Optimizing Optimizations, Declaratively: Optimizing the Higher-Order Functions in Mathematical Optimization with egglog

TL;DR

This paper demonstrates how egglog can be applied to improve mathematical optimization modeling and constraint detection, leading to more natural notation and faster processing in industrial applications.

Contribution

It introduces novel applications of egglog for better notation and constraint detection in mathematical models, with performance improvements through optimized rule premises.

Findings

Enhanced LaTeX output for higher-order functions in models

Declarative multi-step constraint detection with egglog

Reduced detection time from minutes to seconds

Abstract

We present two applications of egglog to mathematical optimization in JijModeling 2, a mathematical modeller whose internal representation is based on simply typed $\lambda$-calculus. First, we use egglog to improve $\LaTeX$ output for mathematical models expressed with higher-order functions. Python comprehensions are desugared into stream operations such as $\textsf{map}$, $\textsf{flat_map}$, and $\textsf{filter}$; emitting these terms directly produces unnatural mathematical notation. We reconstruct comprehension syntax by \emph{ensugaring} higher-order terms and use equality saturation with a custom cost model to minimize temporary variable rebindings. Second, we use egglog as a declarative engine for \emph{constraint detection}, extending the previous egg-based approach presented at EGRAPHS '25. Egglog's datalog-style rules let us express multi-step detection logic directly, without external Rust orchestration code. We encode parametrized constraints using \emph{Henkin-like constants} and propagate side conditions on subterms and indices through egglog facts. Finally, we show that the same ensugaring procedure also reduces large domain-set conditions before saturation, turning a problematic detection case from minutes or nontermination into a few seconds. Through these topics, we want to provide an example of an industrial application of egglog, demonstrate the trick to propagate the constraints using the ideas from mathematical logic, and show the importance of optimizing \emph{premises} of egglog rules to get practical performance in egglog programs.