文章基本信息

标题：NO-GO THEOREMS FOR DISTRIBUTIVE LAWS
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作者：Maaike Zwart ; Dan Marsden
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2022
卷号：18
期号：1
页码：1-61
DOI：10.46298/lmcs-18(1:13)2022
语种：English
出版社：Technical University of Braunschweig
摘要：Monads are commonplace in computer science, and can be composed using Beck's distributive laws. Unfortunately, finding distributive laws can be extremely difficult and error-prone. The literature contains some general principles for constructing distributive laws. However, until now there have been no such techniques for establishing when no distributive law exists. We present three families of theorems for showing when there can be no distributive law between two monads. The first widely generalizes a counterexample attributed to Plotkin. It covers all the previous known no-go results for specific pairs of monads, and includes many new results. The second and third families are entirely novel, encompassing various new practical situations. For example, they negatively resolve the open question of whether the list monad distributes over itself, reveal a previously unobserved error in the literature, and confirm a conjecture made by Beck himself in his first paper on distributive laws. In addition, we establish conditions under which there can be at most one possible distributive law between two monads, proving various known distributive laws to be unique.
关键词：monads;distributive laws;compositionality;no-go theorems