One of the Tuple Types in .net 4 is a Single-Element Tuple. I just wonder what the purpose of this struct is?
The only use I saw is when using in the 8+ Tuple as it can be assigned to TRest, where it actually makes sense. Is that it? Or is there any other purpose?
You'd have to ask the BCL designers to be certain, but I suspect that since there is a 1-tuples in the real world, the .NET framework authors wanted to provide equivalent symmetry in their implementation.
Tuples are the .NET implementation of what you'd consider the mathematical concept of a tuple.
Now since you're asking for programming uses for Tuple<T>, I would also answer that there are .NET languages (like F#) that could use Tuple<> for representation of things like return values from functions. Since an F# function could certainly return a 1-tuple as a result - it adds symmetry and consistency to the behavior and feel of the language.
Your example with 8+ tuples is also probably legitimate, in that the Rest property could be a 1-tuple to represent the "overflow".
All tuple types implement ITuple, so I guess that when you want to have a return type that is an ITuple, you need the option of having a single value, as you suggest.
Tuples automatically implement IStructuralComparable and IStructuralEquatable, among other things. This allows tuples to be compared and sorted right out of the box. From Bill McCarthy's article in December 2009 edition of Visual Studio Magazine, "Types and Tuples in .NET 4":
Although tuples may look simple and nondescript, they do provide strong typing and important comparison and equality functionality. Tuples are useful across method, class or even machine boundaries.
By putting your data type into a tuple, even of only one element, you are guaranteed immutability, equatability, and comparability. For tuples consisting of only one element, the main benefit of using a tuple is going to be immutability: once the tuple is created, it's data can never change for the life of the tuple.