Modular verification of programs with effectsand effects handlers

Abstract

Modern computing systems have grown in complexity, and even though system components are generally carefully designed and even verified by different groups of people, the composition of these components is often regarded with less attention. Inconsistencies between components’ assumptions on the rest of the system can have significant repercussions on this system, and may ultimately lead to safety or security issues. In this article, we introduce FreeSpec, a formalismbuilt upon the key idea that components can bemodeled as programs with algebraic effects to be realized by other components. FreeSpec allows for the modular modeling of a complex system, by defining idealized components connected together, and the modular verification of the properties of their composition. In addition, we have implemented a framework for the Coq proof assistant based on FreeSpec.

Introducing ⦇ λ ⦈, a λ-calculus for effectful computation

“…The idea behind the computable closure is that the left-hand side of a rewrite rule can tell us what are all the possible right-hand sides that still lead to a correct proof of termination. 36 A formal definition of computable closure is given in [77, p. 8]. Informally, r ∈ CC f (l 1 , .…”

“…The problem of the specification and verification of programs with algebraic effects has seen a lot of progress recently [36,37,38,39,40,41,42]. Other interesting developments include the introduction of dependent types [43], a generalization from monads to applicative functors and arrows [44], new mechanisms for abstracting effects [45] and novel implementation techniques [46,47].…”