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arXiv · 2608.09769

Abstract Compilation as Abstraction of Operator Semantics, applied to Cost Analysis

Louis Rustenholz·Alessio Mansutti·Pedro López-García·Félix Ridoux·Niki Vazou·Manuel V. Hermenegildo
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Abstract

Least fixpoints are fundamental to program semantics, but they abstract away the recursive structure that generated them. We introduce operator semantics: a semantic intermediate representation between syntax and classical denotational semantics, which treats programs as operators. Abstract compilation is then understood as the act of abstracting such operators. We develop higher-order abstract domains for functions, operators, and programs themselves, in which composition is the key novel primitive, together with a categorical framework for constructing sound, precise, and modular abstract compilers. We instantiate this framework in the context of recurrence-based static cost analysis, developing solver-independent, optimal recurrence extraction techniques for recursive programs over algebraic data types, that support general function unknowns and catamorphic metrics, a broad class of size metrics beyond traditional approaches.

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Louis Rustenholz, Alessio Mansutti, Pedro López-García, Félix Ridoux, Niki Vazou, Manuel V. Hermenegildo. 2026-08-10. Abstract Compilation as Abstraction of Operator Semantics, applied to Cost Analysis. https://arxiv.org/abs/2608.09769

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