Statistical performance of purely functional maps and sets

These are basically research topics, and the results are generally given in the form of conclusions, while the statistical data is hidden. One can have statistical analysis on their own data though.

For the benchmarks, better go through the implementation details.

The 3rd part of the question is a very subjective matter, and the actual intentions may never be known at the time of implementation. However, languages like perl do their best to implement highly optimized solutions to every operation.

Following might be of help: Purely Functional Data Structures by Chris Okasaki http://www.cs.cmu.edu/~rwh/theses/okasaki.pdf