Convolution as a Unifying Concept

Brijesh Dongol, Ian J. Hayes, Georg Struth
2016 ACM Transactions on Computational Logic  
A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where convolution is the chop operation; and stream interval functions, where convolution is proposed for
more » ... ng the trajectories of dynamical or real-time systems. A Hoare logic can be constructed in a generic fashion on the power series quantale, which applies to each of these examples. In many cases, commutative notions of convolution have natural interpretations as concurrency operations.
doi:10.1145/2874773 fatcat:czhzxgz5xne6xdfjsz2d6q3ka4