This is because a shape to be passed to Iota would often naturally be a vector: for example, Shape always returns a vector, and a function such as Tally to return a scalar length did not exist. Such an extension breaks compatibility with earlier non-nested APLs: although these APLs required the argument of Iota to be a singleton, they always allowed a scalar or vector, and sometimes any singleton. This definition has the property that the shape of each index matches the shape of the argument.
dzaima/APL breaks from this definition by using vector indices whenever the argument is a vector, and scalar indices if the argument is a scalar, so that the result is only simple if the argument was scalar. This is because, when the argument is a singleton, each index in the result is represented as a scalar rather than a 1- element vector. In NARS and later nested APLs which share its definition, the result of Iota is simple when the argument is a singleton and nested otherwise. Works in: J Scalar-vector discrepancy in nested APLs A+ refers to this function as Interval while J calls it Integers. In A+ and J Iota of a vector returns an array which counts up in ravel order, that is, it matches Iota of its bound, reshaped. A Dictionary of APL defines Iota to have function rank 0, and SHARP APL gives it rank 1 but requires each row (1- cell) of the argument to have length 1. Flat APLs do not use this extension, but may extend to multiple argument elements in different ways. In nested APLs, this result may be seen as an array of scalar indices NARS extended Iota to allow a vector argument by making the result for a non- singleton vector be an array of vector indices. In APL/360, and all later APLs, ⍳ l for a scalar l returns a simple numeric vector of length l counting from the index origin up. Originally, Iota was defined only on a single number. In the result, the element at each index is that index.
DEFINE IODA GENERATOR
Index Generator ( ⍳) or Interval, often called by the name of its glyph Iota, is a monadic primitive function which returns an array of indices with shape given by the right argument. See Indexing, Indices, Index of, and Interval Index for other operations named after indices. This page is about generating indices for an array of a given size.
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