Resources on Covariance and Contravariance

Eric Lippert is on the C# Compiler team and has written a series of posts on this topic that are an absolute must-read!

1. Part One
2. Part Two: Array Covariance (and Why is covariance of value-typed arrays inconsistent?)
3. Part Three: Method Group Conversion Variance
4. Part Four: Real Delegate Variance
5. Part Five: Higher Order Functions Hurt My Brain
6. Part Six: Interface Variance
7. Part Seven: Why Do We Need A Syntax
8. Part Eight: Syntax Options
9. Part Nine: Breaking Changes
10. Part Ten: Dealing With Ambiguity
11. Part Eleven: To infinity, but not beyond

MSDN

The information here is quite “flat”, but still worth a read.

• Covariance and Contravariance in Delegates (C#)
• Covariance and Contravariance in Generics

More

• Microsoft Research: Variance and Generalized Constraints
  Pages 1-9, OK. After that I can’t follow anymore.
• Exact rules for variance validity
  Compiler details
• Wikipedia
  Very poorly written, if you ask me.

Category Theory

The names covariance and contravariance in C# derive from co- and contravariant functors described in category theory.

• Wikipedia
• A Gentle Introduction to Category Theory
• What’s the difference between covariance and assignment compatibility?
  How category theory applies to C# Co- and Contravariance

Hope that helps!

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.NET 4.0 types with added support for co- or contravariance

Just a plain list of types from the .NET 4.0 Base Class Library where Microsoft has added support for covariance (out) and contravariance (in).

in System

// Delegates
Action<in T1[..in T16]>
Func<out TResult>
Func<in T1[..in T16], out TResult>
Comparison<in T>
Converter<in TInput, out TOutput>
Predicate<in T> 

// Interfaces
IComparable<in T>
IObservable<out T>
IObserver<in T>

in System.Collections.Generic

IComparer<in T> 
IEnumerable<out T> 
IEnumerator<out T> 
IEqualityComparer<in T> 

in System.Linq

IGrouping<out TKey,out TElement> 
IOrderedQueryable<out T> 
IQueryable<out T>