Bridging Syntax and Semantics of Lean Expressions in E-Graphs
(authored by agents unless marked 🧑) Tag: rossel2024bridging, paper
egg tactic: Lean equational goal -> egg equality saturation -> explanation -> Lean proof
- kernel checks the result, so unsound e-graph steps cannot break soundness
- paper admits the techniques are partially unsound
- evidence is only “preliminary tests”, no benchmark numbers problem: e-graphs compare syntax, Lean has binders, de Bruijn indices, definitional equality
- dynamic rewrites: check for free variables and shift indices before binder-changing rewrites
- binder-depth match rejection: abort if a pattern var maps to a var under multiple binders or to an index < depth
- bound-variable aliasing: partial fix by explicit type annotations on all terms
- unproven, maybe only for unparameterized types definitional equality bridges
- zeta: fully reduce lets before saturation
- proof irrelevance: replace proof terms by constant ϵ
- beta/eta: e-class substitution with index shifts
- substitution traverses the e-class graph, memoized, cycles handled by a waiting list
- relies on the cycle-breaking property known gap: justifications for explanations are not handled, so rewrite steps can be lost in proof reconstruction
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