🤖 AI Summary
本文通过在J语言中引入动词秩来实现NumPy广播，解决了不同形状数组间无显式循环的操作问题。
📝 Abstract
The array programming paradigm applies operations to entire arrays rather than individual elements, eliminating explicit loops and abstracting many low-level details of computation. Two influential approaches have shaped array programming: NumPy's broadcasting and Kenneth Iverson's array-oriented notation, with the latter first introduced in APL and later developed in the J language. Although NumPy's array programming model was influenced by Iverson's work, the two systems formalize array operations differently: NumPy primarily through array shapes and broadcasting, and J through verb rank. This paper establishes a formal correspondence between NumPy broadcasting and J rank and presents an implementation of NumPy broadcasting in J. The results provide a formal connection between two influential approaches to array-oriented computation and show how they address the common problem of applying operations to arrays with differing shapes without explicit loops.