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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.

The first command creates an empty result file. This is necessary to ensure the test suite has something to compare to. The next command runs the test for the first time. Listing 4-2 depicts a typical first-run test result. Notice that the test suite indicated that the test failed. This is because there were no results to compare to. I have omitted a number of the more mundane statements for brevity. Listing 4-2. Running a New Test for the First Time Starting Tests TEST RESULT ------------------------------------------------------cab [ fail ] Errors are (from /home/Chuck/MySQL/mysql-5.1.9-beta/mysql-test/var/log /mysqltest-time) : mysqltest: Result length mismatch (the last lines may be the most important ones) Below are the diffs between actual and expected results: ------------------------------------------------------*** r/cab.result 2006-05-24 03:40:46.000000000 +0300 --- r/cab.reject 2006-05-24 03:42:50.000000000 +0300 *************** Ending Tests Shutting-down MySQL daemon Master shutdown finished Slave shutdown finished ------------------------------------------------------Failed 1/1 tests, 00.0% were successful.

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Note In OO languages, implementing types in multiple ways is commonly called polymorphism, which we

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)

might call polymorphism of implementation. Polymorphism of this kind is present throughout F#, and not just with respect to the OO constructs. In functional programming, polymorphism is used to mean generic type parameters, which is an orthogonal concept discussed in 2 and 5.

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