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How Does FirstOrDefault Test for Equality?

I have a reference type that implements the IEquatable Interface. I have a Hashset that contains a single object. I then create an object that, by IEquatable's standards are example the same. But, when I run
var equivalentEntry = _riskControlATMEntries[grouping.Key].FirstOrDefault(e => e == atmEntry);
on the object I get null.
On the otherhand when I do
var equivalentEntry = _riskControlATMEntries[grouping.Key].FirstOrDefault(e => e.Equals(atmEntry));
I get the object that is considered equal based on the IEquatable interface's implementation.
So why does a HashSet rely on public bool Equals(ReferenceType other) but FirstOrDefault does not? What equality is the == operator in FirstOrDefault(e => e == other) looking for?

FirstOrDefault doesn't compare items for equality at all. You provided a filtering delegate that uses the == operator to compare the two objects in one case and used the Equals method in the other.
The == operator does whatever the class defines it to do by that type, or if not defined, by the closest base type that does (with object being the base type that is always there, and will always have a definition if nothing better was defined; it will compare objects based on their reference). Good design says that you should make sure the == operator for a class is defined to behave exactly the same as the Equals method, but nothing in the language forces you to do this, and apparently this class doesn't ensure they're the same, and it's unsurprisingly causing you problems.

Why do string datatypes always perform value comparison

I was looking for the difference between == and .Equals methods in C# and I found that the first one compares the object references, and the second one compares the objects values, except for the string datatypes both == and .Equals() does a content comparison. I can't really find an explanation for that, is it because the string datatypes are immutable ?
Here's what I want to say
object obj1 = "Test";
object obj2 = new string("Test".ToCharArray());
Console.WriteLine(obj1.Equals(obj2) + " " + (obj1 == obj2));
string a = "Test";
string b = "Test";
Console.WriteLine(a.Equals(b) + " "+ (a == b));
Output
True False
True True
In fact for the first comparison we have two different objects with same value and we got as result True and false, but for the case of string we have true for both comparison

This isn't true at all. == is an overridable operator, and Equals is an overridable method. It's up to the class to define how each of them behaves.
Perhaps you're confusing C# with Java?
If you want to do a reference comparison, use object.ReferenceEquals. Everything else is implementation dependant (though note that operator overrides are checked statically, so e.g. (object)someString == (object)someOtherString will do a reference comparison, not a value comparison; Equals doesn't have this "problem").
Most often, both == and Equals are designed to give the same answer (though == is always stricter about types in the comparison, as mentioned before). This applies double for structs, where a reference comparison doesn't really make much of a sense anyway.
And of course, the compiler doesn't actually do any checks. If I want, I can override the == operator to always return false. Or to only check some ID for equality. Or to change the objects being compared, if you are feeling particularly evil. In the end, it's just a static method like any other (with a few restrictions).
EDIT:
To address your edit directly, string always performs a content comparison because both its == and Equals are overriden to perform a content comparison. However, that doesn't mean that it always performs a costly char-by-char comparison - if you look how string.Equals is actually implemented, you can see that it tries a few things to avoid the costly comparison:
If the string is null, they must be different
If the two strings are reference-equal, they must also be content-equal
If the two strings don't have the same length, they must be different
You can see the actual by-value comparison method here - http://referencesource.microsoft.com/#mscorlib/system/string.cs,11648d2d83718c5e A simple piece of unsafe code, but manually written code nevertheless. There's no automatic value comparison in .NET (though there's tricks that come close).

It's because it makes sense.
Java couldn't do it this way because it doesn't have operator overloading, but that's no argument in C#.
This isn't unique to strings, by the way. Any type could overload the == operator to do something similar.

Any object can override/overload Equals or ==, so they can behave however the library author wants them to behave.

Check if object is null without using ==

In my program, I have objects derived from Dictionary. I need to check if 2 objects are equal, so I made an overload operator ==.
But at a later point, I need to check if a object is null.
If (object == null)
{...}
So at this point, the program goes into the overload operation I have defined, but will throw a NullReferenceException, since one of the objects to compare is null.
So within the overload operation, I need to check if one object is null, but without using ==, since that would give me a StackOverflowException.
How can I check this?

In my program, I have objects derived from Dictionary.
I would strongly reconsider deriving from Dictionary in the first place. That's very rarely a good idea. Favour composition over inheritance in general, and think very carefully about how you want equality (and hash codes) to behave in the face of mutable data. It's usually a bad sign if two objects are equal at one point and then not equal later.
So at this point, the program goes into the overload operation I have defined, but will throw a NullReferenceException, since one of the objects to compare is null.
That's the problem. Your overloaded == operator should not throw an exception - it should compare the value with null.
Typically an overload of == looks something like this:
public static bool ==(Foo left, Foo right)
{
if (ReferenceEquals(left, right))
{
return true;
}
if (ReferenceEquals(left, null))
{
return false;
}
// Equals should be overridden, and should be handling the case where
// right is null (by checking with ReferenceEquals too). Also consider
// implementing IEquatable<Foo>
return left.Equals(right);
}
Here Object.ReferenceEquals is used to perform the reference identity comparison. You could use this outside (in the code that you're currently considering changing) but it would be cleaner just to make == behave correctly.

You either need to cast to object,
(object)obj == null
or use object.ReferenceEquals(obj, null);
(object is not a nice name for an object)

You have to check for null in your implementation of overriden ==, following these guidelines for example :
http://msdn.microsoft.com/en-us/library/ms173147%28v=vs.80%29.aspx
You could also use
object.ReferenceEquals(myInstance, null);
Please note that overriding base operators such as == and/or directly overriding .Net base types such as Dictionary are both not very good practices.

overriding the == operator, as you have discovered, has non-obvious side effects and generally should be avoided.
You might consider having your object implement IComparable instead, and then calling CompareTo instead of ==.

use the is null operator from c# 7
if(object is null)...

How to check if Dictionary already has a key 'x'?

I am trying to implement simple algorithm with use of C#'s Dictionary :
My 'outer' dictionary looks like this : Dictionary<paramID, Dictionary<string, object>> [where paramID is simply an identifier which holds 2 strings]
if key 'x' is already in the dictionary then add specific entry to this record's dictionary, if it doesn't exist then add its entry to the outer Dictionary and then add entry to the inner dictionary.
Somehow, when I use TryGetValue it always returns false, therefore it always creates new entries in the outer Dictionary - what produces duplicates.
My code looks more or less like this :
Dictionary<string, object> tempDict = new Dictionary<string, object>();
if(outerDict.TryGetValue(new paramID(xKey, xValue), out tempDict))
{
tempDict.Add(newKey, newValue);
}
Block inside the ifis never executed, even if there is this specific entry in the outer Dictionary.
Am I missing something ? (If you want I can post screen shots from debugger - or something else if you desire)

If you haven't over-ridden equals and GetHashCode on your paramID type, and it's a class rather than a struct, then the default equality meaning will be in effect, and each paramID will only be equal to itself.
You likely want something like:
public class ParamID : IEquatable<ParamID> // IEquatable makes this faster
{
private readonly string _first; //not necessary, but immutability of keys prevents other possible bugs
private readonly string _second;
public ParamID(string first, string second)
{
_first = first;
_second = second;
}
public bool Equals(ParamID other)
{
//change for case-insensitive, culture-aware, etc.
return other != null && _first == other._first && _second == other._second;
}
public override bool Equals(object other)
{
return Equals(other as ParamID);
}
public override int GetHashCode()
{
//change for case-insensitive, culture-aware, etc.
int fHash = _first.GetHashCode();
return ((fHash << 16) | (fHash >> 16)) ^ _second.GetHashCode();
}
}
For the requested explanation, I'm going to do a different version of ParamID where the string comparison is case-insensitive and ordinal rather than culture based (a form that would be appropriate for some computer-readable codes (e.g. matching keywords in a case-insensitive computer language or case-insensitive identifiers like language tags) but not for something human-readable (e.g. it will not realise that "SS" is a case-insensitive match to "ß"). This version also considers {"A", "B"} to match {"B", "A"} - that is, it doesn't care what way around the strings are. By doing a different version with different rules it should be possible to touch on a few of the design considerations that come into play.
Let's start with our class containing just the two fields that are it's state:
public class ParamID
{
private readonly string _first; //not necessary, but immutability of keys prevents other possible bugs
private readonly string _second;
public ParamID(string first, string second)
{
_first = first;
_second = second;
}
}
At this point if we do the following:
ParamID x = new ParamID("a", "b");
ParamID y = new ParamID("a", "b");
ParamID z = x;
bool a = x == y;//a is false
bool b = z == x;//b is true
Because by default a reference type is only equal to itself. Why? Well firstly, sometimes that's just what we want, and secondly it isn't always clear what else we might want without the programmer defining how equality works.
Note also, that if ParamID was a struct, then it would have equality defined much like what you wanted. However, the implementation would be rather inefficient, and also buggy if it contained a decimal, so either way it's always a good idea to implement equality explicitly.
The first thing we are going to do to give this a different concept of equality is to override IEquatable<ParamID>. This is not strictly necessary, (and didn't exist until .NET 2.0) but:
It will be more efficient in a lot of use cases, including when key to a Dictionary<TKey, TValue>.
It's easy to do the next step with this as a starting point.
Now, there are four rules we must follow when we implement an equality concept:
An object must still be always equal to itself.
If X == Y and X != Z, then later if the state of none of those objects has changed, X == Y and X != Z still.
If X == Y and Y == Z, then X == Z.
If X == Y and Y != Z then X != Z.
Most of the time, you'll end up following all these rules without even thinking about it, you just have to check them if you're being particularly strange and clever in your implementation. Rule 1 is also something that we can take advantage of to give us a performance boost in some cases:
public class ParamID : IEquatable<ParamID>
{
private readonly string _first; //not necessary, but immutability of keys prevents other possible bugs
private readonly string _second;
public ParamID(string first, string second)
{
_first = first;
_second = second;
}
public bool Equals(ParamID other)
{
if(other == null)
return false;
if(ReferenceEquals(this, other))
return true;
if(string.Compare(_first, other._first, StringComparison.InvariantCultureIgnoreCase) == 0 && string.Compare(_second, other._second, StringComparison.InvariantCultureIgnoreCase) == 0)
return true;
return string.Compare(_first, other._second, StringComparison.InvariantCultureIgnoreCase) == 0 && string.Compare(_second, other._first, StringComparison.InvariantCultureIgnoreCase) == 0;
}
}
The first thing we've done is see if we're being compared with equality to null. We almost always want to return false in such cases (not always, but the exceptions are very, very rare and if you don't know for sure you're dealing with such an exception, you almost certainly are not), and certainly we don't want to throw a NullReferenceException.
The next thing we do is to see if the object is being compared with itself. This is purely an optimisation. In this case, it's probably a waste of time, but it can be very useful with more complicated equality tests, so it's worth pointing out this trick here. This takes advantage of the rule that identity entails equality, that is, any object is equal to itself (Ayn Rand seemed to think this was somehow profound).
Finally, having dealt with these two special cases, we get to the actual rule for equality. As I said above, my example considers two objects equal if they have the same two strings, in either order, for case-insensitive ordinal comparisons, so I've a bit of code to work that out.
(Note that the order in which we compare component parts can have a performance impact. Not in this case, but with a class that contains both an int and a string we would compare the ints first because is faster and we will hence perhaps find an answer of false before we even look at the strings)
Now at this point we've a good basis for overriding the Equals method defined in object:
public override bool Equals(object other)
{
return (other as ParamID);
}
Since as will return a ParamID reference if other is a ParamID and null for anything else (including if null was what we were passed in the first place), and since we already handle comparison with null, we're all set.
Try to compile at this point and you will get a warning that you have overriden Equals but not GetHashCode (the same is true if you'd done it the other way around).
GetHashCode is used by the dictionary (and other hash-based collections like HashTable and HashSet) to decide where to place the key internally. It will take the hashcode, re-hash it down to a smaller value in a way that is its business, and use it to place the object in its internal store.
Because of this, it's clear why the following is a bad idea were ParamID not readonly on all fields:
ParamID x = new ParamID("a", "b");
dict.Add(x, 33);
x.First = "c";//x will now likely never be found in dict because its hashcode doesn't match its position!
This means the following rules apply to hash-codes:
Two objects considered equal, must have the same hashcode. (This is a hard rule, you will have bugs if you break it).
While we can't guarantee uniqueness, the more spread out the returned results, the better. (Soft rule, you will have better performance the better you do at it).
(Well, 2½.) While not a strict rule, if we take such a complicated approach to point 2 above that it takes forever to return a result, the nett effect will be worse than if we had a poorer-quality hash. So we want to try to be reasonably quick too if we can.
Despite the last point, it's rarely worth memoising the results. Hash-based collections will normally memoise the value themselves, so it's a waste to do so in the object.
For the first implementation, because our approach to equality depended upon the default approach to equality of the strings, we could use strings default hashcode. For my different version I'll use another approach that we'll explore more later:
public override int GetHashCode()
{
return StringComparer.OrdinalIgnoreCase.GetHashCode(_first) ^ StringComparer.OrdinalIgnoreCase.GetHashCode(_second);
}
Let's compare this to the first version. In both cases we get hashcodes of the component parts. If the values where integers, chars or bytes we would have worked with the values themselves, but here we build on the work done in implementing the same logic for those parts. In the first version we use the GetHashCode of string itself, but since "a" has a different hashcode to "A" that won't work here, so we use a class that produces a hashcode ignoring that difference.
The other big difference between the two is that in the first case we mix the bits up more with ((fHash << 16) | (fHash >> 16)). The reason for this is to avoid duplicate hashes. We can't produce a perfect hashcode where every different object has a different value, because there are only 4294967296 possible hashcode values, but many more possible values for ParamID (including null, which is treated as having a hashcode of 0). (There are cases where prefect hashes are possible, but they bring in different concerns than here). Because of this imperfection we have to think not only about what values are possible, but which are likely. Generally, shifting bits like we've done in the first version avoids common values having the same hash. We don't want {"A", "B"} to hash the same as {"B", "A"}.
It's an interesting experiment to produce a deliberately poor GetHashCode that always returns 0, it'll work, but instead of being close to O(1), dictionaries will be O(n), and poor as O(n) goes for that!
The second version doesn't do that, because it has different rules so for it we actually want to consider values the same but for being switch around as equal, and hence with the same hashcode.
The other big difference is the use of StringComparer.OrdinalIgnoreCase. This is an instance of StringComparer which, among other interfaces, implements IEqualityComparer<string> and IEqualityComparer. There are two interesting things about the IEqualityComparer<T> and IEqualityComparer interfaces.
The first is that hash-based collections (such as dictionary) all use them, it's just that unless passed an instance of one to their constructor they will use DefaultEqualityComparer which calls into the Equals and GetHashCode methods we've described above.
The other, is that it allows us to ignore the Equals and GetHashCode mentioned above, and provide them from another class. There are three advantages to this:
We can use them in cases (string is a classic case) where there is more than one likely definition of "equals".
We can ignore that by the class' author, and provide our own.
We can use them to avoid a particular attack. This attack is based on being in a situation where input you provide will be hashed by the code you are attacking. You pick input so as to deliberately provide objects that are different, but hash the same. This means that the poor performance we talked about avoiding earlier is hit, and it can be so bad that it becomes a denial of service attack. By providing different IEqualityComparer implementations with random elements to the hash code (but the same for every instance of the comparer) we can vary the algorithm enough each time as to twart the attack. The use for this is rare (it has to be something that will hash based purely on outside input that is large enough for the poor performance to really hurt), but vital when it comes up.
Finally. If we override Equals we may or may not want to override == and != too. It can be useful to keep them refering to identity only (there are times when that is what we care most about) but it can be useful to have them refer to other semantics (`"abc" == "ab" + "c" is an example of an override).
In summary:
The default equality of reference objects is identity (equal only to itself).
The default equality of value types is a simple comparison of all fields (but poor in performance).
We can change the concept of equality for our classes in either case, but this MUST involve both Equals and GetHashCode*
We can override this and provide another concept of equality.
Dictionary, HashSet, ConcurrentDictionary, etc. all depend on this.
Hashcodes represent a mapping from all values of an object to a 32-bit number.
Hashcodes must be the same for objects we consider equal.
Hashcodes must be spread well.
*Incidentally, anonymous classes have a simple comparison like that of value types, but better performance, which matches almost any case in which we mght care about the hash code of an anonymous type.

Most likely, paramID does not implement equality comparison correctly.
It should be implementing IEquatable<paramID> and that means especially that the GetHashCode implementation must adhere to the requirements (see "Notes to implementers").
As for keys in dictionaries, MSDN says:
As long as an object is used as a key in the Dictionary(Of TKey,
TValue), it must not change in any way that affects its hash value.
Every key in a Dictionary(Of TKey, TValue) must be unique according to
the dictionary's equality comparer. A key cannot be Nothing, but a
value can be, if the value type TValue is a reference type.
Dictionary(Of TKey, TValue) requires an equality implementation to
determine whether keys are equal. You can specify an implementation of
the IEqualityComparer(Of T) generic interface by using a constructor
that accepts a comparer parameter; if you do not specify an
implementation, the default generic equality comparer
EqualityComparer(Of T).Default is used. If type TKey implements the
System.IEquatable(Of T) generic interface, the default equality
comparer uses that implementation.
Since you don't show the paramID type I cannot go into more detail.
As an aside: that's a lot of keys and values getting tangled in there. There's a dictionary inside a dictionary, and the keys of the outer dictionary aggregate some kind of value as well. Perhaps this arrangement can be advantageously simplified? What exactly are you trying to achieve?

Use the Dictionary.ContainsKey method.
And so:
Dictionary<string, object> tempDict = new Dictionary<string, object>();
paramID searchKey = new paramID(xKey, xValue);
if(outerDict.ContainsKey(searchKey))
{
outerDict.TryGetValue(searchKey, out tempDict);
tempDict.Add(newKey, newValue);
}
Also don't forget to override the Equals and GetHashCode methods in order to correctly compare two paramIDs:
class paramID
{
// rest of things
public override bool Equals(object obj)
{
paramID p = (paramID)obj;
// how do you determine if two paramIDs are the same?
if(p.key == this.key) return true;
return false;
}
public override int GetHashCode()
{
return this.key.GetHashCode();
}
}

C# System.Object.operator==()

I'm tryign to get my head around the use of System.Object.operator==().
My Effective C# book, and the page here (http://www.srtsolutions.com/just-what-is-the-default-equals-behavior-in-c-how-does-it-relate-to-gethashcode), says that:
"System.Object.operator==() will call a.Equals(b) to determine if a and b are equal".
So with my code:
object a = 1;
object b = 1;
if(object.Equals(a, b))
{
// Will get here because it calls Int32.Equals(). I understand this.
}
if(a == b)
{
// I expected it to get here, but it doesn't.
}
I expected (a == b) to call Int32's overriden Equals and compare values in the same way that static objet.Equals() does. What am I missing?
Edit: I should perhaps have added that I can see what (a == b) is testing - it's testing reference equality. I was thrown by the book which seems to suggest it will work internally much as static object.Equals(obect, object) will.

I'm not sure why the book would say that; it is emphatically untrue that the default == calls Equals. Additionally, object does NOT overload ==. The operator == by default performs a value-equality comparison for value types and a reference-equality comparison for reference types. Again, it is NOT overloaded for object (it is for string). Therefore, when you compare object a = 1 and object b = 1 using the == operator you are doing a reference-equality comparison. As these are different instances of a boxed int, they will compare differently.
For all that are confused by this issue, I encourage you to read §7.10 and especially §7.10.6 of the specification extremely carefully.
For more on the subtleties of boxing (or why we need it in the first place), I refer you to a previous post on this subject.

As the object type doesn't override == and == checks for reference equality by default, the references of a and b are compared, as both are objects. If you want to compare value equality, you have to unbox the ints first.

When two objects are tested for equality they are tested to see if they are referencing the same object. (EDIT: this is generally true, however == could be overloaded to provide the functionality that you receive from a.equals)
So
object a = 1;
object b = 1;
These do not point to the same address space.
However if you did
object a = 1;
object b = a;
Then these would point to the same address.
For a real life example, take two different apartments in the same building, they have the exact same layout, same 1 bedroom, same kitchen, same paint everything about them is the same, except that apartment a is #101 and apartment b is #102. In one sense they are the same a.equals(b), but in another sense they are completely different a != b.

== implementation of object checks for identity, not equality. You have two variables that point to two different objects that's why == returns false.

You declared a and b as object which is a reference type and not a value type. So with a==b you are comparing references of objects (which will be different) rather than the values.

System.Object.operator==() will call a.Equals(b) to determine if a and b are equal
This is simply not true. If that were the case then you'd have a == b returning true, since a.Equals(b) returns true. Equals is a virtual method, so it doesn't matter that int values are boxed; if you call a.Equals, that compiles to a callvirt and the vtable is used.
So the static == operator does not use a.Equals(b) internally. It tests for reference equality by default. It only does otherwise if the static == operator has been overloaded for the types in the expression as they are declared at compile time.

System.Object does not overload ==, so a == b just tests for reference equality (and returns false). Since operator overloading is implemented as a static method, it's not virtual.
Object.Equals, on the other side, is specified as follows:
The default implementation of Equals supports reference equality for reference types, and bitwise equality for value types. Reference equality means the object references that are compared refer to the same object. Bitwise equality means the objects that are compared have the same binary representation.
Since a and b have the same binary representation, Object.Equals(a, b) returns true.