2022/09/13 by Pritam Choudhury, Choudhury, Pritam
Computer Science · Decision Sciences · #Advanced Database Systems and Queries #Distributed systems and fault tolerance #FOS: Computer and information sciences #Programming Languages (cs.PL) #Scientific Computing and Data Management
paper · pdf · doi:10.48550/arxiv.2209.06334
openalex publication_date 2022/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dependency analysis is vital to several applications in computer science. It lies at the essence of secure information flow analysis, binding-time analysis, etc. Various calculi have been proposed in the literature for analysing individual dependencies. Abadi et. al., by extending Moggi's monadic metalanguage, unified several of these calculi into the Dependency Core Calculus (DCC). DCC has served as a foundational framework for dependency analysis for the last two decades. However, in spite of its success, DCC has its limitations. First, the monadic bind rule of the calculus is nonstandard and relies upon an auxiliary protection judgement. Second, being of a monadic nature, the calculus cannot capture dependency analyses that possess a comonadic nature, for example, the binding-time calculus, λ∘, of Davies. In this paper, we address these limitations by designing an alternative dependency calculus that is inspired by standard ideas from category theory. Our calculus is both monadic and comonadic in nature and subsumes both DCC and λ∘. Our construction explains the nonstandard bind rule and the protection judgement of DCC in terms of standard categorical concepts. It also leads to a novel technique for proving correctness of dependency analysis. We use this technique to present alternative proofs of correctness for DCC and λ∘.