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5.6.7 Arrays

Arrays are a collection of cells organized into an arbitrary number of dimensions. Each cell can be accessed in constant time by supplying an index for each dimension.

In the current implementation, an array uses a generalized vector for the actual storage of its elements. Any kind of generalized vector will do, so you can have arrays of uniform numeric values, arrays of characters, arrays of bits, and of course, arrays of arbitrary Scheme values. For example, arrays with an underlying c64vector might be nice for digital signal processing, while arrays made from a u8vector might be used to hold gray-scale images.

The number of dimensions of an array is called its rank. Thus, a matrix is an array of rank 2, while a vector has rank 1. When accessing an array element, you have to specify one exact integer for each dimension. These integers are called the indices of the element. An array specifies the allowed range of indices for each dimension via an inclusive lower and upper bound. These bounds can well be negative, but the upper bound must be greater than or equal to the lower bound minus one. When all lower bounds of an array are zero, it is called a zero-origin array.

Arrays can be of rank 0, which could be interpreted as a scalar. Thus, a zero-rank array can store exactly one object and the list of indices of this element is the empty list.

Arrays contain zero elements when one of their dimensions has a zero length. These empty arrays maintain information about their shape: a matrix with zero columns and 3 rows is different from a matrix with 3 columns and zero rows, which again is different from a vector of length zero.

Generalized vectors, such as strings, uniform numeric vectors, bit vectors and ordinary vectors, are the special case of one dimensional arrays.