The term "default comparer" can refer to several different things:

• Any type implementing IComparable<T> (or IComparable) has a built-in .NET "default comparer" Comparer<T>.Default (or Comparer.Default). Similarly, every type has a built-in .NET "default equality comparer" EqualityComparer<T>.Default (or Object.Equals).
• The Comparers library also provides a "default comparer" Compare<T>.Default() and a "default equality comparer" EqualityCompare<T>.Default().
• Several methods in the Comparers library take an IComparer<T> (or IEqualityComparer<T>) argument, which may be null. When it is null, the method uses the default comparer (or equality comparer) provided by the Comparers library.

The built-in .NET Comparer<T>.Default does not implement IEqualityComparable<T> (or IEqualityComparable). For this reason, the Comparers library provides Compare<T>.Default(), which does implement all relevant interfaces. Compare<T>.Default() is just a combination of Comparer<T>.Default and EqualityComparer<T>.Default, unless T is a sequence type without a default comparer (see below).

Note: the .NET StringComparer type does implement IEqualityComparable<string> (and IEqualityComparable), so the Comparers library does not provide any string comparers.

If the compared type implements IEnumerable<U> and does not define its own default comparer (i.e., IComparable<T>), then Compare<T>.Default() will return a sequence comparer that uses lexicographical sorting. Similarly, EqualityCompare<T>.Default() will return a sequence comparer that will test lexicographic equality.

For example, this allows Compare<int[]>.Default() to have expected semantics.

If an IComparer<T> argument is null, the Comparers library will use Compare<T>.Default(). Furthermore, if the .NET Comparer<T>.Default is passed as an argument, the Comparers library will replace that argument with Compare<T>.Default().

Similarly, IEqualityComparer<T> arguments that are null or EqualityComparer<T>.Default are replaced with EqualityCompare<T>.Default().