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val (|Rect|) : complex -> float * float val (|Polar|) : complex -> float * float These types are identical, but they implement completely different views of the same data. The definitions of addViaRect and mulViaPolar can also be written using pattern matching in argument position: let add2 (Rect (ar, ai)) (Rect (br, bi)) = Complex (ar+br, ai+bi) let mul2 (Polar (r1, th1)) (Polar (r2, th2)) = Complex (r1*r2, th1+th2)

Note The second argument given to the defaultArg function is evaluated before the function is called. This means you should take care that this argument is not expensive to compute and doesn t need to be disposed. In the previous example, we used a match expression to specify the default for the font argument for this reason.

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(see http://lists.mysql.com/ for more details and to see the available lists). You can also submit your tests for inclusion by sending an e-mail message to the list. You should upload your test files to the ftp:// ftp.mysql.com/pub/mysql/upload/ FTP site. If you decide to send your tests to MySQL AB for inclusion in the test suite, be sure you are using data that you can show the world. The tests are available to everyone. For example, I am sure your friends and relatives would not want their phone numbers showing up in every installation of MySQL!

One of the useful things about active patterns is that they let you use pattern matching with existing.NET object types. For example, the .NET object type System.Type is a runtime representation of types in .NET and F#. Here are the members found on this type: type System.Type with member IsGenericType : bool member GetGenericTypeDefinition : unit -> Type member GetGenericArguments : unit -> Type[] member HasElementType : bool member GetElementType : unit -> Type member IsByRef : bool member IsPointer : bool member IsGenericParameter : bool member GenericParameterPosition : int This type looks very much like one you d like to pattern-match against. There are clearly three or four distinct cases here, and pattern matching helps you isolate them. You can define an active pattern to achieve this, as shown in Listing 9-4. Listing 9-4. Defining an Active Pattern for Matching on System.Type Values let (|Named|Array|Ptr|Param|) (typ : System.Type) = if typ.IsGenericType then Named(typ.GetGenericTypeDefinition(),typ.GetGenericArguments()) elif typ.IsGenericParameter then Param(typ.GenericParameterPosition) elif not typ.HasElementType then Named(typ, [| |]) elif typ.IsArray then Array(typ.GetElementType(),typ.GetArrayRank()) elif typ.IsByRef then Ptr(true,typ.GetElementType()) elif typ.IsPointer then Ptr(false,typ.GetElementType()) else failwith "MSDN says this can't happen" This then lets you use pattern matching against a value of this type:

Throughout this book we have been using a second technique to specify configuration parameters when creating objects, which is using initial property settings for objects. For example, in 2 we used the following code: open System.Windows.Forms let form = new Form(Visible=true,TopMost=true,Text="Welcome to F#") The constructor for the System.Windows.Forms.Form class takes no arguments, so in this case the named arguments actually indicate post-hoc set operations for the given properties. The code is shorthand for this:

open System let rec formatType typ = match typ with | Named (con, [| |]) -> sprintf "%s" con.Name | Named (con, args) -> sprintf "%s<%s>" con.Name (formatTypes args) | Array (arg, rank) -> sprintf "Array(%d,%s)" rank (formatType arg) | Ptr(true,arg) -> sprintf "%s&" (formatType arg) | Ptr(false,arg) -> sprintf "%s*" (formatType arg) | Param(pos) -> sprintf "!%d" pos and formatTypes typs = String.Join(",", Array.map formatType typs) or collect the free generic type variables: let rec freeVarsAcc typ acc = match typ with | Array (arg, rank) -> freeVarsAcc arg acc | Ptr (_,arg) -> freeVarsAcc arg acc | Param _ -> (typ :: acc) | Named (con, args) -> Array.foldBack freeVarsAcc args acc let freeVars typ = freeVarsAcc typ []

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