transform the program representation

To other commenters: in Python, we have two program representations. The human readable string representation and the bytecode representation. The syntactical errors are a kind of static analysis. To me, the maps between the Python string representation and the bytecode representation and the classes of errors we can catch without running the program is far more interesting than pigeon-holing Python in the "compiled" or "interpreted" hole.

http://dataphys.org/list/gaudis-hanging-chain-models/

Definitely not an expert, just excited to have more tools on which to work with graph data!

[0] Graph Embeddings - Neo4J. Talk by Alicia Frame. https://www.youtube.com/watch?v=oQPCxwmBiWo

* Predicting the color of a node in a graph, could be used for example speculative devirtualization.

* Predicting edges weight could give us a better estimate of hot basic blocks statically.

* Running performance experiments is as easy as running the benchmark and introducing some metric of performance which you can give back to the GNN to learn from.

Imagine also for debugging and IDEs. I haven't played with copilot, but I imagine that something like guessing the graph based on node labels and on some edges is feasible using GNN? This means that the IDE could try to match the name of your variables, the control flow, and the name of the function to other known functions and could potentially point out differences. Potentially giving us a way to fix logic errors, or better algos. E.g., "Mmm... it looks like you are implementing your own bubble sort from scratch. Would you like to click here and use ."

I am not an expert on GNN, but if anyone has resources for someone to learn more about the state of the art of GNNs (a link to a literature review or something similar) do let me know.