Bicategorical type theory: semantics and syntax

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-10-17 DOI:10.1017/s0960129523000312
Benedikt Ahrens, Paige Randall North, Niels van der Weide
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引用次数: 3

Abstract

Abstract We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured bicategories. We start by developing the semantics, in the form of comprehension bicategories . Examples of comprehension bicategories are plentiful; we study both specific examples as well as classes of examples constructed from other data. From the notion of comprehension bicategory, we extract the syntax of bicategorical type theory, that is, judgment forms and structural inference rules. We prove soundness of the rules by giving an interpretation in any comprehension bicategory. The semantic aspects of our work are fully checked in the Coq proof assistant, based on the UniMath library.
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双范畴类型理论:语义和句法
摘要:我们发展了双范畴类型理论的语义和句法。双范畴类型理论的特点是语境、类型、术语和术语之间的直接约简。这种类型理论自然地被解释为一类结构化的双范畴。我们从发展语义开始,以理解双范畴的形式。理解分类的例子很多;我们既研究具体的示例,也研究从其他数据构造的示例类。从理解双范畴的概念出发,我们提取了双范畴类型论的句法,即判断形式和结构推理规则。我们通过在任何理解范畴中给出解释来证明规则的合理性。我们工作的语义方面在基于UniMath库的Coq证明助手中进行了全面检查。
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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