Modularity in Denotational Semantics

✍ Scribed by John Power

• Book ID: 104445297
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 758 KB
• Volume: 6
• Category: Article
• ISSN: 1571-0661
• DOI: 10.1016/s1571-0661(05)80153-7

✦ Synopsis

We consider a modular approach to denotational semantics. We reformulate and extend the idea of monads as notions of computation to algebraic structure together with a construction of an extended semantic category. We show that upon making that reformulation, one can obtain some account of modularity, in particular accounting for the interaction between side-e ects and various forms of nondeterminism. That involves extending the notion of distributivity of a monad over another monad to distributivity of a monad over any algebraic structure. We give a general theorem which asserts when algebraic structure extends along a Kleisli category, thus allowing modularity.