We acknowledge your contribution in reviewing JFP submissions. Your work will improve the functional programming community, and it will provide you with an opportunity to broaden your horizon.
For notes on the revision cycle, see further down.
If this is your first journal review (or if you have never received any advice on how to review journal submissions), here are some basic points.
A managing editor may choose to (1) accept a paper, (2) request revisions, or (3) reject a paper. We will BCC you on the decision letter so that you find out what happened and have anonymous access to the write-ups of the other reviewers.
In case (2), the authors have a limited amount of time to improve the paper, usually via editing prose, occasionally via new research, e.g., fixing a proof, running additional benchmarks. Once the authors submit their revised version, we assign it the same number as before PLUS a suffix: R1 for the first revision, R2 for the second, and so on. By default, we assign the same managing editor and those reviewers who have declared their willingness to inspect the revision.
When you review a revision, you ought to read the entire paper again with a special focus on those spots that your review marked up as questionable before. The authors are expected to provide a covering letter explaining how the paper has been revised, so you should not have to work hard to discover this. Your review may simply state "this revision takes care of all my complaints" or you may point to previous complaints like this "the revised paper still does not address reviewer 2's point about theorem 42 and the benchmark suites in section 17." The decision letter for the original manuscript shows you how your review was listed.
You may also wish to inspect how the authors addressed the complaints of other reviewers. If you wish to point out problems, use the same neutral language as above: "the revised paper still does not address reviewer 1's point about the possibilities of unicorns ruining the cooling system of the benchmark machines."
Peer review is the foundation of quality in research for both books and journals, ensuring that published research is rigorous and ethical. Peer reviewers can access a number of resources to assist them with their peer reviewing duties: