You are previewing Functional Programming in C#: Classic Programming Techniques for Modern Projects.

Functional Programming in C#: Classic Programming Techniques for Modern Projects

  1. Cover
  2. Title
  3. Copyright
  4. About the Author
  5. Credits
  6. Contents
  7. Introduction
  8. Part I : Introduction to Functional Programming
    1. Chapter 1 : A Look at Functional Programming History
      1. What Is Functional Programming?
      2. Functional Languages
      3. The Relationship to Object Oriented Programming
      4. Summary
    2. Chapter 2 : Putting Functional Programming into a Modern Context
      1. Managing Side Effects
      2. Agile Programming Methodologies
      3. Declarative Programming
      4. Functional Programming Is a Mindset
      5. Is Functional Programming in C# a Good Idea?
      6. Summary
  9. Part II : C# Foundations of Functional Programming
    1. Chapter 3 : Functions, Delegates, and Lambda Expressions
      1. Functions and Methods
      2. Reusing Functions
      3. Anonymous Functions and Lambda Expressions
      4. Extension Methods
      5. Referential Transparency
      6. Summary
    2. Chapter 4 : Flexible Typing with Generics
      1. Generic Functions
      2. Generic Classes
      3. Constraining Types
      4. Other Generic Types
      5. Covariance and Contravariance
      6. Summary
    3. Chapter 5 : Lazy Listing with Iterators
      1. The Meaning of Laziness
      2. Enumerating Things with .NET
      3. Implementing Iterator Functions
      4. Chaining Iterators
      5. Summary
    4. Chapter 6 : Encapsulating Data in Closures
      1. Constructing Functions Dynamically
      2. The Problem with Scope
      3. How Closures Work
      4. Summary
    5. Chapter 7 : Code Is Data
      1. Expression Trees in .NET
      2. Analyzing Expressions
      3. Generating Expressions
      4. .NET 4.0 Specifics
      5. Summary
  10. Part III : Implementing Well-known Functional Techniques in C#
    1. Chapter 8 : Currying and Partial Application
      1. Decoupling Parameters
      2. Calling Parts of Functions
      3. Why Parameter Order Matters
      4. Summary
    2. Chapter 9 : Lazy Evaluation
      1. What’s Good about Being Lazy?
      2. Passing Functions
      3. Explicit Lazy Evaluation
      4. Comparing the Lazy Evaluation Techniques
      5. How Lazy Can You Be?
      6. Summary
    3. Chapter 10 : Caching Techniques
      1. The Need to Remember
      2. Precomputation
      3. Memoization
      4. Summary
    4. Chapter 11 : Calling Yourself
      1. Recursion in C#
      2. Tail Recursion
      3. Accumulator Passing Style
      4. Continuation Passing Style
      5. Indirect Recursion
      6. Summary
    5. Chapter 12 : Standard Higher Order Functions
      1. Applying Operations: Map
      2. Map, Filter, and Fold in LINQ
      3. Standard Higher Order Functions
      4. Summary
    6. Chapter 13 : Sequences
      1. Understanding List Comprehensions
      2. A Functional Approach to Iterators
      3. Ranges
      4. Restrictions
      5. Summary
    7. Chapter 14 : Constructing Functions from Functions
      1. Composing Functions
      2. Advanced Partial Application
      3. Combining Approaches
      4. Summary
    8. Chapter 15 : Optional Values
      1. The Meaning of Nothing
      2. Implementing Option(al) Values
      3. Summary
    9. Chapter 16 : Keeping Data from Changing
      1. Change Is Good — not!
      2. False Assumptions
      3. Implementing Immutable Container Data Structures
      4. Alternatives to Persistent Data Types
      5. Summary
    10. Chapter 17 : Monads
      1. What’s in a Typeclass?
      2. What’s in a Monad?
      3. Why Do a Whole Abstraction?
      4. A Second Monad: Logging
      5. Syntactic Sugar
      6. Binding with SelectMany?
      7. Summary
  11. Part IV : Putting Functional Programming into Action
    1. Chapter 18 : Integrating Functional Programming Approaches
      1. Refactoring
      2. Writing New Code
      3. Finding Likely Candidates for Functional Programming
      4. Summary
    2. Chapter 19 : The MapReduce Pattern
      1. Implementing MapReduce
      2. Abstracting the Problem
      3. Summary
    3. Chapter 20 : Applied Functional Modularization
      1. Executing SQL Code from an Application
      2. Rewriting the Function with Partial Application and Precomputation in Mind
      3. Summary
    4. Chapter 21 : Existing Projects Using Functional Techniques
      1. The .NET Framework
      2. LINQ
      3. Google MapReduce and Its Implementations
      4. NUnit
      5. Summary
  12. Index
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COVARIANCE AND CONTRAVARIANCE

The topic of variance is complex because it applies to many different code constructs. Designers of programming language make (hopefully conscious) decisions to support variance in a variety of different scenarios, or not to do so.

There is a distinction being made between covariance and contravariance. Very roughly, an operation is covariant if it preserves the ordering of types, and contravariant if it reverses this order. The ordering itself is meant to represent more general types as larger than more specific types.

Here’s one example of a situation where C# supports covariance. First, this is an array of objects:

object[] objects = new object[3];

objects[0] = new object( );

objects[1] = "Just a string";

objects[2] = 10;

Of course it is possible to insert different values into the array because in the end they all derive from Object in .NET. In other words, Object is a very general or large type. Now here’s a spot where covariance is supported: assigning a value of a smaller type to a variable of a larger type.

string[] strings = new string[] { "one", "two", "three" };

objects = strings;

The variable objects, which is of type object[], can store a value that is in fact of type string[]. Think about it — to a point, it’s what you expect, but then again it isn’t. After all, while string derives from object, string[] doesn’t derive from object[]. The language support for covariance in this example makes the assignment possible anyway, which is ...

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