Does every function has to be inside a type like in C#? Or does F# has free functions?
Also what about functions I have seen all over some F# code like, cos, sin, etc. Are they calls to Math.Cos, Math.Sin?
Also why did they provide cos, sin, etc like that instead of Math.Cos, Math.Sin?
F# can have functions scoped in modules (instead of classes).
The CLR implements these, internally, as:
as a common language runtime (CLR) class that has only static members
They look like "free functions" within the scope of a module.
As Reed mentioned, functions can be defined within modules a la other ML languages, but they can also be defined on types like other .NET languages (and in fact modules are also compiled to classes). Within F#, modules can be opened to access the functions without having to use the module name each time, and modules are automatically created on a per-file basis if they aren't explicitly declared.
As to why there are separate cos, etc. functions instead of merely relying on .NET's built-in Math.Cos, etc., there are probably several reasons:
cos looks much more idiomatic in F# than calling the static method System.Math.Cos.cos doesn't just work on floats in F#, it also works on float32s and on any type which exposes a static Cos method, so you can create your own types to which the cos function can be applied.I'd guess that truly free functions aren't allowed because there are many .NET languages which don't expose convenient access to them, so using them would present a barrier to cross-language interoperability. The CLR itself does support free functions, and some languages such as C++/CLI do use them, but most languages compile functions into classes (even if that's not how it looks from a source code perspective, as in F#).
@Reed's answer is good. I just wanted to add that in F# you can 'open' modules so that module-bound functions can be called in an unqualified way, and that is where various 'top level' functions and operators come from, e.g.
http://msdn.microsoft.com/en-us/library/ee353754(VS.100).aspx
That is, F# is still subject to the CLR mechanisms, which means that every function must be in a class, but F# modules map to static classes on the CLR, modules can be 'opened' to provide the functions at the top level, and a handful of modules are 'auto-opened' so that the most common/convenient functions are available right away.
Having a variety of common functions available is very useful for scripting or interactive sessions, where you don't want to have to open a bunch of namespaces or spell out in 15 characters "System.Math.Cos" just to compute a cosine.
Joan,
Rather than all these questions about which features F# supports or does not support, maybe you'd be better served to start with a book on F#. Consider these two resources as a starting point:
http://en.wikibooks.org/wiki/F_Sharp_Programming
And also:
There's also Chris Smith's book which is an excellent introductory text.
Maybe you want to read them and work through them and then you can ask more directed questions. Just an idea.