15.1 Array Concepts

15.1.1 Array Elements

An array contains a set of objects called elements that can be referenced individually according to a rectilinear coordinate system. Array Indices

An array element is referred to by a (possibly empty) series of indices. The length of the series must equal the rank of the array. Each index must be a non-negative fixnum less than the corresponding array dimension. Array indexing is zero-origin. Array Dimensions

An axis of an array is called a dimension.

Each dimension is a non-negative fixnum; if any dimension of an array is zero, the array has no elements. It is permissible for a dimension to be zero, in which case the array has no elements, and any attempt to access an element is an error. However, other properties of the array, such as the dimensions themselves, may be used. Implementation Limits on Individual Array Dimensions

An implementation may impose a limit on dimensions of an array, but there is a minimum requirement on that limit. See the variable array-dimension-limit. Array Rank

An array can have any number of dimensions (including zero). The number of dimensions is called the rank.

If the rank of an array is zero then the array is said to have no dimensions, and the product of the dimensions (see array-total-size) is then 1; a zero-rank array therefore has a single element. Vectors

An array of rank one (i.e., a one-dimensional array) is called a vector. Fill Pointers

A fill pointer is a non-negative integer no larger than the total number of elements in a vector. Not all vectors have fill pointers. See the functions make-array and adjust-array.

An element of a vector is said to be active if it has an index that is greater than or equal to zero, but less than the fill pointer (if any). For an array that has no fill pointer, all elements are considered active.

Only vectors may have fill pointers; multidimensional arrays may not. A multidimensional array that is displaced to a vector that has a fill pointer can be created. Multidimensional Arrays Storage Layout for Multidimensional Arrays

Multidimensional arrays store their components in row-major order; that is, internally a multidimensional array is stored as a one-dimensional array, with the multidimensional index sets ordered lexicographically, last index varying fastest. Implementation Limits on Array Rank

An implementation may impose a limit on the rank of an array, but there is a minimum requirement on that limit. See the variable array-rank-limit.

15.1.2 Specialized Arrays

An array can be a general array, meaning each element may be any object, or it may be a specialized array, meaning that each element must be of a restricted type.

The phrasing “an array specialized to type type” is sometimes used to emphasize the element type of an array. This phrasing is tolerated even when the type is t, even though an array specialized to type t is a general array, not a specialized array.

Figure 15–1 lists some defined names that are applicable to array creation, access, and information operations. Array Upgrading

The upgraded array element type of a type T1 is a type T2 that is a supertype of T1 and that is used instead of T1 whenever T1 is used as an array element type for object creation or type discrimination.

During creation of an array, the element type that was requested is called the expressed array element type. The upgraded array element type of the expressed array element type becomes the actual array element type of the array that is created.

Type upgrading implies a movement upwards in the type hierarchy lattice. A type is always a subtype of its upgraded array element type. Also, if a type Tx is a subtype of another type Ty, then the upgraded array element type of Tx must be a subtype of the upgraded array element type of Ty. Two disjoint types can be upgraded to the same type.

The upgraded array element type T2 of a type T1 is a function only of T1 itself; that is, it is independent of any other property of the array for which T2 will be used, such as rank, adjustability, fill pointers, or displacement. The function upgraded-array-element-type can be used by conforming programs to predict how the implementation will upgrade a given type. Required Kinds of Specialized Arrays

Vectors whose elements are restricted to type character or a subtype of character are called strings. Strings are of type string. Figure 15–2 lists some defined names related to strings.

Strings are specialized arrays and might logically have been included in this chapter. However, for purposes of readability most information about strings does not appear in this chapter; see instead Chapter 16 (Strings).

Vectors whose elements are restricted to type bit are called bit vectors. Bit vectors are of type bit-vector. Figure 15–3 lists some defined names for operations on bit arrays.

Figure 15–3. Operators that Manipulate Bit Arrays