This PR adds the option `grind.ematch.diagnostics`, which tracks how
E-matching theorem instances depend on each other. When enabled, `grind`
records, for every new theorem instance, the set of previous instances
whose generated terms participated in the match. This produces a
hyper-graph `{thm_1, ..., thm_n} => thm` describing the provenance of
each instantiation.
The hyper-graph is stored in `Grind.Result` so downstream tooling can
inspect it. The trace class `trace.grind.ematch.diagnostics.compact`
prints a compact textual view of the hyper-graph, restricted to
constant-name origins. Example output:
```
[grind.ematch.diagnostics.compact] ✅️ instances
[inst] [] => th1
[inst] [th1] => th3
[inst] [th1] => th2
[inst] [th2, th3] => th4
[inst] [th4] => th5
```
The implementation stores an `ematchDiagSource` field on each `ENode`
and threads a `withEmatchDiagSource` reader through fact assertion so
that newly internalized terms inherit the origin of the instance that
produced them. During E-matching, `Choice` collects the sources of every
matched argument, and the resulting set becomes the predecessor set of
the new instance.
This PR notifies satellite solvers about asserted equalities `lhs = rhs`
even though `lhs = rhs` is not internalized in the E-graph (an existing
optimization). The notification lets solvers that do not inspect
equivalence classes (such as the homomorphism extension) react to
asserted equalities directly. It fires before the equivalence-class
merge so that solvers that mark `lhs` and `rhs` as their internal terms
have them registered before `Solvers.mergeTerms` fires `processNewEq`.
`cutsat` opts out of the notification when the equality has not been
internalized, since it already handles equalities through its `newEq`
handler. The homomorphism demo opts in by forcing `e` to be
internalized, enabling its rewrite rules to apply to asserted equalities
(e.g., `add b b = b` rewrites via `a = b ↔ toInt a = toInt b`).
Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
