7,718 research outputs found
Algebraic optimization of recursive queries
Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud
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In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud
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The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems
Hierarchical Schur complement preconditioner for the stochastic Galerkin finite element methods
Use of the stochastic Galerkin finite element methods leads to large systems
of linear equations obtained by the discretization of tensor product solution
spaces along their spatial and stochastic dimensions. These systems are
typically solved iteratively by a Krylov subspace method. We propose a
preconditioner which takes an advantage of the recursive hierarchy in the
structure of the global matrices. In particular, the matrices posses a
recursive hierarchical two-by-two structure, with one of the submatrices block
diagonal. Each one of the diagonal blocks in this submatrix is closely related
to the deterministic mean-value problem, and the action of its inverse is in
the implementation approximated by inner loops of Krylov iterations. Thus our
hierarchical Schur complement preconditioner combines, on each level in the
approximation of the hierarchical structure of the global matrix, the idea of
Schur complement with loops for a number of mutually independent inner Krylov
iterations, and several matrix-vector multiplications for the off-diagonal
blocks. Neither the global matrix, nor the matrix of the preconditioner need to
be formed explicitly. The ingredients include only the number of stiffness
matrices from the truncated Karhunen-Lo\`{e}ve expansion and a good
preconditioned for the mean-value deterministic problem. We provide a condition
number bound for a model elliptic problem and the performance of the method is
illustrated by numerical experiments.Comment: 15 pages, 2 figures, 9 tables, (updated numerical experiments
Total Haskell is Reasonable Coq
We would like to use the Coq proof assistant to mechanically verify
properties of Haskell programs. To that end, we present a tool, named
hs-to-coq, that translates total Haskell programs into Coq programs via a
shallow embedding. We apply our tool in three case studies -- a lawful Monad
instance, "Hutton's razor", and an existing data structure library -- and prove
their correctness. These examples show that this approach is viable: both that
hs-to-coq applies to existing Haskell code, and that the output it produces is
amenable to verification.Comment: 13 pages plus references. Published at CPP'18, In Proceedings of 7th
ACM SIGPLAN International Conference on Certified Programs and Proofs
(CPP'18). ACM, New York, NY, USA, 201
An Effect System for Algebraic Effects and Handlers
We present an effect system for core Eff, a simplified variant of Eff, which
is an ML-style programming language with first-class algebraic effects and
handlers. We define an expressive effect system and prove safety of operational
semantics with respect to it. Then we give a domain-theoretic denotational
semantics of core Eff, using Pitts's theory of minimal invariant relations, and
prove it adequate. We use this fact to develop tools for finding useful
contextual equivalences, including an induction principle. To demonstrate their
usefulness, we use these tools to derive the usual equations for mutable state,
including a general commutativity law for computations using non-interfering
references. We have formalized the effect system, the operational semantics,
and the safety theorem in Twelf
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