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F# includes a beautiful feature in its type system called units of measure. It lets you annotate numeric types with annotations such as kg, m, and sec that indicate the kind of number the quantity represents that is, its unit of measure. You can also use the feature to annotate other, user-defined types that are ultimately based on numeric quantities. This feature is simplest explained using code for physical simulations and is rooted in scalable quantities. However, it also has a wide range of surprising applications outside physical simulation, including annotating code with units for integer quantities such as pixels, currencies, or click-counts. To define a new kind of measure annotation, you use a type definition with a Measure attribute: [<Measure>] type m [<Measure>] type s [<Measure>] type kg The F# version 2.0 core library doesn t come with predefined units, although a set of definitions matching the Syst me International (SI) standard is included in the F# Power Pack (an open source project available at www.codeplex.com). Once a set of measures are defined, the basic numeric types and literals can include these qualifications. For example: let gravityOnEarth = 9.81<m/s^2> let heightOfMyOfficeWindow = 3.5<m> A calculation involving these quantities is shown here: let speedOfImpact = sqrt (2.0 * gravityOnEarth * heightOfMyOfficeWindow) The inferred type of speedOfImpact is float<m/s> (a speed). If a mismatched unit type is used in such a calculation, then a type error is normally reported.
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CHAPTER 5 MASTERING TYPES AND GENERICS
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When you define a new type, you may include measure parameters as part of the definition of the type. These parameters must be marked with the Measure attribute. For example: type Vector2D<[<Measure>] 'u> = { DX: float<'u>; DY: float<'u> } You can use units of measure in conjunction with object-oriented programming, discussed in 6. For example, here is a vector type generic over units of measure: /// Two-dimensional vectors type Vector2D<[<Measure>] 'u>(dx: float<'u>, dy: float<'u>) = /// Get the X component of the vector member v.DX = dx /// Get the Y component of the vector member v.DY = dy /// Get the length of the vector member v.Length = sqrt(dx * dx + dy * dy) /// Get a vector scaled by the given factor member v.Scale k = Vector2D(k*dx, k*dy) /// Return a vector shifted by the given delta in the X coordinate member v.ShiftX x = Vector2D(dx+x, dy) /// Return a vector shifted by the given delta in the Y coordinate member v.ShiftY y = Vector2D(dx, dy+y) /// Get the zero vector static member Zero = Vector2D<'u>(0.0<_>, 0.0<_>) /// Return a constant vector along the X axis static member ConstX dx = Vector2D<'u>(dx, 0.0<_>) /// Return a constant vector along the Y axis static member ConstY dy = Vector2D<'u>(0.0<_>, dy) /// Return the sum of two vectors static member (+) (v1: Vector2D<'u>, v2: Vector2D<'u>) = Vector2D(v1.DX + v2.DX, v1.DY + v2.DY) /// Return the difference of two vectors static member (-) (v1: Vector2D<'u>, v2: Vector2D<'u>) = Vector2D(v1.DX - v2.DX, v1.DY - v2.DY) /// Return the pointwise-product of two vectors static member (.*) (v1: Vector2D<'u>, v2: Vector2D<'u>) = Vector2D(v1.DX * v2.DX, v1.DY * v2.DY)
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CHAPTER 5 MASTERING TYPES AND GENERICS
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Note that some measure annotations are needed on zero values in this sample. In addition, a vector type like this should normally implement the IComparable interface, and the Equals and GetHashCode methods, as described in 8.
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Note F# units of measure are covered only briefly in this book. For more information, see the MSDN
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documentation, or Andrew Kennedy s four-part introduction to the topic: search for Andrew Kennedy Units of Measure Part One, or visit http://blogs.msdn.com/andrewkennedy.
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Troubleshooting Type-Inference Problems
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The following sections cover some of the techniques you can use to understand the type-inference process and to debug problems when inferred types aren t as expected.
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