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Simple types are related in simple ways; for example, values of the type int are distinct from values of the type float, and values of one record type are distinct from values of another. This approach to types is powerful and often sufficient, partly because type inference and function values make it easy to write generic code. However, .NET and F# also support hierarchical relationships between types through subtyping. Subtyping is a key concept of object-oriented programming and is discussed in more detail in 6. In addition, you can use subtyping in conjunction with pure functional programming, because it offers one technique to make algorithms generic over a restricted family of types. The following sections explain how these constructs appear to the F# programmer and the role they play in F# programming. Subtyping in F# is the same as that used by the .NET Framework, so if you re familiar with another .NET language, you already know how things work.

Historically, the Mac OS has had only rudimentary facilities for application identification, and really no methods for application authentication That is, an application can identify itself, but there was no way for it to absolutely prove its identity With the original Mac OS, application identification was stored primarily in an application s resource fork in the form of a four-byte string called the creator code This creator code was then used by the operating system to associate data files with their respective application, and thus there was no need for the standard three-letter extension used by other operating systems (exe, doc, txt) In the old days, this actually worked out very well, and is one of the reasons that in the early days the Mac had been considered to a be more userfriendly platform.

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You can explore how subtyping works by using F# Interactive. First, let s look at how some of the F# types you ve already seen relate to the type obj: > let xobj = (1 :> obj);; val xobj : obj = 1 > let sobj = ("abc" :> obj);; val sobj : obj = "abc" This example shows the subtyping relationship through the use of the built-in coercion (or upcast) operator, which is :>. This operator converts a value to any of its supertypes in precisely the same way as the box function. The previous code indicates the subtyping between ordinary types and the type obj. Subtyping occurs between other kinds of types as well (s 3 and 6 discuss the various kinds of type definitions, such as records, discriminated unions, classes, and interfaces): All types are subtypes of System.Object (called obj in F#). Record and discriminated union types are subtypes of the interface types they implement. Interfaces types are subtypes of the other interfaces they extend. Class types are subtypes of both the interfaces they implement and the classes they extend. Array types are subtypes of the .NET type System.Array. Value types (types such as int32 that are abbreviations of .NET value types) are subtypes of the .NET type System.ValueType. Likewise, .NET enumeration types are subtypes of System.Enum.

Unfortunately the system just didn t hold up in the modern day for a number of reasons Four bytes of data equate to four characters, and certainly the possibility for collisions (two applications with the same creator code) is fairly high To address this issue, Apple provided a registration system and database that ensured that all Mac OS developers applications had unique identifiers It was cumbersome, but it worked, and developers could reasonably assume that their application s identifier was unique The other problem with creator codes as a means for application identification is that there is absolutely no way to prevent your creator code from being hijacked: if an unscrupulous party wants to create an application using your creator code, there is nothing to stop them from doing so.

Values that may have subtypes carry a runtime type, and you can use runtime-type tests to query the type of an object and convert it to one of the subtypes. You can do this in three main ways: the unbox

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