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Note particularly that upcasts aren t applied automatically for the result of a function. For example, an upcast is needed here, to coerce a StreamReader to a TextReader, despite the presence of an explicit type annotation for the return type: let getTextReader () : TextReader = (File.OpenText("input.txt") :> TextReader)

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The following code from Listing 6-5 implements the object interface type IShape using an object expression: let circle(center:Point,radius:int) = { new IShape with member x.Contains(p:Point) = let dx = float32 (p.X - center.X) let dy = float32 (p.Y - center.Y) sqrt(dx*dx+dy*dy) <= float32 radius member x.BoundingBox = Rectangle(center.X-radius,center.Y-radius,2*radius+1,2*radius+1) } The type of the function circle is as follows:

F# also has the notion of a flexible type constraint, which is shorthand for a generic function and a constraint on the type variable. You could equally write this: > open System.Windows.Forms;; > let setTextOfControl (c : 'T when 'T :> Control) (s:string) = c.Text <- s;; val setTextOfControl: #Control -> string -> unit

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Once the test is created, you need to execute the test and create the baseline of expected results. Execute the following commands to run the newly created test named cab.test from the mysql-test directory: %> %> %> %> touch r/cab.result ./mysql-test-run.pl cab cp r/cab.reject r/cab.result ./mysql-test-run.pl cab

The construct in the braces, { new IShape with ... }, is the object expression. This is a new expression form that you haven t encountered previously in this book, because it is generally used only when implementing object interface types. An object expression must give implementations for all the members of an object interface type. The general form of this kind of expression is simple: { new Type optional-arguments with member-definitions optional-extra-interface-definitions } The member definitions take the same form as members for type definitions described earlier in this chapter. The optional arguments are given only when object expressions inherit from a constructed class type, and the optional interface definitions are used when implementing additional interfaces that are part of a hierarchy of object interface types. You can use the function circle as follows: > let bigCircle = circle(Point(0,0), 100);; val bigCircle : IShape > bigCircle.BoundingBox;; val it : Rectangle = {X=-100,Y=-100,Width=201,Height=201} > bigCircle.Contains(Point(70,70));; val it : bool = true > bigCircle.Contains(Point(71,71));; val it : bool = false Listing 6-5 also contains another function square that gives a different implementation for IShape, also using an object expression: > let smallSquare = square(Point(1,1), 1);; val smallSquare : IShape > smallSquare.BoundingBox;; val it : Rectangle = {X=0,Y=0,Width=3,Height=3} > smallSquare.Contains(Point(0,0));; val it : bool = false

Automatic generalization lifts the constraints implicit in types of the form #type to the nearest enclosing function or member definition. Flexible type constraints sometimes occur when you re working with sequence values. For example, consider the following two functions from the F# library: module Seq = ... val concat : seq<#seq<'T>> -> seq<'T> ... When implicit flexibility or arguments is taken into account, the signature of concat means that Seq.concat accepts a list of lists, or a list of arrays, or an array of lists, and so forth. For example: Seq.concat [ [1;2;3]; [4;5;6] ] Seq.concat [ [| 1;2;3 |]; [| 4;5;6 |] ]

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