If you think you know everything you need to know about binary search, but have not read Netty van Gasteren and Wim Feijen’s note The Binary Search Revisited, you should.
If every solution returned by
D is no better than some solution returned by
X, any optimal solution by
X must be no worse than some optimal solution by
D “What? How could this be true?” It turned out that the reasoning can be correct, and the proof uses indirect equality in an unusual way.
A list of numbers is called steep if each element is larger than the sum of elements to its right. It is an example we often use when we talk about tupling. Can we determine the steepness of a list by a list homomorphism?
Reviewing Zantema’s “windowing” technique for computing the longest segment of the input that satisfies a suffix-closed predicate.
Translating Zantema’s work to Bird-Meertens style, to compute the longest consecutive segment of the input that satisfies a predicate that is suffix and overlap-closed.
I was puzzled by the fact stated in a number of places that axiom of choice, proof irrelevance, and extensional equality together entail the law of excluded middle.