We Keep Coding

Enum cast integer and number [duplicate]

Just out of curiosity: why can I assign 0.0 to a variable that is of an enumeration type, but not 1.0? Have a look at the following code:
public enum Foo
{
Bar,
Baz
}
class Program
{
static void Main()
{
Foo value1 = 0.0;
Foo value2 = 1.0; // This line does not compile
Foo value3 = 4.2; // This line does not compile
}
}
I thought that conversions between numerical types and enumeration values are only allowed via casts? That is I could write Foo value2 = (Foo) 1.0; so that line 2 in Main can compile. Why is there an exception for the value 0.0 in C#?

It's a bug that you can use 0.0. The compiler implicitly treats all constant expressions with a value of zero as just 0.
Now, it's correct for the compiler to allow an implicit conversion from a constant int expression of 0 to your enum as per section 6.1.3 of the C# 5 specification:
An implicit enumeration conversion permits the decimal-integer-literal 0 to be converted to any enum-type and to any nullable-type whose underlying type is an enum-type. In the latter case the conversion is evaluated by converting to the underlying enum-type and wrapping the result (§4.1.10).
I've spoken with the C# team about this before: they'd have liked to have removed the accidental conversion from 0.0 (and indeed 0.0m and 0.0f) to enum values, but unfortunately I gather it broke too much code - even though it should never have been allowed in the first place.
The Mono mcs compiler prohibits all of these floating point conversions, although it does allow:
const int Zero = 0;
...
SomeEnum x = Zero;
despite the fact that Zero is a constant expression but not a decimal-integer-literal.
I wouldn't be surprised to see the C# specification change in the future to allow any integer constant expression with a value of 0 (i.e. to mimic mcs), but I wouldn't expect the floating point conversions to ever officially be correct. (I've been wrong before about predicting the future of C#, of course...)

Jon's answer is correct. I would add to it the following points.
I caused this silly and embarrassing bug. Many apologies.
The bug was caused by me misunderstanding the semantics of an "expression is zero" predicate in the compiler; I believed it was checking only for integer zero equality, when in fact it was checking for more along the lines of "is this the default value of this type?" In fact, in an earlier version of the bug it was actually possible to assign the default value of any type to an enum! It is now only default values of numbers. (Lesson: Name your helper predicates carefully.)
The behaviour I was attempting to implement that I messed up was in fact a workaround for a slightly different bug. You can read the whole terrible story here: https://learn.microsoft.com/en-us/archive/blogs/ericlippert/the-root-of-all-evil-part-one and
https://learn.microsoft.com/en-us/archive/blogs/ericlippert/the-root-of-all-evil-part-two
(Lesson: It is very easy to introduce new worse bugs while fixing old ones.)
The C# team decided to enshrine this buggy behaviour rather than fixing it because the risk of breaking existing code for no compelling benefit was too high. (Lesson: get it right the first time!)
The code I wrote in Roslyn to preserve this behaviour can be found in the method IsConstantNumericZero in https://github.com/dotnet/roslyn/blob/master/src/Compilers/CSharp/Portable/Binder/Semantics/Conversions/ConversionsBase.cs -- see it for more details of what exactly the Roslyn behaviour is. I wrote almost all the code in the Conversions directory; I encourage you to read all of it as there are many interesting facts about how C# diverges from the specification in the comments. I decorated each with SPEC VIOLATION to make them easy to find.
One more point of interest: C# also allows any enum value to be used in an enum initializer regardless of its zeroness:
enum E { A = 1 }
enum F { B = E.A } // ???
The spec is somewhat vague as to whether this should be legal or not, but again, as this has been in the compiler for a long time, the new compilers are likely to maintain the behaviour.

Enumerations in C# are by definition integral values. For consistency C# shouldn’t accept either of these assignments, but 0.0 is silently treated as integral 0. This is probably a holdover from C, where the literal 0 was treated specially and could essentially take any given type – integer, floating point number, null pointer … you name it.

enum is really intended (in all languages which support it) to be a way to work with meaningful and unique strings (labels) rather than a numeric values. Thus, in your example, you should only be using Bar and Baz when dealing with a Foo enumerated data type. You should never use (compare to, or assign) an integer, even though many compilers will let you get away with it (enums are usually integers internally), and in this case, a 0.0 is carelessly treated as a 0 by the compiler.
Conceptually, it should be all right to add an integer n to an enumerated value, to get n values further down the line, or to take val2-val1 to see how far apart they are, but unless the language specification explicitly allows this, I'd avoid it. (Think of an enumerated value as being like a C pointer, in the ways you can use it.) There's no reason enums couldn't be implemented with floating point numbers, and a fixed increment between them, but I haven't heard of this being done in any language.

Type Inference Causes Null References

I'm using the ILNumerics library for a project, but I found that variables declared with "var" will sometimes change value in the middle of computation, for example:
// A is a matrix
var x = A[full, 0];
double xNorm = (double)norm(x);
The x is valid in the first line, however causes "NullReference" exception after execution of the second line.
But If I do:
// A is a matrix
ILArray<double> x = A[full, 0];
double xNorm = (double)norm(x);
The computation will be fine. So what is the problem here? Does that mean we need to be cautious when using "var"?

It's not a bug - it's a feature :)
The var keyword is not allowed to be used in this context. This is part of a collection of three ILNumerics specific rules. It can also be found in the guickstart guide.
In short, the ILNumerics memory management relies heavily on implicit type conversions. All functions / properties return array types of ILRetArray<T>. These return types are volatile by design: they dispose off their storage after the first use. Always. So one can give them to some other function or query some information from them. But you would rather not try to access it a second time!
However, the only way to access such an object twice would be to have a reference (a regular local variable) around. ILNumerics specifies that all local variables must be of type ILArray, ILLogical or ILCell. Once you assign an array to a variable of one of those types, implicit type conversions kick in and 'turn' the volatile return object into something more stable and safe to access several times.
This is why the var keyword is forbidden in C# with ILNumerics. Similar thing for Visual Basic, where you also must declare the type of local array variables explicitly. I once made a blog post about the issue:
http://ilnumerics.net/blog/why-the-var-keyword-is-not-allowed-in-ilnumerics/

When declared with var, x is referring to something of type ILRetArray'1; if declared as ILArray<double>, it's ILArray'1. Those are sibling subclasses of a common base (ILDenseArray). A's type is ILArray<double> and its array-indexing operator returns type ILRetArray<ElementType>.
There are implicit conversion operators going both ways here between those two classes.
It looks like when A[full, 0] is assigned to a variable whose type is left up to type inference, the compiler makes it the return type of A's array indexing operator: ILRetArray<ElementType>. But if you declare x's type explicitly as ILArray<double>, an implicit conversion operator is invoked and you get a different actual object.
Then you pass it to norm, which expects ILInArray, and yet another implicit conversion operator is invoked. And there's a bug in that one. It breaks something in the internal state of ILRetArray. Try this line before the call to norm:
var d = (ILInArray<double>)x;
...and it will have the same effect on x as the call to norm did. So it's that conversion.
I haven't downloaded the source to ILNumerics to identify the details of the bug. It's possible that this is meant to be a forbidden operation, in which case I'd wish they had better error reporting (UPDATE see #HaymoKutschbach's answer below: This is in fact the case; ILRetArray is a volatile type by design, intended to be valid only until the first implicit conversion operator is called on it).
It might be fun to submit a bug report to ILNumerics and see what you hear back (UPDATE: There's a guy from ILN in this thread, so never mind).
But in answer to your question: You do need to be a bit cautious when using var; avoid it when there's any possibility of ambiguity. You need to be especially cautious when implicit conversion operators are involved. I had forgotten those things even existed in C#. I'm not fond of them. Of course the bug wasn't caused by their use of an implicit conversion operator; it's just a bug. But the operators vastly and invisibly confused the issue of what was going on in the code. I prefer type conversions to be visible in the source.
Thanks for posting this, it was fun.

Upcasting in C#

Can we consider value type conversions like int to float conversion as upcasting and float to int as downcasting? I believe when we talk about upcasting and downcasting, we specifically mean reference conversions.

No, conversions between value types cannot be seen as upcasting or downcasting, as these do not share a hierarchical link (they do not inherit from each other in any way or form).
Upcasting means specifically that you are changing a subtype reference to a super type reference.
Downcasting is the other way around.

No, a float is not a special case (I.E. subclass of) an int. They are different types.

No, up- and downcasting is only valid in the context of inheritance. When you are converting between value types that can hold more or less data you are using plain type conversions. Of that, there are two different types:
1. Implicit conversions. These are conversions that can be made as the conversion is "safe", that is there will be no data lost. For example, you can safely convert an int value to a long value.
2. Explicit conversions. These are conversions that can result in the losing of data and therefore you have to do an explicit cast to do the conversion. For example, converting a long value to an int is unsafe.
For more importation, see: http://msdn.microsoft.com/en-us/library/ms173105.aspx

These are not examples of upcasting and downcasting, as others have described. However, we can talk about widening and narrowing primitive type conversions (for instance, going from int to long is a widening conversion and hence can be done implicitly.) In this particular case (float/int), however, the conversion is a bit different.
There is an implicit conversion from int to float, but the conversion can actually still lose precision, due to the inability of float to represent integral numbers exactly. This is worth knowing, as it bends the general rule that implicit conversions should never lose information. This is really only noticeable if you convert integers to floats, do a bunch of accumulating math with them and then try converting back to an int. In these cases, the approximation error can accumulate, producing incorrect results if you assumed the floats were perfect representations of decimal numbers.

Delegate.CreateDelegate won't box a return value - deliberate, or an ommission?

I have a static method:
public class Example
{
//for demonstration purposes - just returns default(T)
public static T Foo<T>() { return default(T); }
}
And I need to be able to invoke it using a Type parameter calls to which could be numerous, so my standard pattern is to create a thread-safe cache of delegates (using ConcurrentDictionary in .Net 4) which dynamically invoke the Foo<T> method with the correct T. Without the caching, though, the code is this:
static object LateFoo(Type t)
{
//creates the delegate and invokes it in one go
return (Func<object>)Delegate.CreateDelegate(
typeof(Func<object>),
typeof(Example).GetMethod("Foo", BindingFlags.Public | BindingFlags.Static).
MakeGenericMethod(t))();
}
This is not the first time I've had to do this - and in the past I have use Expression trees to build and compile a proxy to invoke the target method - to ensure that return type conversion and boxing from int -> object (for example) is handled correctly.
Update - example of Expression code that works
static object LateFoo(Type t)
{
var method = typeof(Example)
.GetMethod("Foo", BindingFlags.Public | BindingFlags.Static)
.MakeGenericMethod(t);
//in practise I cache the delegate, invoking it freshly built or from the cache
return Expression.Lambda<Func<IField, object>>(Expression.Convert(
Expression.Call(method), typeof(object))).Compile()();
}
What's slightly amusing is that I learned early on with expressions that an explicit Convert was required and accepted it - and in lieu of the answers here it does now make sense why the .Net framework doesn't automatically stick the equivalent in.
End update
However, this time I thought I'd just use Delegate.CreateDelegate as it makes great play of the fact that (from MSDN):
Similarly, the return type of a delegate is compatible with the return type of a method if the return type of the method is more restrictive than the return type of the delegate, because this guarantees that the return value of the method can be cast safely to the return type of the delegate.
Now - if I pass typeof(string) to LateFoo method, everything is fine.
If, however, I pass typeof(int) I get an ArgumentException on the CreateDelegate call, message: Error binding to target method. There is no inner exception or further information.
So it would seem that, for method binding purposes, object is not considered more restrictive than int. Obviously, this must be to do with boxing being a different operation than a simple type conversion and value types not being treated as covariant to object in the .Net framework; despite the actual type relationship at runtime.
The C# compiler seems to agree with this (just shortest way I can model the error, ignore what the code would do):
public static int Foo()
{
Func<object> f = new Func<object>(Foo);
return 0;
}
Does not compile because the Foo method 'has the wrong return type' - given the CreateDelegate problem, C# is simply following .Net's lead.
It seems to me that .Net is inconsistent in it's treatment of covariance - either a value type is an object or it's not; & if it's not it should not expose object as a base (despite how much more difficult it would make our lives). Since it does expose object as a base (or is it only the language that does that?), then according to logic a value type should be covariant to object (or whichever way around you're supposed to say it) making this delegate bind correctly. If that covariance can only be achieved via a boxing operation; then the framework should take care of that.
I dare say the answer here will be that CreateDelegate doesn't say that it will treat a box operation in covariance because it only uses the word 'cast'. I also expect there are whole treatises on the wider subject of value types and object covariance, and I'm shouting about a long-defunct and settled subject. I think there's something I either don't understand or have missed, though - so please enlighten!
If this is unanswerable - I'm happy to delete.

You can only convert a delegate in this way if the parameters and return value can be converted using a representation conserving conversion.
Reference types can only be converted to other reference types in this way
Integral values can be converted to other integer values of the same size (int, uint, and enums of the same size are compatible)
A few more relevant blog articles:
This dichotomy motivates yet another classification scheme for conversions (†). We can divide conversions into representation-preserving conversions (B to D) and representation-changing conversions (T to U). (‡) We can think of representation-preserving conversions on reference types as those conversions which preserve the identity of the object. When you cast a B to a D, you’re not doing anything to the existing object; you’re merely verifying that it is actually the type you say it is, and moving on. The identity of the object and the bits which represent the reference stay the same. But when you cast an int to a double, the resulting bits are very different.
This is why covariant and contravariant conversions of interface and delegate types require that all varying type arguments be of reference types. To ensure that a variant reference conversion is always identity-preserving, all of the conversions involving type arguments must also be identity-preserving. The easiest way to ensure that all the non-trivial conversions on type arguments are identity-preserving is to restrict them to be reference conversions.
http://blogs.msdn.com/b/ericlippert/archive/2009/03/19/representation-and-identity.aspx
"but how can a value type, like int, which is 32 bits of memory, no more, no less, possibly inherit from object? An object laid out in memory is way bigger than 32 bits; it's got a sync block and a virtual function table and all kinds of stuff in there." Apparently lots of people think that inheritance has something to do with how a value is laid out in memory. But how a value is laid out in memory is an implementation detail, not a contractual obligation of the inheritance relationship! When we say that int inherits from object, what we mean is that if object has a member -- say, ToString -- then int has that member as well.
http://ericlippert.com/2011/09/19/inheritance-and-representation/

It seems to me that .Net is inconsistent in it's treatment of covariance - either a value type is an object or it's not; if it's not it should not expose object as a base
It depends on what the meaning of "is" is, as President Clinton famously said.
For the purposes of covariance, int is not object because int is not assignment compatible with object. A variable of type object expects a particular bit pattern with a particular meaning to be stored in it. A variable of type int expects a particular bit pattern with a particular meaning, but a different meaning than the meaning of a variable of object type.
However, for the purposes of inheritance, an int is an object because every member of object is also a member of int. If you want to invoke a method of object -- ToString, say -- on int, you are guaranteed that you can do so, because an int is a kind of object, and an object has ToString.
It is unfortunate, I agree, that the truth value of "an int is an object" varies depending on whether you mean "is assignment-compatible with" or "is a kind of".
If that covariance can only be achieved via a boxing operation; then the framework should take care of that.
OK. Where? Where should the boxing operation go? Someone, somewhere has to generate a hunk of IL that has a boxing instruction. Are you suggesting that when the framework sees:
Func<int> f1 = ()=>1;
Func<object> f2 = f1;
then the framework should automatically pretend that you said:
Func<object> f2 = ()=>(object)f1();
and thereby generate the boxing instruction?
That's a reasonable feature, but what are the consequences? Func<int> and Func<object> are reference types. If you do f2 = f1 on reference types like this, do you not expect that f2 and f1 have reference identity? Would it not be exceedingly strange for this test case to fail?
f2 = f1;
Debug.Assert(object.ReferenceEquals(f1, f2));
Because if the framework implemented that feature, it would.
Similarly, if you said:
f1 = MyMethod;
f2 = f1;
and you asked the two delegates whether they referred to the same method or not, would it not be exceedingly weird if they referred to different methods?
I think that would be weird. However, the VB designers do not. If you try to pull shenanigans like that in VB, the compiler will not stop you. The VB code generator will generate non-reference-equal delegates for you that refer to different methods. Try it!
Moral of the story: maybe C# is not the language for you. Maybe you prefer a language like VB, where the language is designed to take a "make a guess about what the user probably meant and just make it work" attitude. That's not the attitude of the C# designers. We are more "tell the user when something looks suspiciously wrong and let them figure out how they want to fix it" kind of people.

Even though I think #CodeInChaos is absolutely right, I can't help pointing this Eric Lippert's blog post out. In reply to the last comment to his post (at the very bottom of the page) Eric explains the rationale for such behaviour, and I think this is exactly what you're interested in.
UPDATE: As #Sheepy pointed out Microsoft moved old MSDN blogs into archive and removed all comments. Luckily, the Wayback Machine preserved the blog post in its original form.

Question regarding implicit conversions in the C# language specification

Section 6.1 Implicit conversions defines an identity conversion thusly:
An identity conversion converts from any type to the same type. This conversion exists such that an entity that already has a required type can be said to be convertible to that type.
Now, what is the purpose of sentences such as these?
(In §6.1.6 Implicit reference conversions)
The implicit reference conversions are:
[...]
From any reference-type to a reference-type T if it has an implicit identity or reference conversion to a reference-type T0 and T0 has an identity conversion to T.
and:
(In §6.1.7 Boxing conversions)
A value type has a boxing conversion to an interface type I if it has a boxing conversion to an interface type I0 and I0 has an identity conversion to I.
Initially they seem redundant (tautologous). But they must be there for a purpose, so why are they there?
Can you give an example of two types T1, T2 such that T1 would not be implicitly convertible to T2 if it weren’t for the above-quoted paragraphs?

Update on 22-Sep-2010:
I doubt anybody is going to read this besides Timwi. Even so, I wanted to make a few edits to this answer in light of the fact that a new answer has now been accepted and the debate still continues (at least in my perhaps imaginary world) on whether or not the quoted excerpts of the spec are technically redundant. I am not adding much, but it's too substantial to fit in a comment. The bulk of the update can be found under the heading "Conversion involving the dynamic type" below.
Update on 19-Sep-2010:
In your comment:
[T]his doesn’t make sense.
Damn, Timwi, you say that a lot. But all right, then; you've put me on the defensive, so here goes!
Disclaimer: I have definitely not examined the spec as closely as you have. Based on some of your recent questions it seems like you've been looking into it quite a bit lately. This is naturally going to make you more familiar with a lot of details than most users on SO; so this, like most answers you're likely to receive from anyone other than Eric Lippert, may not satisfy you.
Different premises
Firstly, the premise of your question is that if the statements highlighted are redundant, then they serve no purpose. My answer's premise is that redundant statements are not necessarily without purpose if they clarify something that isn't obvious to everyone. These are contradictory premises. And if we can't agree on premises, we can't have a straightforward logical argument. I was simply asking you to rethink your premise.
Your response, however, was to reiterate your premise: "If the sentences are truly redundant, then they only confuse the reader and don't clarify anything."
(I like how you set yourself up as the representative for all readers of the spec there, by the way.)
I can't blame you for holding this position, exactly. I mean, it does seem obvious. And I didn't give any concrete examples in my original answer. So below I will try to include some concrete examples. But first, let me take a step back and offer my take on why this weird identity conversion concept exists in the spec in the first place.
The purpose of the identity conversion definition
Upon first glance, this definition seems rather superfluous; isn't it just saying that an instance of any type T is convertible to ... well, to T? Yes, it is. But I hypothesize* that the purpose of this definition is to provide the spec with the proper vocabulary to utilize the concept of type identity in the context of discussing conversions.
This allows for statements about conversions which are essentially transitive in nature. The first point you quoted from the spec as an example of a tautological statement falls into this category. It says that if an implicit conversion is defined for some type (I'll call it K) to another type T0 and T0 has an identity conversion to T, then K is implicitly convertible to T. By the definition of identity conversion given above, "has an identity conversion to" really means "is the same type as." So the statement is redundant.
But again: the identity conversion definition exists in the first place to equip the spec with a formal language for describing conversions without having to say things like "if T0 and T are really the same type."
OK, time for concrete examples.
Where the existence of an implicit conversion might not be obvious to some developers
Note: A much better example has been provided by Eric Lippert in his answer to the question. I leave these first two examples as only minor reinforcements of my point. I have also added a third example that concretizes the identity conversion that exists between object and dynamic as pointed out in Eric's answer.
Transitive reference conversion
Let's say you have two types, M and N, and you've got an implicit conversion defined like this:
public static implicit operator M(N n);
Then you can write code like this:
N n = new N();
M m = n;
Now let's say you've got a file with this using statement up top:
using K = M;
And then you have, later in the file:
N n = new N();
K k = n;
OK, before I proceed, I realize that this is obvious to you and me. But my answer is, and has been from the beginning, that it might not be obvious to everyone, and therefore specifying it--while redundant--still has a purpose.
That purpose is: to make clear to anyone scratching his or her head, looking at that code, it is legal. An implicit conversion exists from N to M, and an identity conversion exists from M to K (i.e., M and K are the same type); so an implicit conversion exists from N to K. It isn't just logical (though it may be logical); it's right there in the spec. Otherwise one might mistakenly believe that something like the following would be necessary:
K k = (M)n;
Clearly, it isn't.
Transitive boxing conversion
Or take the type int. An int can be boxed as an IComparable<int>, right? So this is legal:
int i = 10;
IComparable<int> x = i;
Now consider this:
int i = 10;
IComparable<System.Int32> x = i;
Again, yes, it may be obvious to you, me, and 90% of all developers who might ever come across it. But for that slim minority who don't see it right away: a boxing conversion exists from int to IComparable<int>, and an identity conversion exists from IComparable<int> to IComparable<System.Int32> (i.e., IComparable<int> and IComparable<System.Int32> are the same type); so a boxing conversion exists from int to IComparable<System.Int32>.
Conversion involving the dynamic type
I'm going to borrow from my reference conversion example above and just tweak it slightly to illustrate the identity relation between object and dynamic in version 4.0 of the spec.
Let's say we have the types M<T> and N, and have defined somewhere the following implicit conversion:
public static implicit operator M<object>(N n);
Then the following is legal:
N n = new N();
M<dynamic> m = n;
Clearly, the above is far less obvious than the two previous examples. But here's the million-dollar question: would the above still be legal even if the excerpts from the spec quoted in the question did not exist? (I'm going to call these excerpts Q for brevity.) If the answer is yes, then Q is in fact redundant. If no, then it is not.
I believe the answer is yes.
Consider the definition of identity conversion, defined in section 6.1.1 (I am including the entire section here as it is quite short):
An identity conversion converts from any type to the same type. This conversion exists such that an entity that already has a required type can be said to be convertible to that type.
Because object and dynamic are considered equivalent there is an identity conversion between object and dynamic, and between constructed types that are the same when replacing all occurences of dynamic with object. [emphasis mine]
(This last part is also included in section 4.7, which defines the dynamic type.)
Now let's look at the code again. In particular I'm interested in this one line:
M<dynamic> m = n;
The legality of this statement (disregarding Q -- remember, the issue being discussed is the hypothetical legality of the above statement if Q did not exist), since M<T> and N are custom types, depends on the existence of a user-defined implicit conversion between N and M<dynamic>.
There exists an implicit conversion from N to M<object>. By the section of the spec quoted above, there is an identity conversion between M<object> and M<dynamic>. By the definition of identity conversion, M<object> and M<dynamic> are the same type.
So, just as in the first two (more obvious) examples, I believe it is true that an implicit conversion exists from N to M<dynamic> even without taking Q into account, just as it is true that an implicit conversion exists from N to K in the first example and that a boxing conversion exists from int to IComparable<System.Int32> in the second example.
Without Q, this is much less obvious (hence Q's existence); but that does not make it false (i.e., Q is not necessary for this behavior to be defined). It just makes it less obvious.
Conclusion
I said in my original answer that this is the "obvious" explanation, because it seemed to me you were barking up the wrong tree. You initially posed this challenge:
Can you give an example of two types T1, T2 such that T1 would not be implicitly convertible to T2 if it weren’t for the above-quoted paragraphs?
No one's going to meet this challenge, Timwi, because it's impossible. Take the first excerpt about reference conversions. It is saying that a type K is implicitly convertible to a type T if it is implicitly convertible to T0 and T0 is the same as T. Deconstruct this, put it back together, and you're left with an obvious tautology: K is implicitly convertible to T if it's implicitly convertible to T. Does this introduce any new implicit conversions? Of course not.
So maybe Ben Voigt's comment was correct; maybe these points that you're asking about would've been better placed in footnotes, rather than in the body of the text. In any case, it's clear to me that they are redundant, and so to start with the premise they cannot be redundant, or else they wouldn't be there is to embark on a fool's errand. Be willing to accept that a redundant statement may still shed some light on a concept that may not be obvious to everyone, and it will become easier to accept these statements for what they are.
Redundant? Yes. Tautologous? Yes. Pointless? In my opinion, no.
*Obviously, I did not have any part in writing the C# language specification. If I did, this answer would be a lot more authoritative. As it is, it simply represents one guy's feeble attempt to make sense of a rather complex document.
Original answer
I think you're (perhaps intentionally) overlooking the most obvious answer here.
Consider these two sentences in your question:
(1) Initially they seem redundant
(tautologous). (2) But they must be there
for a purpose, so why are they there?
To me, the implication of these two sentences together is that a tautologous statement serves no purpose. But just because a statement follows logically from established premises, that does not make it obvious to everyone. In other words even if (1) is true, the answer to (2) may simply be: to make the described behavior clear to anyone reading the spec.
Now you might argue that even if something is not obvious, it still does not belong in a specification if it is providing a redundant definition. To this potential objection, I can only say: be realistic. It's not really practical (in my opinion) to comb through a document stripping out all statements which are simply stating facts that could have been deduced from prior statements.
If this were a common practice, I think you'd find a lot of literature out there -- not just specs, but research papers, articles, textbooks, etc. -- would be a lot shorter, denser, and more difficult to understand.
So: yes, perhaps they are redundant. But that does not negate their purpose.

Section 4.7 of the specification notes that there is an identity conversion from Foo<dynamic> to Foo<object> and vice versa. The portion of the spec you quoted is written to ensure that this case is handled. That is, if there is an implicit reference conversion from T to C<object, object> then there is also an implicit reference conversion to C<object, dynamic>, C<dynamic, object> and C<dynamic, dynamic>.
One might reasonably point out that (1) the intention of these phrases is unobvious - hence your question - and confusing, and (2) that the section on identity conversions ought to cross-reference the section on dynamic conversions, and (3) phrases like this in the spec make it difficult for an implementor of the specification to clearly translate the spec language into an implementation. How is one to know if any such type exists? The spec need not specify exact algorithms, but it would be nice if it gave more guidance.
The spec is, sadly, not a perfect document.

An identity conversion converts from
any type to the same type. This
conversion exists such that an entity
that already has a required type can
be said to be convertible to that
type.
This says that in C#-land, 1==1; a Spade is a Spade. This is the basis of assigning an object reference to a variable of the same type; if a variable typed T1 and one typed T2 are in reality both Spades, it is possible to assign one to the other without having to explicitly cast one as a Spade. Imagine a C# variant where assignments had to look like this:
Spade mySpade = new Spade();
Spade mySpade2;
mySpade2 = (Spade)mySpade; //explicit cast required
Also, an "identity" in mathematics states that an expression that evaluates to a result given a set of inputs is equivalent to another expression that produces the same result given the same inputs. In programming, this means that an expression or function that evaluates to an instance of a type is equivalent to that type, without explicit conversion. If that didn't hold, the following code would be required:
public int myMethod() { /*Do something*/ }
...
int myInt = (int)myMethod(); //required even though myMethod() evals to an int.
...
int myInt = (int)(1 + 2); //required even though 1, 2, and 1+2 eval to an int.
The second rule basically says that a value type can be assigned to a member variable on a class if, in part, the member variable (a boxed type by definition, as its container is a reference type) is declared to be the same type. If this rule were not specified, theoretically, a version of C# could exist in which pure value types would have to be explicitly converted to their reference analog in order to be stored as a member variable on a class. Imagine, for example, a version of C# in which the blue keyword types (int, float, decimal) and the light blue class names (Int32, Float, Decimal) referred to two very different, only-explicitly-convertible types, and int, float, decimal etc. were not legal as member variable types because they were not reference types:
public class MyClass
{
Int32 MyBoxedValueType; //using "int" not legal
}
...
MyClass myClass = new MyClass();
int theInt = 2;
myClass.MyBoxedValueType = (Int32)theInt; //explicit cast required
I know it sounds silly, but at some level, these things must be known, and in computers, you have to specify EVERYTHING. Read the USA Hockey rulebook for ice hockey sometime; the very first rule in the book is that the game shall be played on an ice surface. It's one of the ultimate "well duhs", but also a fundamental truth of the game that must be understood in order for any other rule to make sense.

May it is such that the code guarantees pass-through when called like Convert.ChangeType(client, typeof(Client)) regardless if IConvertible is implemented.
Look into the source of ChangeType from mscorlib with Reflector and notice the conditions at which value is returned as-is.
Remember a = operator is not a conversion, just a reference set. So code like Client client_2 = client_1 does not perform any implicit conversions. If an identity implicit conversion is declared then error CS0555 is issued.
I guess the spec says let the C# compiler handle such cases, and thus dot not manually try to define identity conversions.