On 4 March 2017 at 05:57, <enz...@gmx.com> wrote: what is the reason? do you know their reasoning > > cause 1 is 1 element and 1 2 3 is 3 elements so ⍴ 1 2 3 is 3 > and ⍴ 1 should have been 1
But that's wrong. 1 is not a one-element array. 1 is just a number. 1 2 is a two-element array. Each element being a number. The fact that 1 is interpreted as a number, as opposed to a single-element array is just an artifact of the language. One could easily modify the APL parser to yield such result, but it wouldn't be very useful in most cases. I guess that by now you're wondering why even have the concept of a scalar? Why not make numbers being a one-dimensional array with size 1? Well, for some operations, behaviour would remain the same, but there are situations you definitely want to be able to tell "a single number" (i.e. a scalar) vs. "an array". For example, A=B behaves differently depending on whether A is a single-element array or a scalar value. Note that this beahviour isn't limited to APL. Lisp also has a concept of zero-dimensional arrays (although it doesn't take it as far as APL in that numbers and zero-dimensional arrays still have different types). From the Hyperspec <http://clhs.lisp.se/Body/15_aac.htm>: *If the rank of an array <http://clhs.lisp.se/Body/26_glo_a.htm#array> is zero then the array <http://clhs.lisp.se/Body/26_glo_a.htm#array> is said to have no dimensions <http://clhs.lisp.se/Body/26_glo_d.htm#dimension>, and the product of the dimensions (see array-total-size <http://clhs.lisp.se/Body/f_ar_tot.htm#array-total-size>) is then 1; a zero-rank array <http://clhs.lisp.se/Body/26_glo_a.htm#array> therefore has a single element.* Finally, the idea of scalars being zero-dimensional arrays makes sense from a maths standpoint as well: https://math.stackexchange.com/questions/664594/why-mathbf0-vector-has-dimension-zero https://en.wikipedia.org/wiki/Dimension_(vector_space) Regards, Elias
