Write u = take n xs, v = drop n xs, and len = length xs. Part (c) gives xs = u ++ v; part (d) gives length v = len-n because . Use the finite-list laws take (length v) (v ++ w) = v, length (reverse v) = length v, and reverse (reverse v) = v. Then equational reasoning gives
reverse (take (len-n) (reverse xs))
= reverse (take (length v) (reverse (u ++ v)))
= reverse (take (length (reverse v)) (reverse v ++ reverse u))
= reverse (reverse v)
= v
= drop n xs
The first and second steps use the decomposition and the length equation; the third uses reversal of a concatenation; the fourth uses the stated take law. This is an algebraic proof using established laws, rather than a new induction proof.

Ancestors (12)

  1. e
  2. 1
  3. Functional programming, design and analysis of algorithms (resit)
  4. 2016
  5. Past exam of the year 1 of the computer science course of the University of Oxford
  6. Year 1 of the computer science course of the University of Oxford
  7. Computer science course of the University of Oxford
  8. Undergraduate course of the University of Oxford
  9. Course of the University of Oxford
  10. University of Oxford
  11. List of universities
  12. Home

View article source

Discussion (0) New discussion

There are no discussions about this article yet.

Articles by others on the same topic (0)

There are currently no matching articles.
See all articles in the same topic Create my own version