Handlers of Algebraic Effects

Abstract. We present an algebraic treatment of exception handlers and, more generally, introduce handlers for other computational effects representable by an algebraic theory. These include nondeterminism, interactive input/output, concurrency, state, time, and their combinations; in all cases the computation monad is the free-model monad of the theory. Each such handler corresponds to a model of the theory for the effects at hand. The handling construct, which applies a handler to a computation, is based on the one introduced by Benton and Kennedy, and is interpreted using the homomorphism induced by the universal property of the free model. This general construct can be used to describe previously unrelated concepts from both theory and practice.

A Model of Cooperative Threads

We develop a model of concurrent imperative programming with threads. We focus on a small imperative language with cooperative threads which execute without interruption until they terminate or explicitly yield control. We define and study a trace-based denotational semantics for this language; this semantics is fully abstract but mathematically elementary. We also give an equational theory for the computational effects that underlie the language, including thread spawning. We then analyze threads in terms of the free algebra monad for this theory.Comment: 39 pages, 5 figure

Tracing monadic computations and representing effects

In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a computation. To make that possible, in this paper we introduce monad transformers that add the ability to automatically accumulate observations about the course of execution as an effect. We discover that if we treat the resulting trace as the actual result of the computation, we can find new functionality in existing monads, notably when working with non-terminating computations.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Facilitating modular property-preserving extensions of programming languages

We will explore an approach to modular programming language descriptions and extensions in a denotational style. Based on a language core, language features are added stepwise on the core. Language features can be described separated from each other in a self-contained, orthogonal way. We present an extension semantics framework consisting of mechanisms to adapt semantics of a basic language to new structural requirements in an extended language preserving the behaviour of programs of the basic language. Common templates of extension are provided. These can be collected in extension libraries accessible to and extendible by language designers. Mechanisms to extend these libraries are provided. A notation for describing language features embedding these semantics extensions is presented

The Reverse Cuthill-McKee Algorithm in Distributed-Memory

Ordering vertices of a graph is key to minimize fill-in and data structure size in sparse direct solvers, maximize locality in iterative solvers, and improve performance in graph algorithms. Except for naturally parallelizable ordering methods such as nested dissection, many important ordering methods have not been efficiently mapped to distributed-memory architectures. In this paper, we present the first-ever distributed-memory implementation of the reverse Cuthill-McKee (RCM) algorithm for reducing the profile of a sparse matrix. Our parallelization uses a two-dimensional sparse matrix decomposition. We achieve high performance by decomposing the problem into a small number of primitives and utilizing optimized implementations of these primitives. Our implementation shows strong scaling up to 1024 cores for smaller matrices and up to 4096 cores for larger matrices