30 research outputs found
Implementing ÎČ-Reduction by Hypergraph Rewriting
AbstractThe aim of this paper is to implement the ÎČ-reduction in the lambda;-calculus with a hypergraph rewriting mechanism called collapsed lambda;-tree rewriting. It turns out that collapsed lambda;-tree rewriting is sound with respect to ÎČ-reduction and complete with respect to the Gross-Knuth strategy. As a consequence, there exists a normal form for a collapsed lambda;-tree if and only if there exists a normal form for the represented λ-term.I am grateful to Renate Klempien-Hinrichs, Detlef Plump, and to the referees for their helpful comments
Multicore Mining of Correlated Patterns
6 pagesInternational audienceIn this paper, we present a new approach relevant to the discovery of correlated patterns, based on the use of multicore architectures. Our work rests on a full KDD system and allows one to extract Decision Correlation Rules based on the Chi-squared criterion that include a target column from any database. To achieve this objective, we use a levelwise algorithm as well as contingency vectors, an alternate and more powerful representation of contingency tables, in order to prune the search space. The goal is to parallelize the processing associated with the extraction of relevant rules. The parallelization invokes the PPL (Parallel Patterns Library), which allows a simultaneous access to the whole available cores / processors on modern computers. We finally present first results on the reached performance gains
Paraiso : An Automated Tuning Framework for Explicit Solvers of Partial Differential Equations
We propose Paraiso, a domain specific language embedded in functional
programming language Haskell, for automated tuning of explicit solvers of
partial differential equations (PDEs) on GPUs as well as multicore CPUs. In
Paraiso, one can describe PDE solving algorithms succinctly using tensor
equations notation. Hydrodynamic properties, interpolation methods and other
building blocks are described in abstract, modular, re-usable and combinable
forms, which lets us generate versatile solvers from little set of Paraiso
source codes.
We demonstrate Paraiso by implementing a compressive hydrodynamics solver. A
single source code less than 500 lines can be used to generate solvers of
arbitrary dimensions, for both multicore CPUs and GPUs. We demonstrate both
manual annotation based tuning and evolutionary computing based automated
tuning of the program.Comment: 52 pages, 14 figures, accepted for publications in Computational
Science and Discover
Introduction to the Literature on Semantics
An introduction to the literature on semantics. Included are pointers to the literature on axiomatic semantics, denotational semantics, operational semantics, and type theory
No solvable lambda-value term left behind
In the lambda calculus a term is solvable iff it is operationally relevant.
Solvable terms are a superset of the terms that convert to a final result
called normal form. Unsolvable terms are operationally irrelevant and can be
equated without loss of consistency. There is a definition of solvability for
the lambda-value calculus, called v-solvability, but it is not synonymous with
operational relevance, some lambda-value normal forms are unsolvable, and
unsolvables cannot be consistently equated. We provide a definition of
solvability for the lambda-value calculus that does capture operational
relevance and such that a consistent proof-theory can be constructed where
unsolvables are equated attending to the number of arguments they take (their
"order" in the jargon). The intuition is that in lambda-value the different
sequentialisations of a computation can be distinguished operationally. We
prove a version of the Genericity Lemma stating that unsolvable terms are
generic and can be replaced by arbitrary terms of equal or greater order.Comment: 43 page
Introduction to the Literature on Programming Language Design
This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search
Term rewriting systems from Church-Rosser to Knuth-Bendix and beyond
Term rewriting systems are important for computability theory of abstract data types, for automatic theorem proving, and for the foundations of functional programming. In this short survey we present, starting from first principles, several of the basic notions and facts in the area of term rewriting. Our treatment, which often will be informal, covers abstract rewriting, Combinatory Logic, orthogonal systems, strategies, critical pair completion, and some extended rewriting formats