608 research outputs found
Bialgebraic Semantics for Logic Programming
Bialgebrae provide an abstract framework encompassing the semantics of
different kinds of computational models. In this paper we propose a bialgebraic
approach to the semantics of logic programming. Our methodology is to study
logic programs as reactive systems and exploit abstract techniques developed in
that setting. First we use saturation to model the operational semantics of
logic programs as coalgebrae on presheaves. Then, we make explicit the
underlying algebraic structure by using bialgebrae on presheaves. The resulting
semantics turns out to be compositional with respect to conjunction and term
substitution. Also, it encodes a parallel model of computation, whose soundness
is guaranteed by a built-in notion of synchronisation between different
threads
On CSP and the Algebraic Theory of Effects
We consider CSP from the point of view of the algebraic theory of effects,
which classifies operations as effect constructors or effect deconstructors; it
also provides a link with functional programming, being a refinement of Moggi's
seminal monadic point of view. There is a natural algebraic theory of the
constructors whose free algebra functor is Moggi's monad; we illustrate this by
characterising free and initial algebras in terms of two versions of the stable
failures model of CSP, one more general than the other. Deconstructors are
dealt with as homomorphisms to (possibly non-free) algebras.
One can view CSP's action and choice operators as constructors and the rest,
such as concealment and concurrency, as deconstructors. Carrying this programme
out results in taking deterministic external choice as constructor rather than
general external choice. However, binary deconstructors, such as the CSP
concurrency operator, provide unresolved difficulties. We conclude by
presenting a combination of CSP with Moggi's computational {\lambda}-calculus,
in which the operators, including concurrency, are polymorphic. While the paper
mainly concerns CSP, it ought to be possible to carry over similar ideas to
other process calculi
A Proof Strategy Language and Proof Script Generation for Isabelle/HOL
We introduce a language, PSL, designed to capture high level proof strategies
in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system
generates and combines various tactics to explore a large search space with low
memory usage. Upon success, PSL generates an efficient proof script, which
bypasses a large part of the proof search. We also present PSL's monadic
interpreter to show that the underlying idea of PSL is transferable to other
ITPs.Comment: This paper has been submitted to CADE2
Extending monads with pattern matching
Sequencing of effectful computations can be neatly captured using monads and elegantly written using do notation. In practice such monads often allow additional ways of composing computations, which have to be written explicitly using combinators. We identify joinads, an abstract notion of computation that is stronger than monads and captures many such ad-hoc extensions. In particular, joinads are monads with three additional operations: one of type m a → m b → m (a, b) captures various forms of parallel composition, one of type m a → m a → m a that is inspired by choice and one of type m a → m (m a) that captures aliasing of computations. Algebraically, the first two operations form a near-semiring with commutative multiplication. We introduce docase notation that can be viewed as a monadic version of case. Joinad laws imply various syntactic equivalences of programs written using docase that are analogous to equiva-lences about case. Examples of joinads that benefit from the nota-tion include speculative parallelism, waiting for a combination of user interface events, but also encoding of validation rules using the intersection of parsers
Intel Concurrent Collections for Haskell
Intel Concurrent Collections (CnC) is a parallel programming model in which a network of steps (functions) communicate through message-passing as well as a limited form of shared memory. This paper describes a new implementation of CnC for Haskell. Compared to existing parallel programming models for Haskell, CnC occupies a useful point in the design space: pure and deterministic like Evaluation Strategies, but more explicit about granularity and the structure of the parallel computation, which affords the programmer greater control over parallel performance. We present results on 4, 8, and 32-core machines demonstrating parallel speedups over 20x on non-trivial benchmarks
Parallel evaluation strategies for lazy data structures in Haskell
Conventional parallel programming is complex and error prone. To improve programmer
productivity, we need to raise the level of abstraction with a higher-level
programming model that hides many parallel coordination aspects. Evaluation
strategies use non-strictness to separate the coordination and computation aspects
of a Glasgow parallel Haskell (GpH) program. This allows the specification of high
level parallel programs, eliminating the low-level complexity of synchronisation and
communication associated with parallel programming.
This thesis employs a data-structure-driven approach for parallelism derived through
generic parallel traversal and evaluation of sub-components of data structures. We
focus on evaluation strategies over list, tree and graph data structures, allowing
re-use across applications with minimal changes to the sequential algorithm.
In particular, we develop novel evaluation strategies for tree data structures, using
core functional programming techniques for coordination control, achieving more
flexible parallelism. We use non-strictness to control parallelism more flexibly. We
apply the notion of fuel as a resource that dictates parallelism generation, in particular,
the bi-directional flow of fuel, implemented using a circular program definition,
in a tree structure as a novel way of controlling parallel evaluation. This is the first
use of circular programming in evaluation strategies and is complemented by a lazy
function for bounding the size of sub-trees.
We extend these control mechanisms to graph structures and demonstrate performance
improvements on several parallel graph traversals. We combine circularity
for control for improved performance of strategies with circularity for computation
using circular data structures. In particular, we develop a hybrid traversal strategy
for graphs, exploiting breadth-first order for exposing parallelism initially, and
then proceeding with a depth-first order to minimise overhead associated with a full
parallel breadth-first traversal.
The efficiency of the tree strategies is evaluated on a benchmark program, and
two non-trivial case studies: a Barnes-Hut algorithm for the n-body problem and
sparse matrix multiplication, both using quad-trees. We also evaluate a graph search
algorithm implemented using the various traversal strategies.
We demonstrate improved performance on a server-class multicore machine with
up to 48 cores, with the advanced fuel splitting mechanisms proving to be more
flexible in throttling parallelism. To guide the behaviour of the strategies, we develop
heuristics-based parameter selection to select their specific control parameters
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