Computing Gamma Calculus on Computer Cluster

Computing Gamma Calculus on Computer Cluster

Hong Lin, Jeremy Kemp, Padraic Gilbert
DOI: 10.4018/978-1-4666-1752-0.ch020
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Gamma Calculus is an inherently parallel, high-level programming model, which allows simple programming molecules to interact, creating a complex system with minimum of coding. Gamma calculus modeled programs were written on top of IBM’s TSpaces middleware, which is Java-based and uses a “Tuple Space” based model for communication, similar to that in Gamma. A parser was written in C++ to translate the Gamma syntax. This was implemented on UHD’s grid cluster (, and in an effort to increase performance and scalability, existing Gamma programs are being transferred to Nvidia’s CUDA architecture. General Purpose GPU computing is well suited to run Gamma programs, as GPU’s excel at running the same operation on a large data set, potentially offering a large speedup.
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The basic term of a Gamma program is molecules (or γ-expressions), which can be simple data or programs (γ-abstractions). The execution of the Gamma program can be seen as the evolution of a solution of molecules, which react until the solution becomes inert. Molecules are recursively defined as constants, γ-abstractions, multisets or solution of molecules. The following is their syntax:

M::= 0 | 1 | … | ‘a’ | ‘b’ | … ; constants| γP[C].M ; γ-abstraction| M1, M2 ; multiset| <M> ; solution

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