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AW: AW: AW: Several comments | Michael Burschik | 10 Apr 2003 06:01 UTC |
AW: AW: AW: Several comments Michael Burschik 10 Apr 2003 06:01 UTC
> They are like the empty set: they seem odd only until they seem second > nature, at which point they are ordinary and boring. Rather like > zero, actually. > > What is slightly odder is a matrix of dimension zero; such a matrix > necessarily has no elements. This is unusual, because for any other > dimension, a single-element matrix is possible. That means that you > can convert scalars to matrixes for any dimension but zero. > > Still, not a big deal. All right then, from a mathematical point of view, zero-dimensional vectors are nothing special. But what about the usage of vectors as a type of data structure? In general, vectors are allocated with a fixed length, in order to allow access to the individual elements of the vector in constant time. In some programming languages, the length of a vector is immutable, once defined, while other programming languages allow vectors to be resized (R5RS does not). Still, I would claim that vectors are not dynamical data structures that routinely have length zero. On the other hand, I have to admit that several functions defined by SRFI-43 will return zero-dimensional vectors on occasion. Probably, I'm just too conservative. Anyway, I retract any objections against defining the predicates vector-empty? and vector-nonempty?. Regards Michael Burschik