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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INDIRECT RECURSION

So far, all of the recursion examples have had one thing in common: one single function involved that called itself, which is called direct recursion. There is also indirect recursion, where several functions depend upon one another. For instance, function A calls function B, which calls function C. If function C, under any circumstances, calls back to function A, this is a case of indirect recursion.

There is a simple case of indirect recursion called mutual recursion. It involves only two functions that depend upon one another. In reality, the logic behind the dependency can be quite complex. Nonetheless, here’s an example that involves odd and even numbers:

    static bool IsOdd(int number) {

      return number == 0 ? false : IsEven(Math.Abs(number) - 1);

    }

 

    static bool IsEven(int number) {

      return number == 0 ? true : IsOdd(Math.Abs(number) - 1);

    }

As you can see, the definition of an odd integer is this: if the number is zero, it is a known fact that the number is not odd. Otherwise, the number is odd if the number before it is even. The definition of an even number is exactly the other way around: zero is known to be even, otherwise a number is even if the number before it is odd.

The two functions IsOdd and IsEven depend upon each other; they are therefore called mutually recursive. The example scenario also has two different base cases that are checked in the two functions. Obviously, this can get quite complex — if you employ code ...

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