← 研踪 PaperTrailarXiv:2611.08685 · v1
Fibered Separation Logic: Weakest Preconditions, Universal Constructions, and Local Independence
首次提交 2026-11-06 04:43
版本更新 2026-11-06 04:43
雷达观测 2026-11-09 10:16
摘要
This paper introduces a categorical framework for models of higher-order separation logic including the weakest precondition modality. Weakest preconditions are interpreted by strong monads on a category fibered over a model of Moggi's computational lambda calculus. The fibered categories in question are termed bunched fibrations and shown to be equivalent to BI hyperdoctrines. Well-known heuristic techniques for obtaining weakest preconditions are shown to be expressible in categorical terms and are proved sound. The ``baking in the frame rule'' trick is shown to satisfy a universal property. Constructions are given for extending a program logic with cost credits. Our largest case study is parametrized by a category having local independent product (LIP) structure, a notion due to Simpson that axiomatizes name generation, randomness, and local state. From an LIP category, we construct an allocation monad, a bunched fibration, and a monad lifting. We instantiate our construction to obtain a novel probabilistic separation logic for measure-theoretic probability that both simplifies and clarifies prior work.
作者备注：41 pages, 5 figures
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v2 · 2026-11-10 09:23 · 最新观测版本
Fibered Separation Logic: Weakest Preconditions, Universal Constructions, and Local Independence
This paper introduces a categorical framework for models of higher-order separation logic including the weakest precondition modality. Weakest preconditions are interpreted by strong monads on a category fibered over a model of Moggi's computational lambda calculus. The fibered categories in question are termed bunched fibrations and shown to be equivalent to BI hyperdoctrines. Well-known heuristic techniques for obtaining weakest preconditions are shown to be expressible in categorical terms and are proved sound. The ``baking in the frame rule'' trick is shown to satisfy a universal property. Constructions are given for extending a program logic with cost credits. Our largest case study is parametrized by a category having local independent product (LIP) structure, a notion due to Simpson that axiomatizes name generation, randomness, and local state. From an LIP category, we construct an allocation monad, a bunched fibration, and a monad lifting. We instantiate our construction to obtain a novel probabilistic separation logic for measure-theoretic probability that both simplifies and clarifies prior work.
查看此版本解读 →查看此版本原文 ↗v1 · 2026-11-06 04:43
Fibered Separation Logic: Weakest Preconditions, Universal Constructions, and Local Independence
This paper introduces a categorical framework for models of higher-order separation logic including the weakest precondition modality. Weakest preconditions are interpreted by strong monads on a category fibered over a model of Moggi's computational lambda calculus. The fibered categories in question are termed bunched fibrations and shown to be equivalent to BI hyperdoctrines. Well-known heuristic techniques for obtaining weakest preconditions are shown to be expressible in categorical terms and are proved sound. The ``baking in the frame rule'' trick is shown to satisfy a universal property. Constructions are given for extending a program logic with cost credits. Our largest case study is parametrized by a category having local independent product (LIP) structure, a notion due to Simpson that axiomatizes name generation, randomness, and local state. From an LIP category, we construct an allocation monad, a bunched fibration, and a monad lifting. We instantiate our construction to obtain a novel probabilistic separation logic for measure-theoretic probability that both simplifies and clarifies prior work.
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