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In 3, you saw in passing that you can use sequence expressions as a way to generate interesting array values. For example: > let arr = [| for i in 0 .. 5 -> (i,i*i) |];; val arr : (int*int)[] > arr;; val it : (int*int)[] = [|(0, 0); (1, 1); (2, 4); (3, 9); (4, 16); (5, 25)|] You can also use a convenient syntax for extracting subarrays from existing arrays; this is called slice notation. A slice expression for a single-dimensional array has the form arr.[start..finish] where one of start and finish may optionally be omitted, and index zero or the index of the last element of the array is assumed instead. For example: > let arr = [| for i in 0 .. 5 -> (i,i*i) |] val arr : (int*int)[] > arr;; val it : (int*int)[] = [|(0, 0); (1, 1); (2, 4); (3, 9); (4, 16); (5, 25)|] > arr.[1..3];; val it : (int*int)[] = [| (1, 1); (2, 4); (3, 9); |] > arr.[..2];; val it : (int*int)[] = [| (0, 0); (1, 1); (2, 4); |] > arr.[3..];; val it : (int*int)[] = [| (3, 9); (4, 16); (5, 25) |] We use slicing syntax extensively in the example Verifying Circuits with Propositional Logic in 12. You can also use slicing syntax with strings and several other F# types such as vectors and matrices, and the operator can be overloaded to work with your own type definitions. The F# library definitions of vectors and matrices can be used as a guide.

Note Slices on arrays generate fresh arrays. Sometimes it can be more efficient to use other techniques,

such as to access the array via an accessor function or object that performs one or more internal index adjustments before looking up the underlying array. If you add support for the slicing operators to your own types, you can choose whether they return copies of data structures or an accessor object.

Like other .NET languages, F# directly supports two-dimensional array values that are stored flat, that is, where an array of dimensions (N, M) is stored using a contiguous array of N * M elements. The types for these values are written using [,], such as in int[,] and double[,], and these types also support slicing syntax. Values of these types are created and manipulated using the values in the Array2 module. Likewise, there is a module for manipulating three-dimensional array values whose types are written int[,,]. You can also use the code in those modules as a template for defining code to manipulate arrays of higher dimension.

The .NET Framework comes equipped with an excellent set of imperative collections under the namespace System.Collections.Generic. You have seen some of these already. In the following sections, we ll take a look at some simple uses of these collections.

As mentioned in 3, the .NET Framework comes with a type System.Collections. Generic.List<'a>, which, although named List, is better described as a resizeable array. The F# library includes the following type abbreviation for this purpose: type ResizeArray<'a> = System.Collections.Generic.List<'a> Here is a simple example of using this data structure: > let names = new ResizeArray<string>();; val names : ResizeArray<string> > for name in ["Claire"; "Sophie"; "Jane"] do names.Add(name);; val it : unit = () > names.Count;; val it : int = 3 > names.[0];; val it : string = "Claire"

> names.[1];; val it : string = "Sophie" > names.[2];; val it : string = "Jane" Resizable arrays use an underlying array for storage and support constant-time randomaccess lookup. This makes a resizable array more efficient than an F# list in many situations, which supports efficient access only from the head (left) of the list. You can find the full set of members supported by this type in the .NET documentation. Commonly used properties and members include Add, Count, ConvertAll, Insert, BinarySearch, and ToArray. A module ResizeArray is included in the F# library that provides operations over this type in the style of the other F# collections. Like other .NET collections, values of type ResizeArray<'a> support the seq<'a> interface. There is also an overload of the new constructor for this collection type that lets you specify initial values via a seq<'a>. This means you can create and consume instances of this collection type using sequence expressions: > let squares = new ResizeArray<int>(seq { for i in 0 .. 100 -> i*i });; val squares : ResizeArray<int> = [0; 1; 4; 9; ...] > for x in squares do printfn "square: %d" x;; square: 0 square: 1 square: 4 square: 9 ...