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The Haskell School of Expression by Paul Hudak

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CHAPTER ELEVEN

Proof by Induction

 

 

 

 

 

In this chapter I will introduce a powerful proof technique based on mathematical induction. With it we will be able to prove complex and important properties of programs that cannot be accomplished with proof-by- calculation alone. The inductive proof method is one of the most powerful and common methods for proving program properties.

11.1 Induction and Recursion

Induction is very closely related to recursion. In fact, in certain contexts the terms are used interchangeably; in others, one is preferred over the other primarily for historical reasons. I like to think of them as being duals of each other: Induction is used to describe things starting with something very simple, and building up from ...

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