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.
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.
43544513
Conservativeness of Lambda over lambda-sigma-Calculus
42514309
Performance of cluster-enabled OpenMP for the SCASH software distributed shared memory system
OpenMP has attracted widespread interest because it is an easy-to-use parallel programming model for shared memory multiprocessor systems. Implementation of a "cluster-enabled" OpenMP compiler is presented. Compiled programs are linked to the page-based software distributed-shared-memory system, SCASH, which runs on PC clusters. This allows OpenMP programs to be run transparently in a distributed memory environment. The compiler converts programs written for OpenMP into parallel programs using the SCASH static library, moving all shared global variables into SCASH shared address space at runtime. As data mapping has a great impact on the performance of OpenMP programs compiled for software distributed-shared-memory, extensions to OpenMP directives are defined for specifying data mapping and loop scheduling behavior, allowing data to be allocated to the node where it is to be processed. Experimental results of benchmark programs on PC clusters using both Myrinet and fast Ethernet are reported.
206034930
Performance Evaluation of a Workstation Cluster, TMC CM-5, and Intel Paragon/XP Using a Parallel Homology Analysis Program
Abstract In the homology analysis, required memory size and computing time proportionally increase with the square of the number of amino acids in protein. In order to expand the limit of size and to carry out analysis effectively, we parallelized for homology analysis program adopting the wavefront method with tiling. The performance of a workstation cluster, CM5, and Paragon was compared by using our program. For performance evaluation of these machines, we have made a model of our parallel homology analysis computation. Using the model, we can understand the characteristics of these machines with respect to our program. Execution time estimated by the execution model is in good agreement with the observation. The averaged error of the estimation to the observation on a workstation cluster, CM5, and Paragon are 0.1%, 5%, and 2%. Almost linear speed-up has been observed from 1PU to 20PUs on them. The ratio of the performance of Paragon, CM5, and the workstation cluster is 1:0.38:0.22. This ratio is constant to the variety of the size of problem and the number of processors.
195869612
The EM-X parallel computer: architecture and basic performance
Latency tolerance is essential in achieving high performance on parallel computers for remote function calls and fine-grained remote memory accesses. EM-X supports interprocessor communication on an execution pipeline with small and simple packets. It can create a packet in one cycle, and receive a packet from the network in the on-chip buffer without interruption. EM-X invokes threads on packet arrival, minimizing the overhead of thread switching. It can tolerate communication latency by using efficient multi-threading and optimizing packet flow of fine grain communication. EM-X also supports the synchronization of two operands, direct remote memory read/write operations and flexible packet scheduling with priority. The paper describes distinctive features of the EM-X architecture and reports the performance of small synthetic programs and larger more realistic programs.
37253602
The Omni OpenMP Compiler on the Distributed Shared Memory of Cenju-4
This paper describes an implementation and a preliminary evaluation of the Omni OpenMP compiler on a parallel computer Cenju- 4. The Cenju-4 is a parallel computer which support hardware distributed shared memory (DSM) system. The shared address space is explicitly allocated at the initialization phase of the program. The Omni converts all global variable declarations into indirect references through the pointers, and generates code to allocate those variables in the shared address space at runtime. The OpenMP programs can execute on a distributed memory machine with hardware DSM by using the Omni. The preliminary results using benchmark programs show that the performance of OpenMP programs didn't scales. While its performance of OpenMP benchmark programs scales poorly, it enables users to execute the same program on both a shared memory machine and a distribute memory machine.
18311501
TACO -- Dynamic Distributed Collections with Templates and Topologies
High-level data-parallel programming with distributed object sets eases many aspects of parallel programming. In this paper we describe the design and implementation of Taco, a template library that provides higher-order operations on polymorphic regular and irregular distributed object sets by means of reusable topology classes and C++ function templates.