32331384
Intuitionistic and Classical Natural Deduction Systems with the Catch and the Throw Rules
1580777
Classical Brouwer-Heyting-Kolmogorov Interpretation
The Brouwer-Heyting-Kolmogorov interpretation explains the meaning of logical operations as operators that construct proofs from proofs of the operands. The BHK interpretation is usually understood as giving intuitionistic interpretation for the logical operators, but, as pointed out by Troelstra and van Dalen [12], it is possible to understand the BHK interpretation classically. We elaborate this idea and develop a classical theory of proofs as abstract mathematical entities where the truth of a proposition becomes equivalent to the existence of proofs of the proposition.
10509424
A Simply Typed Context Calculus with First-class Environments
We introduce a simply typed λ-calculus λϰƐ" which has both contexts and environments as first-class values. In λϰƐ", holes in contexts are represented by ordinary variables of appropriate types and hole filling is represented by the functional application together with a new abstraction mechanism which takes care of packing and unpacking of the term which is used to fill in the holes of the context. λϰƐ" is a conservative extension of the simply typed λβ-calculus, enjoys subject reduction property, is confluent and strongly normalizing. 
 
The traditional method of defining substitution does not work for our calculus. So, we also introduce a new method of defining substitution. Although we introduce the new definition of substitution out of necessity, the new definition turns out to be conceptually simpler than the traditional definition of substitution.
1796136
Strong normalizability of the non-deterministic catch/throw calculi
The catch/throw mechanism in Common Lisp provides a simple control mechanism for non-local exits. We study typed calculi by Nakano and Sato which formalize the catch/throw mechanism. These calculi correspond to classical logic through the Curry-Howard isomorphism, and one of their characteristic points is that they have non-deterministic reduction rules. These calculi can represent various computational meaning of classical proofs. This paper is mainly concerned with the strong normalizability of these calculi. Namely, we prove the strong normalizability of these calculi, which was an open problem. We first formulate a non-deterministic variant of Parigot's λμ-calculus, and show it is strongly normalizing. We then translate the catch/throw calculi to this variant. Since the translation preserves typing and reduction, we obtain the strong normalization of the catch/throw calculi. We also briefly consider second-order extension of the catch/throw calculi. Copyright 2002 Elsevier Science B.V
8686702
Theory of Judgments and Derivations
We propose a computational and logical framework NF (Natural Framework) which is suitable for presenting mathematics formally. Our framework is an extendable framework since it is open-ended both computationally and logically in the sense of Martin-Lof's theory or types. NF is developed in three steps. Firstly, we introduce a theory of expressions and schemata which is used to provide a universe for representing mathematical objects, in particular, judgments and derivations as well as other usual mathematical objects. Secondly, we develop a theory of judgments within the syntactic universe of expressions. Finally, we introduce the notions of derivation and derivation game and will show that we can develop mathematics as derivation games by regarding mathematics as an open-ended process of defining new concepts and deriving new judgments. Our theory is inspired by Martin-Lof's theory of expressions and Edinburgh LF, but conceptually much simpler. Our theory is also influenced by Gentzen's natural deduction systems.
27739305
Explicit Environments
We introduce λƐ, a simply typed calculus with environments as first class values. As well as the usual constructs of λ and application, we have e[[a]] which evaluates term a in an environment e. Our environments are a set of variable-value pairs, but environments can also be computed by function application and evaluation in some other environments. The notion of environments here is a generalization of explicit substitutions and records. We show that the calculus has desirable properties such as subject reduction, confluence, conservativity over the simply typed λβ-calculus and strong normalizability.
206591385
A Parallel Method for Large Sparse Generalized Eigenvalue Problems by OmniRPC in a Grid Environment
In this paper we present a parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem Ax = λBx, where A and B are large sparse matrices. A moment-based method by which to find all of the eigenvalues that lie inside a given domain is used. In this method, a small matrix pencil that has only the desired eigenvalues is derived by solving large sparse systems of linear equations constructed from A and B. Since these equations can be solved independently, we solve them on remote hosts in parallel. This approach is suitable for master-worker programming models. We have implemented and tested the proposed method in a grid environment using a grid RPC (remote procedure call) system called OmniRPC. The performance of the method on PC clusters that were used over a wide-area network was evaluated.
26140229
Heterogeneous Remote Computing System for Computational Astrophysics with OmniRPC
37770987
A Blocking Algorithm for Parallel 1-D FFT on Clusters of PCs
In this paper, we propose a blocking algorithm for a parallel one-dimensional fast Fourier transform (FFT) on clusters of PCs. Our proposed parallel FFT algorithm is based on the six-step FFT algorithm. The six-step FFT algorithm can be altered into a block nine-step FFT algorithm to reduce the number of cache misses. The block nine-step FFT algorithm improves performance by utilizing the cache memory effectively. We use the block nine-step FFT algorithm to design the parallel one-dimensional FFT algorithm. In our proposed parallel FFT algorithm, since we use cyclic distribution, all-to-all communication is required only once. Moreover, the input data and output data are both can be given in natural order. We successfully achieved performance of over 1.3 GFLOPS on an 8-node dual Pentium III 1 GHz PC SMP cluster.
280911
Multiple instruction streams in a highly pipelined processor
In a highly pipelined processor, instruction dependencies involving both and control information often limit its potential performance. A cyclic pipeline machine allows multiple instruction streams to share these pipeline stages in time to remove the data and control dependencies. These multiple instruction streams exploit more parallelism in parallel programs. It provides an alternative architectural solution for new technologies such as GaAs and Josephson logic device, which prefer a highly pipelined architecture. The authors define the basic model of a cyclic pipeline machine, and examine the performance improvement of various configurations of cyclic pipeline machines compared to the same degree of pipelining of a conventional pipelined processor. The simulation results indicate that pipelining in the individual instruction streams increases the performance to maximize the utilization of resources in a highly pipelined processor.<<ETX>>
41634108
Utilizing the Metaserver Architecture in the Ninf Global Computing System
Rapid increase in speed and availability of global-network is opening up the possibilities of globally-distributed supercomputing, including our Ninf system. Ninf is designed to utilize existing numerical libraries and resources on the Web. It also has global scheduling server called the Ninf Metaserver, which is responsible for scheduling and load-distribution of parallel tasks. The metaserver keeps track of computational servers, and gathers information needed for scheduling. Using the information, it balances loads over computational servers. We performed preliminary benchmarks using the metaserver. There, we observed that scheduling cost can be ignored and dynamic scheduling by the server gained better score than static-cyclic distribution. We also report on our collaborative efforts in bridging Ninf with NetSolve, a similar system being developed at Univ. of Tennessee/ORNL.