Chapter 2: Recursion and Induction

• Fixed-Length Processes
• Variable-Length Processes
• Describing the Dictionary Searching Process
• Another Description
• Making Paper Chains
• Factorial
• Strategies for Using Recursion
• Recursion for Factorial
• Factorial in Scheme
• Visualizing Factorial
• Tracing Factorial in Scheme
• Proving That A Procedure Does What You Claim It Does
• An Example
• Informal Verification
• Formal Verification
• Mathematical Induction
• General Strategy
• Strategy for foo
• An Inductive Proof of the Correctness of foo
• The Meaning of "Proof"
• Recursive Thinking
• One-Layer Thinking
• Example: Computing Quotients
• Solution: Computing Quotients
• Defining quot Recursively
• Enhancing quot
• Enhancing quot: Solution
• The cond Statement
• Redefining Scheme Procedures
• Problem: Determine the Number of Digits in an Integer
• Remainders