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F# functions can be declared to accept parameters that are any subtype of a particular type by using type annotations of the form #type, where type is some type that supports subtyping. This is particularly common when working with .NET libraries that use subtyping heavily. For example: > open System.Windows.Forms > let setTextOfControl (c : #Control) (s:string) = c.Text <- s;; val setTextOfControl: #Control -> string -> unit This notation is called a flexible type constraint and is shorthand for a generic function and a constraint on the type variable, and we could equally have written this: > open System.Windows.Forms;; > let setTextOfControl (c : 'a when 'a :> Control) (s:string) = c.Text <- s;; val setTextOfControl: #Control -> string -> unit Automatic generalization lifts the constraints implicit in types of the form #type to the nearest enclosing function or member definition. Flexible type constraints occur frequently when working with sequence values. For example, consider the following two functions from the F# library: module Seq = ... val append : #seq<'a> -> #seq<'a> -> seq<'a> val concat : #seq<#seq<'a>> -> seq<'a> ... You can read the first signature of append as Seq.append accepts two arguments, each of which must be compatible with the type seq<'a>, and it produces a seq<'a>. In practice, this means you can use Seq.append to append two F# lists, or an F# list and an F# array, or an F# sequence and an F# list, or two F# arrays, and so on. This is shown by the following calls, all of which result in a seq<int> yielding values 1 through 6: Seq.append Seq.append Seq.append Seq.append [1;2;3] [4;5;6] [| 1;2;3 |] [4;5;6] (seq { for x in 1 .. 3 -> x }) [4;5;6] [| 1;2;3 |] [| 4;5;6 |]

Mutable, resizable integer-indexed arrays, usually called ResizeArray<'T> in F#. Mutable, resizable lists implemented using sorted arrays. Mutable, resizable dictionaries implemented using hash tables. Mutable, resizable dictionaries implemented using sorted arrays. Mutable, first-in, first-out queues of unbounded size.

However, the element types of the two collections must be the same: the flexibility applies to the collection type rather than the element type. You can see a similarly advanced use of flexible types in the type signature for the function Seq.concat. You can use this function with 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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Yes, even though the classes don t exist you still write the tests The tests form a hybrid of integration, system, and interface testing (all white-box techniques) where each test exercises one of the classes in the domain model..

Mutable, first-in, last-out stacks of unbounded size. Mutable, resizable sets implemented using hash tables. New in .NET 3.5. The F# library also defines a Microsoft.FSharp.Collections.HashSet type usable in conjunction with earlier versions of .NET.

Most object-oriented languages automatically apply upcasts whenever a function or method is called or wherever a value is used. F# takes a different approach on this matter: on the whole, upcasts are applied only when a function or member signature indicates that it may be used in a flexible way. In practice, this means you sometimes have to add explicit upcasts to your code to throw away information. For example, if each branch of an if ... then ... else ... construct returns different types, then you will need to upcast the results of one or both of the branches, as shown by the type error given for the following code that returns Console.In (a TextReader) from one branch and the results of File.OpenText (a StreamReader) from the other branch: open System open System.IO let textReader = if DateTime.Today.DayOfWeek = DayOfWeek.Monday then Console.In else File.OpenText("input.txt") The error reported is as follows: > ...(enter the text above)...;; else File.OpenText("input.txt") ^^^^^^^^^^^^^^^^^^^^^^^^^^ error: FS0001: This expression has type StreamReader but is here used with type TextReader stopped due to error StreamReader is a subtype of TextReader, so the code can be corrected by throwing away the information that the returned type is a StreamReader: let textReader = if DateTime.Today.DayOfWeek = DayOfWeek.Monday then Console.In else (File.OpenText("input.txt") :> TextReader) Upcasts are applied automatically in the following situations: When calling functions with flexible parameter types such as #TextReader. When passing arguments to members associated with .NET and F# objects and types. When accessing members using the dot notation. For example, given a value of type StreamReader, all the members associated with TextReader can also be accessed without needing to apply an upcast.

Note White-box testing is testing without knowledge of how the system is constructed. Black-box testing

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