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| -rw-r--r-- | TODO | 9 |
1 files changed, 3 insertions, 6 deletions
@@ -5,14 +5,11 @@ This is a rough outline of upcoming tasks: [ ] Prove that CompleteTree.heapUpdateAt returns the element at the given index [ ] Prove that CompleteTree.heapRemoveLastWithIndex and CompleteTree.heapRemoveLast yield the same tree [ ] Prove that CompleteTree.heapRemoveLastWithIndex and CompleteTree.heapRemoveLast yield the same element -[ ] Prove that CompleteTree.heapRemoveLastWithIndex only removes one element and leaves the rest unchanged +[x] Prove that CompleteTree.heapRemoveLastWithIndex only removes one element and leaves the rest unchanged - This automatically serves as a proof for CompleteTree.heapRemoveLast, once it is shown that they yield the same tree - - A potential approach is to show that any index in the resulting tree can be converted into an index - in the original tree (by adding one if it's >= the returned index of heapRemoveLastWithIndex), and getting - elements from both trees. - - Maybe easier: Or show that except for the n=1 case the value is unchanged. - The type signature proves the rest, so try, like induction maybe? + - Done by showing that each element of the input tree is in the output tree, except for the one at the + returned index. [ ] Prove that if CompleteTree.indexOf returns some, CompleteTree.get with that result fulfills the predicate. [ ] Prove that CompleteTree.heapUpdateRoot indeed exchanges the value at the root. - Straightforward, but hard to prove: |