一句话：提出混合线性与非线性递归类型的 LNL-FPC，并给出其范畴模型与递归域方程求解技术。
本文提出 LNL-FPC，一个混合线性、非线性与递归类型的类型系统，旨在兼顾线性类型安全性与非线性类型编程便利性。类似 FPC，它支持类型级递归并导出项级递归，还支持隐式弱化与收缩规则。作者给出该系统可靠且计算充分的范畴模型，刻画直觉主义线性逻辑的子结构运算在所有非线性类型（含递归类型）上的范畴结构。关键技术是在笛卡尔范畴中通过预嵌入求解递归域方程，并利用非线性类型的典范余幺半群结构建模隐式规则。作者还构造一大类具体模型，涵盖函数式编程、量子编程与电路描述语言等应用，表明抽象模型条件合理。
We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports non-linear typing as well, which makes the type system more convenient for programming. Just as in FPC, we show that LNL-FPC supports type-level recursion, which in turn induces term-level recursion. We also provide sound and computationally adequate categorical models for LNL-FPC that describe the categorical structure of the substructural operations of Intuitionistic Linear Logic at all non-linear types, including the recursive ones. In order to do so, we describe a new technique for solving recursive domain equations within cartesian categories by constructing the solutions over pre-embeddings. The type system also enjoys implicit weakening and contraction rules that we are able to model by identifying the canonical comonoid structure of all non-linear types. We also show that the requirements of our abstract model are reasonable by constructing a large class of concrete models that have found applications not only in classical functional programming, but also in emerging programming paradigms that incorporate linear types, such as quantum programming and circuit description programming languages.
@article{paperbot1320,
title = {LNL-FPC: The Linear/Non-linear Fixpoint Calculus},
author = {Bert Lindenhovius and Michael Mislove and Vladimir Zamdzhiev},
journal = {Logical Methods in Computer Science},
volume = {Volume 17, Issue 2},
year = {2021},
doi = {10.23638/lmcs-17(2:9)2021}
}