A tale of two puzzles

As I begin to write this, I’m in a small cubicle in Philadelphia airport, on my way back from CodeMash – a wonderful conference (yet again) which I feel privileged to have attended. Personal top highlights definitely include Dustin Campbell’s talk on C# 6 (I’m practically dribbling with anticipation – bits please!) and playing Settlers of Catan on an enormous board. Kevin Pilch-Bisson’s talk on scriptcs was fabulous too, not least because he demonstrated its NuGet support using Noda Time. I’m very likely to use scriptcs as a tool to ease folks into the language gently if I ever get round to writing my introductory C# book. (To follow my own advice from the talk I gave, I should really just start writing it – whether the initial attempt is good or not, it’s better than having nothing.)

First puzzle

During Dustin’s talk, he set some puzzles around refactoring – where an "inline" operation had to be smarter than it originally appeared, for various reasons. The final puzzle particularly piqued my interest, as Dustin explained that various members of the C# team hadn’t actually worked out why the code behaved the way it did… the refactoring in Roslyn worked in that it didn’t change the behaviour, but more through a good general strategy than any attempt to handle this specific case.

So, the code in question is:

using System;

class X
    static int M(Func<int?, byte> x, object y) { return 1; }
    static int M(Func<X, byte> x, string y) { return 2; }

    const int Value = 1000;

    static void Main()
        var a = M(X => (byte) X.Value, null);

            Console.WriteLine(M(X => (byte) X.Value, null));

This produces output of:


Is this correct? Is it a compiler bug from the old native compiler, faithfully reproduced in Roslyn? Why would moving the expression into an "unchecked" block cause different behaviour?

In an attempt to give you enough space and time to avoid accidentally reading the answer, which is explained below, I’d like to take the time to mention the source of this puzzle. A few years ago, Microsoft hired Vladmir Reshetnikov into testing part of the C#/VB team. Vladmir had previously worked at JetBrains on Resharper, so it’s not like he was new to C#. Every year when I see Kevin and Dustin at CodeMash, they give me more reports of the crazy things Vladmir has come up with – perversions of the language way beyond my usual fare. The stories are always highly entertaining, and I hope to meet Vladmir in person one day. He has a twitter account which I’ve only just started following, but which I suspect I’ll find immensely distracting.


I massively overthought this for a while. I then significantly underthought it for a while. I played around with the code by:

  • Removing the second parameter from M
  • Changing the name of the parameter
  • Changing the parameter types in various ways
  • Making X.Value non-const (just static readonly)
  • Changing the value of X.Value to 100
  • Changing the lambda expression to make a call to a method using (byte) X.Value instead of returning it directly
  • Using a statement lambda

These gave me clues which I then failed to follow up on properly – partly because I was looking for something complicated. I was considering the categorization of a "cast of a constant value to a different numeric type" and similar details – instead of following through the compiler rules in a systematic way.

The expression we need to focus on is this:

M(X => (byte) X.Value, null)

This is just a method call using a lambda expression, using overload resolution to determine which overload to call and type inference to determine the type arguments to the method. In a very crude description of overload resolution, we perform the following steps:

  • Determine which overloads are applicable (i.e. which ones make sense in terms of the supplied arguments and the corresponding parameters)
  • Compare the applicable overload to each other in terms of "betterness"
  • If one applicable overload is "better" than all the others, use that (modulo a bit more final checking)
  • If there are no applicable overload, or no one applicable method is better than all the others, then the call is invalid and leads to a compile-time error

My mistake was jumping straight to the second bullet point, assuming that both overloads are valid in each case.

Overload 1 – a simple parameter

First let’s look at the first overload: the one where the first parameter is of type Func<int?, byte>. What does the lambda expression of X => (byte) X.Value mean when converted to that delegate type? Is it always valid?

The tricky part is working out what the simple-name X refers to as part of X.Value within the lambda expression. The important part of the spec here is the start of section 7.6.2 (simple names):

A simple-name is either of the form I or of the form I<A1, …, AK>, where I is a single identifier and <A1, …, AK> is an optional type-argument-list. When no type-argument-list is specified, consider K to be zero. The simple-name is evaluated and classified as follows:

  • If K is zero and the simple-name appears within a block and if the block’s (or an enclosing block’s) local variable declaration space (§3.3) contains a local variable, parameter or constant with name I, then the simple-name refers to that local variable, parameter or constant and is classified as a variable or value.

(The spec continues with other cases.) So X refers to the lambda expression parameter, which is of type int? – so X.Value refers to the underlying value of the parameter, in the normal way.

Overload 2 – a bit more complexity

What about the second overload? Here the first parameter to M is of type Func<X, byte>, so we’re trying to convert the same lambda expression to that type. Here, the same part of section 7.6.2 is used, but also section comes into play when determining the meaning of the member access expression X.Value:

In a member access of the form E.I, if E is a single identifier, and if the meaning of E as a simple-name (§7.6.2) is a constant, field, property, local variable, or parameter with the same type as the meaning of E as a type-name (§3.8), then both possible meanings of E are permitted. The two possible meanings of E.I are never ambiguous, since I must necessarily be a member of the type E in both cases. In other words, the rule simply permits access to the static members and nested types of E where a compile-time error would otherwise have occurred.

It’s not spelled out explicitly here, but the reason that it can’t be ambiguous is that you can’t have two members of the same name within the same type (other than for method overloads). You can have method overloads that are both static and instance methods, but then normal method overloading rules are enforced.

So in this case, X.Value doesn’t involve the use of the parameter called X at all. Instead, it’s the constant called value within the class X. Note that this is only the case because the type of the parameter is the same as the type that the parameter’s name refers to. (It isn’t quite the same as the names being the same. If you have a using directive introducing an alias, such as using Y = X; then the condition can be satisfied with different names.)

So what difference does unchecked make?

Now that we know what the conversions from the lambda expression to the two different delegate types mean, we can consider whether they’re always valid. Taking the overload resolution out of the picture, when is each of these lines valid at compile-time?

Func<int?, byte> foo = X => (byte) X.Value;
Func<X, byte> bar = X => (byte) X.Value;

Note that we’re not trying to consider whether they might throw an exception – clearly if you call foo(null) then that will fail. But will it at least compile?

The first line is always valid… but the second depends on your context, in terms of checked or unchecked arithmetic. For the most part, if you’re not explicitly in a checked or unchecked context, the language assumes a default context of unchecked, but allows "external factors" (such as a compiler flag). The Microsoft compiler is unchecked by default, and you can make an assembly use checked arithmetic "globally" using the /checked compiler argument (or going to the Advanced settings in the build properties of a Visual Studio project.

However, one exception to this "default" rule is constant expressions. From section 7.6.12 of the spec:

For constant expressions (expressions that can be fully evaluated at compile-time), the default overflow checking context is always checked. Unless a constant expression is explicitly placed in an unchecked context, overflows that occur during the compile-time evaluation of the expression always cause compile-time errors.

The cast of X.Value to byte is still a constant expression – and it’s one that overflows at compile-time, because 1000 is outside the range of byte. So unless we’re explicitly in an unchecked context, the code snippet above will fail for the second line.

Back to overloading

Given all of that, how does it fit in with our problem? Well, at this point it’s reasonably simple – so long as we’re careful. Look at the first assignment, which occurs outside the unchecked statement:

var a = M(X => (byte) X.Value, null);

Which overloads are applicable here? The second argument isn’t a problem – the null literal is convertible to both object and string. So can we convert the first argument (the lambda expression) to the first parameter of each overload?

As noted earlier, it’s fine to convert it to a Func<int?, byte>. So the first method is definitely applicable. However, the second method requires us to convert the lambda expression to Func<X, byte>. We’re not in an explicitly unchecked context, so the conversion doesn’t work. Where the rule quoted above talks about "overflows that occur during the compile-time evaluation of the expression always cause compile-time errors" it doesn’t mean we actually see an error message when the compiler speculatively tries to convert the lambda expression to the Func<X, byte> – it just means that the conversion isn’t valid.

So, there’s only one applicable method, and that gets picked and executed. As a result, the value of a is 1.

Now in the second call (inside the unchecked statement) both methods are applicable: the conversion from the lambda expression to the Func<X, byte> is valid because the constant conversion occurs within an explicitly unchecked context. We end up with two applicable methods, and need to see if one of them is definitively better than the other. This comes down to section of the C #5 spec, which gives details of a "better function member" test. This in turn ends up talking about better conversions from arguments to parameter types. The lambda expression conversions are effectively equal, but the conversion of null to string is "better than" the conversion to object, because there’s an implicit conversion from string to object but not vice versa. (In that sense the string conversion is "more specific" to borrow Java terminology.) So the second overload is picked, and we print 2 to the console.



This all comes down to the cast from a constant to byte being valid in an explicitly unchecked context, but not otherwise.

One odd part is that I spotted that reasonably quickly, and assumed the problem was actually fairly straightforward. It’s only when I started writing it up for this blog post that I dug into the spec to check the exact rules for the meaning of simple names in different situations. I’d solved the crux of the puzzle, but the exact details were somewhat involved. Indeed, while writing this blog post I’ve started two separate emails to the C# team reporting potential (equal and opposite) bugs – before discarding those emails as I got further into the specification.

This is reasonably common, in my experience: the C# language has been well designed so that we can intuitively understand the meaning of code without knowing the details of the exact rules. Those rules can be pretty labyrinthine sometimes, because the language is very precisely specified – but most of the time you don’t need to read through the rules in detail.

Didn’t you mention two puzzles?

Yes, yes I did.

The second puzzle is much simpler to state – and much harder to solve. To quote Vladmir’s tweet verbatim:

C# quiz: write a valid C# program containing a sequence of three tokens `? null :` that remains valid after we remove the `null`.

Constructing a valid program containing "? null :" is trivial.

Constructing a valid program containing "? :" is slightly trickier, but not really hard.

Constructing a program which is valid both with and without the null token is too hard for me, at the moment. I’m stuck – and I know I’m in good company, as Kevin, Dustin and Bill Wagner were all stuck too, last time I heard. I know of two people who’ve solved this so far… but I’m determined to get it…

31 thoughts on “A tale of two puzzles”

  1. It seems to me that the key to the second puzzle may be the ability for the “?” to be either part of a ternary operator or the Nullable suffix, but I can’t make that fit in a broader expression/statement yet.


  2. I nearly have one, taking advantage of both “?” being usable as a ternary component or the nullable indicator, and colon being used for all three of the ternary component, statement labels, and the case label of a switch statement. I’m struggling finding a form of the construct that doesn’t have type conversion problems, though, since C# doesn’t allow nullables as constants.


  3. Still not figured this one out, but one craziness I found while looking for a solution is this:

    (T is a struct type, x is a variable of a struct type)

    var z1 = x is T? || x is T ? null : x;
    var z2 = x is T? | x is T ? null : x;
    var z3 = x is T? && x is T ? null : x;
    var z4 = x is T? & x is T ? null : x;

    All of these compile fine, except the last one, where the compiler reads the attempted non-shortcircuiting AND as an address-of operator, and so reinterprets the first question mark as a conditional operator rather than a nullable type annotation.

    It’s a peculiar precedence clash, because the error goes away if the & operator isn’t preceded by a nullable type name that can be interpreted as a conditional:

    var z4 = x is T & x is T? ? null : x;

    Here the compiler reads it as a boolean operation.

    This is all particularly annoying because if you remove the null from the original form,

    var z5 = y is T? & y is T ? : x;

    it comes perilously close to compiling (in an unsafe context) – the lexer can make sense of this and the only complaint the compiler has there is that ‘is’ doesn’t work on pointer types.


  4. I don’t doubt that the noted behavior is correct per the spec. However, I have to admit that the strangest thing to me is that overload resolution itself can depend on checked/unchecked.

    That is, my naive philosophy would to require overload resolution to always produce the same list of candidate methods, given an identical invocation of a method.

    In this particular case, it would lead to an overt compile-time error, as both methods would be allowed, the better one chosen, and then an error generated (that the user would actually see) due to the default-checked context.

    My naive philosophies usually wind up being refuted as valid by some scenario I hadn’t considered. But that’s how I’d do it, given what I know today. :)


  5. @pete.d: Well it’s just a matter of context. “Which variables are in scope” affects the meaning of lambda expressions in a similar way, which can affect overload resolution… it’s the same as that, really. This isn’t an “identical invocation of a method” because the context is different… it’s just it’s different in a way which is more subtle than most contextual differences.


  6. Don’t forget ?? . I have gotten pretty far with that:

    unsafe static void Test()
    where T : struct
    object o = null;
    var x = o is T ? o as T? ?? o as T? null : o;

    That *nearly* compiles (T is not a class type), it does compile when the null is removed.


  7. @Jonathan: ?? is one token, not two ? tokens. Relaxing the token requirement makes it trivial ( string trivial = “? null :”)


  8. Am I missing something?

    bool result= (condition) ? someMethod(null) : someOtherMethod();

    public bool someMethod(object){return true;}
    public bool someMethod{return true;}
    public bool someOtherMethod{return true;}


  9. @Lior: Yes – that doesn’t contain the sequence of tokens we’re looking for. It contains the tokens, in the right order, but with other tokens in between.


  10. This problem *is* hard.

    *very minor spoilers*
    I have gotten pretty far — I can get the compilation problems arbitrarily far away from these tokens, but unable to unify at the end…yet.


    Jon, can you post when you get it.


          1. Interesting – it compiles under mono 3.12 and 4.0 as well… I suspect it’s a Mono bug rather than a Roslyn bug, but I’m honestly not sure without delving further.


  11. My personal take on this, is that the question says to “remove” null, rather than to “replace” null

    bool? x = (true) ? null : default(bool?);

    replace null…

    bool? x = (true) ? true is bool? : default(bool?);

    both compile.


    1. But that isn’t removing null – it’s replacing null with true is bool?. Yes, if you can replace null with whatever you like, it’s just trivial. It’s pure removal that is much, much harder.


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