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Two additional libraries of .NET collections deserve particular attention. The first is PowerCollections, currently provided by Wintellect. It provides additional generic types such as Bag<'T>, MultiDictionary<'Key,'Value>, OrderedDictionary<'Key,'Value>, OrderedMultiDictionary<'T>, and OrderedSet<'T>. The second is the C5 collection library, provided by ITU in Denmark. It includes implementations of some persistent/functional data structures such as persistent trees and thus may be of particular interest for use from F#.

In the following sections, we cover some of the techniques you can use to understand the type inference process and to debug problems when inferred types are not as expected.

For most agile practices, it is at this point that the lessons learned from the first iteration of this sequence are incorporated into the appropriate parts of the design (use case, sequence diagram, etc.) and the appropriate changes are made.

The F# Power Pack is an open source library found on www.codeplex.com. It includes a namespace Microsoft.FSharp.Math that defines a number of mathematical-related constructs, including matrix and vector types, double-precision complex numbers (type Complex, abbreviated complex), and arbitraryprecision rationals (type BigNum, abbreviated bignum).

The best and most important technique to debug and understand type inference is to use a visual editing environment for F# such as Visual Studio that performs interactive type checking as you are writing your code. These tools display errors interactively and show inferred types as you move the mouse pointer over identifiers.

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Note Some agile practitioners add another modeling step to the process by using robustness diagrams.

The F# Power Pack includes matrix and column vector types, which are generic and called Matrix<'T> and Vector<'T>, respectively. For symmetry, a type of row vectors, RowVector<'T>, is also included. Most commonly, the element types are instantiated to be double (that is, float), so the following abbreviations are used: type vector = Vector<float> type matrix = Matrix<float> type rowvec = RowVector<float> The modules Matrix, Vector, and RowVector in the Microsoft.FSharp.Math namespace have many additional functions for creating and working with these types. The functions are specialized for use with floating-point matrices, but versions to work with generic types are available at Microsoft.FSharp.Math.Matrix.Generic and Microsoft.FSharp.Math.Vector.Generic. The functions vector and matrix are also available for creating literal values. Here are some examples that use these types and functions:

Note At the time of writing, the F# distribution comes with the component FSharp.Compiler.dll that

This adaptation closely resembles the ICONIX process. For more information about the ICONIX process, see Agile Development with ICONIX Process.3

> #r "FSharp.PowerPack.dll";; > open Microsoft.FSharp.Math;; > vector [ 1.0; 2.0 ; 3.0 ] + vector [ 1.0; 2.0 ; 3.0 ];; val it : Vector<float> = vector [2.0; 4.0; 6.0] > matrix [ [ 1.0; 2.0 ]; [ 1.0; 3.0 ] ] * matrix [ [ 1.0; -2.0 ]; [ 0.5; 3.0 ] ];; val it : Math.matrix = matrix [[2.0; 4.0]; [2.5; 7.0];] Table 10-11 summarizes the primary properties of these types. Table 10-11. The Microsoft.FSharp.Math Matrix and Vector Types

Type inference in F# works through a process of type constraint propagation. As a programmer, you can add further type constraints to your code in several ways. For example, you can do the following: Add a rigid type constraint using the : notation, such as let t : float = 5.0. Add a flexible type constraint using the # notation, such as let setTextOfControl (c : #Control) (s:string) = c.Text <- s. Apply a function that accepts only a particular type of argument, such as let f x = String.length x. Here the use of String.length generates a constraint on the type of x. Adding and removing type annotations from your code is the standard technique to troubleshoot type inference problems. For example, the following code does not type check: > let transformData inp = inp |> Seq.map (fun (x,y) -> (x,y.Length)) ;; inp |> Seq.map (fun (x,y) -> (x,y.Length)) --------------------------------^^^^^^^^ stdin(11,36): error: Lookup on object of indeterminate type. A type annotation may be needed prior to this program point to constrain the type of the object. This may allow the lookup to be resolved. You can easily solve this problem simply by adding a type annotation, such as to y: let transformData inp = inp |> Seq.map (fun (x,y:string) -> (x,y.Length))

: int * int -> 'T with set, get : int * int : int : int : int * int * int * int -> Matrix<'T> : Matrix<'T>

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