Typed Flexible-Arity Slotted E-Graphs: A Soundness Construction and an Alloy Case Study

Abstract: Slotted e-graphs represent open terms modulo consistent renaming, while algebraic operators benefit from canonical sequence, bag, or set children. We compose the two at a specification level: typed slot-mapped invocations inhabit operator-declared ports whose sibling quotient and recursive flattening licenses are certified separately. A generic finite quotient presentation proves exactness of its least-orbit normal form, while certified records specify effective-support kernel extraction and collision. For abstract obligation traces carrying local endpoint certificates, we prove finite-unfolding equational soundness. An Alloy case study compares seven related pipeline arms on a frozen corpus and a controlled transformation suite. Its measurements characterize bounded capability and structural consolidation; they do not establish refinement of the Java artifact or experimental replay against the formal model.