2017/02/21 by Satoshi Egi, Egi, Satoshi · 2 citations
Computer Science · #Embedded Systems Design Techniques #FOS: Computer and information sciences #Mathematical Software (cs.MS) #Parallel Computing and Optimization Techniques #Programming Languages (cs.PL) #Teaching and Learning Programming #cs.MS #cs.PL
paper · pdf · doi:10.48550/arxiv.1702.06343
Scheme and Functional Programming Workshop 2017
openalex publication_date 2017/02/21 · arxiv created 2017/08/08 · arxiv updated 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a method for importing tensor index notation, including Einstein summation notation, into functional programming. This method involves introducing two types of parameters, i.e, scalar and tensor parameters, and simplified tensor index rules that do not handle expressions that are valid only for the Cartesian coordinate system, in which the index can move up and down freely. An example of such an expression is "c = Ai Bi". As an ordinary function, when a tensor parameter obtains a tensor as an argument, the function treats the tensor argument as a whole. In contrast, when a scalar parameter obtains a tensor as an argument, the function is applied to each component of the tensor. In this paper, we show that introducing these two types of parameters and our simplified index rules enables us to apply arbitrary user-defined functions to tensor arguments using index notation including Einstein summation notation without requiring an additional description to enable each function to handle tensors.