Lineal: A linear-algebraic Lambda-calculus
Lineal: A linear-algebraic Lambda-calculus
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线性：线性代数 Lambda 演算
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Gilles Dowek
中科院分区：
文献类型：
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作者：
P. Arrighi;Gilles Dowek
我们提供了向量空间和概念的计算定义
We provide a computational definition of the notions of vector space and
bilinear functions. We use this result to introduce a minimal language
combining higher-order computation and linear algebra. This language extends
the Lambda-calculus with the possibility to make arbitrary linear combinations
of terms alpha.t + beta.u. We describe how to "execute" this language in terms
of a few rewrite rules, and justify them through the two fundamental
requirements that the language be a language of linear operators, and that it
be higher-order. We mention the perspectives of this work in the field of
quantum computation, whose circuits we show can be easily encoded in the
calculus. Finally, we prove the confluence of the entire calculus.