Semantic Equivalence of Task-Oriented Programs in TopHat

Abstract

AbstractTask-oriented programming (top) is a new programming paradigm for specifying multi-user workflows. To reason formally abouttopprograms, a formal language calledTopHathas been designed, together with its operational semantics. For proving properties about task-oriented programs, it is desirable to know when twoTopHat-programs are semantically equivalent. This paper aims to answer this question. We show that a task can be in either one of five conditions, and for every two tasks in the same condition, we define what it means for them to be semantically equivalent. Using this definition, we study a number of transformation laws forTopHat-programs, which can be used by developers and compilers to optimisetop-programs. We show that the "Image missing"operation on types inTopHatis a functor but cannot be a monad. We support our findings with proofs formalised in the dependently typed programming languageIdris.