• Quiz Today
• READ CHAPTER 9 NEXT
• (skipping 6, 7, 8 for now)

• Procedure invokes itself

• decomposing problem
• base case
• recursive case which gets closer to solution
• Factorial
  • n! = n * (n-1)!
  • 0! = 1

• Raw multiplications
  • X^N = X * X * X * ... * X
  • N-1 multiplications
• Save work; clump things together
  • SX = X * X
  • X^N = SX * SX * ... * SX
  • roughly N/2 times ...
• Refine this latter approach

• Base case: X^0 = 1.0
• N is even case: X^N = X^(N/2) * X^(N/2)
• N is odd case: X^N = X * X^(N/2) * X^(N/2)

Any nontrivial computer language that one can invent is apparently capable of computing no more and no fewer functions that all the other nontrivial programming languages.

• The part of Pascal covered lets you solve all kinds of algorithms.
• Any algorithm that you can describe in English (or any other natural language) can be programmed on a computer.

• Robustness
• Testing
• Documentation
• Customer Support
• Training
• Follow-on products

• Defining the Product
• Developing the Program Specification
• Designing the System Structure
• Coding the System (small part!)
• Testing the Code
• Revision
• Documentation
• Delivery and Training
• Maintenance and Upgrade

• Proofs
  • Formal definition of specs
  • Formal definition languages
• Very hard

• Comments on Comments
  • Program Header
  • Block Header
  • Line Comments
  • Procedure Specs
  • Variable Descriptions
• Manuals
  • User Manual
  • Software Logic/Technical Manual

• The "Committee"
• Communication
• Interaction
  • training
• Creator Independence

• Chief Programmer Team