Bridging Syntax and Semantics of Lean Expressions in E-Graphs
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to prove theorems. A significant means of achieving this is by improving proof automation. We have implemented an early prototype of proof automation for equational reasoning in Lean by using equality saturation. To achieve this, we need to bridge the gap between Lean’s expression semantics and the syntactically driven e-graphs in equality saturation. This involves handling bound variables, implicit typing, as well as Lean’s definitional equality, which is more general than syntactic equality and involves notions like α-equivalence, β-reduction, and η-reduction. In this extended abstract, we highlight how we attempt to bridge this gap, and which challenges remain to be solved. Notably, while our techniques are partially unsound, the resulting proof automation remains sound by virtue of Lean’s proof checking. This work is actively being developed at github.com/marcusrossel/lean-egg.
Mon 24 JunDisplayed time zone: Windhoek change
16:00 - 17:40 | |||
16:00 25mTalk | Automated Proof Generation for Associative and Distributive Rewriting with E-Graphs EGRAPHS Adrian Lehmann University of Chicago, Ben Caldwell University of Chicago, John Reppy University of Chicago, USA, Robert Rand University of Chicago Media Attached | ||
16:25 25mTalk | superVer: Verifying Probabilistic Independence of Systems of Expressions using Equality Saturation EGRAPHS Alexander Treff University of Lübeck, Pajam Pauls University of Lübeck, Maximilian Orlt TU Darmstadt, Marc Gourjon Hamburg University of Technology and NXP Semiconductors Germany GmbH Media Attached | ||
16:50 25mTalk | Bridging Syntax and Semantics of Lean Expressions in E-Graphs EGRAPHS Pre-print Media Attached | ||
17:15 25mTalk | Disequalities in E-Graphs: An Experiment EGRAPHS George Zakhour University of St. Gallen, Pascal Weisenburger University of St. Gallen, Guido Salvaneschi University of St. Gallen Pre-print Media Attached |