A formalism for expressing the operational semantics of proof languages used in procedural theorem provers is proposed. It is argued that this formalism provides an elegant way to describe the computational features of proof languages, such as side effects, exception handling, and backtracking. The formalism, called proof monads, finds its roots in category theory, and in particular satisfies t...

Traditionally a vectorising compiler matches the iterative constructs of a program against a set of predeened templates. If a loop contains no dependency cycles then a map template can be used; other simple dependencies can often be expressed in terms of fold or scan templates. This paper addresses the template matching problem within the context of functional programming. A small collection of...

Verifying soundness of symbolic execution-based program verifiers is a significant challenge. This especially true if the resulting tool needs to be usable outside proof assistant, in which case we cannot rely on shallowly embedded assertion logics and meta-programming. The manipulate deeply assertions, it crucial for efficiency eagerly prune unreachable paths simplify intermediate assertions w...

Over the past two decades the notion of a strong monad has found wide applicability in computing. Arising out of a need to interpret products in computational and semantic settings, different approaches to this concept have arisen. In this paper we introduce and investigate the connections between these approaches and also relate the results to monad composition. We also introduce new methods f...

Resumptions appear in many forms as a convenient abstraction, such as in semantics of concurrency and as a programming pattern. In this paper we introduce generalised resumptions in a categorytheoretic, coalgebraic context and show their basic properties: they form a monad, they come equipped with a corecursion scheme in the sense of Adámek et al.’s notion of completely iterative monads (cims),...

We consider sets of monad rules derived by focussing on the Kleisli category of a monad, and from these we derive some constructions for compound monads. Under certain conditions these constructions correspond to a distributive law connecting the monads. We also show how these relate to some constructions for compound monads described previously.

Bahr and Hutton recently developed a new approach to calculating correct compilers directly from specifications of their correctness. However, the methodology only considers converging behaviour source language, which means that compiler could potentially produce arbitrary, erroneous code for programs diverge. In this article, we show how can naturally be extended support calculation address bo...