egglog VS libclc

The herbie project using egraphs to explore different ways of rewriting floating point expressions. https://herbie.uwplse.org/ One can also write custom rulesets in egglog (a new egraph rewriting system / language / datalog) https://egraphs-good.github.io/egglog/?example=herbie

The approach is not yet anywhere near being able to touch all the domains sympy can handle. Destructive term rewriting tends to be a bit more forgiving to unsoundness in the rules and still returning roughly meaningful results. EGraph rewriting (and other automated reasoning systems) tend to just return junk as soon as you aren't careful about your semantics. Associativity and commutativity are ubiquitous in CAS applications and encoding these concepts in general purpose terms is rather unsatisfying. The post above emphasizes specialty methods for polynomials, which it would be desirable to find a clean way to integrate into egraph techniques. Variable binding (which is treated in a rather mangled form in CAS systems) is seemingly important for treating summation, differentiation, and integration correctly. The status of doing variable binding efficiently and correctly in egraphs is also unclear imo.

For semantic analyzers, check out egg and egglog. They're custom data structures for representing compiler rewrite rules in a non-destructive way.

The recent work on relational, datalog-inspired egraphs in PLDI this year ("Unifying Datalog and Equality Saturation") is actually interesting because it can solve cases like the y/x*x -> y identity example, by the power of an interval analysis on x (among other things.) Sort of like adding a postulate but instead it's by adding relations between terms in the graph.

https://github.com/egraphs-good/egglog

https://arxiv.org/pdf/2304.04332.pdf

Close, but the link is on Page 13, and it points here: https://github.com/mwillsey/egg-smol

Unfortunately the naming is all a bit confusing, isn't it....

This is something I planned (2015) on sharing at some point but then years flew by and here we are .. :}

It is a cacheline sized 'container' (CLC) of machine-word length records, with one record used to store the record order and remaining bits for metadata. So you can project different kinds of container semantics, such as FIFO or LRU -- any ordered set semantics -- on this meta record. Using arrays of CLCs you can create e.g. a segmented LRU, where the overhead per item is substantially less than a conventional pointer-based datastructure, and, is naturally suited for concurrent operations (for example by assigning a range to distinct worker threads), and ops require a few or couple of lines to be touched. The LRU (or whatever) semantics in aggregate will be probabilistic, as the LRU order is deterministic per unit container only. It is very fast :)

https://github.com/alphazero/libclc/blob/master/include/libc...

https://github.com/alphazero/libclc/blob/master/include/libc...

As for the non-deterministic aspects: Since container semantics e.g. LRU order is only applied at unit level, the overall cache is ~LRU. We can strictly quantify the 'ordering error' by observing the age of items in FIFO mode as they are removed: for a deterministic container the age of the item is equal to the total capacity of the queue, for a segmented (array) composed of FIFO queues, the age will have a effectively gaussian distribution around the capacity (number of units x unit capacity). But since these containers can use as few as 9 bits per entry vs 24 or more bytes for pointer based solutions (which use linked-lists), for the same allocation of memory, the capacity of the array of CLCs will be much greater, so, the distribution tail of 'short-lived' items will actually be longer lived than items in a strict queue for the same exact memory. Additional techniques, such as n-array hashing, and low order 'clock' bits at container level, can tighten this distribution significantly (i.e. ~LRU -> LRU) via better loading factors.