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Purpose of Verification

• Given: input condition I and output condition O.
  • Abstract definition of a function ("what is to be done").
  • May be inconstructive (does not immediately yield an algorithm).
  • Even if constructive, the corresponding algorithm may be too inefficient.
• Given: definition of a function f.
  • Concrete definition of a function ("how is it done").
  • Intended to yield (efficient) algorithm.
• Verification: show that f implements corresponding specification.

Definition of such a function and its verification needs more knowledge; more knowledge gives better algorithms.