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What is this thing you call a "type"? Part one

| Tuesday, August 30, 2011
(Eric is out camping; this posting is prerecorded. I'll be back in the office after Labour Day.)

The word "type" appears almost five thousand times in the C# 4 specification, and there is an entire chapter, chapter 4, dedicated to nothing but describing types. We start the specification by noting that C# is "type safe" and has "a unified type system" (*). We say that programs "declare" types, and that declared types can be organized by namespace. Clearly types are incredibly important to the design of C#, and incredibly important to C# programmers, so it is a more than a little bit surprising that nowhere in the eight hundred pages of the specification do we ever actually define the word "type".

We sort of assume that the developer reading the specification already has a working understanding of what a "type" is; the spec does not aim to be either a beginner programming tutorial or a mathematically precise formal language description. But if you ask ten working line-of-business developers for a formal definition of "type", you might get ten different answers. So let's consider today the question: what exactly is this thing you call a "type"?

A common answer to that question is that a type consists of:

* A name
* A set (possibly infinite) of values

And possibly also:

* A finite list of rules for associating values not in the type with values in the type (that is, coercions; 123.45 is not a member of the integer type, but it can be coerced to 123.)

Though that is not a terrible definition as a first attempt, it runs into some pretty nasty problems when you look at it more deeply.

The first problem is that of course not every type needs to have a name; C# 3 has anonymous types which have no names by definition. Is "string[][]" the name of a type? What about "List<string[][]>" -- does that name a type? Is the name of the string type "string" or "String", or "System.String", or "global::System.String", or all four? Does a type's name change depending on where in the source code you are looking?

This gets to be a bit of a mess. I prefer to think of types as logically not having names at all. Program fragments "12" and "10 + 2" and "3 * 4" and "0x0C" are not names for the number 12, they are expressions which happen to all evaluate to the number 12. That number is just a number; how you choose to notate it is a fact about your notational system, not a fact about the number itself. Similarly for types; the program fragment "List<string[][]>" might, in its context, evaluate to refer to a particular type, but that type need not have that fragment as its name. It has no name.

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