Regarding the issue of representing symbolic expression and controlling their evaluation or simplification, are there precedents of using e-graphs to memoize and reuse work rather than simple trees with destructive updates?
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.
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Regarding the issue of representing symbolic expression and controlling their evaluation or simplification, are there precedents of using e-graphs to memoize and reuse work rather than simple trees with destructive updates?
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.