alt Hacker NewsOk, let's say that it is not JS, but an untyped, closure-based programming language with a strikingly similar array and sort API to JS. Sadly, this comparator is still wrong for any sorting API that expects a general three-way comparison, because it does not handle equality as a separate case.
And to tie it down to the mathematics: if a sorting algorithm asks for a full comparison between a and b, and your function returns only a bool, you are conflating the "no" (a is before b) with the "no" (a is the same as b). This fails to represent equality as a separate case, which is exactly the kind of imprecision the author should be trying to teach against.
Replies
It's obviously not a general 3-way comparison API, _because_ it's returning bool!
Extremely strange to see a sort that returns bool, which is one of two common sort comparator APIs, and assume it's a wrong implementation of the other common sort API.
I do see why you're assuming JS, but you shouldn't assume it's any extant programming language. It's explanatory pseudocode.
It could be a typed programming language where the sort function accepts a strict ordering predicate, like for example in C++ (https://en.cppreference.com/cpp/named_req/Compare).
> an untyped closure-based programming language with a similar array and sort api to JS
Ah! You're talking about Racket or Scheme!
```
> (sort '(3 1 2) (lambda (a b) (< a b)))
'(1,2,3)
```
I suppose you ought to go and tell the r6rs standardisation team that a HN user vehemently disagrees with their api: https://www.r6rs.org/document/lib-html-5.96/r6rs-lib-Z-H-5.h...
To address your actual pedantry, clearly you have some implicit normative belief about how a book about category theory should be written. That's cool, but this book has clearly chosen another approach, and appears to be clear and well explained enough to give a light introduction to category theory.
> Sadly, this comparator is still wrong for any sorting API that expects a general three-way comparison, because it does not handle equality as a separate case.
Let's scroll up a little bit and read from the section you're finding fault with:
Rather than the usual "harrumph! This writer knows NOTHING of mathematics and has no business writing about it," maybe a simple counter-example would do, i.e. present an ordering "in which every object has its place depending on every other object" and "leaves no room for ambiguity in terms of which element comes before which" but also satisfies your requirement of allowing 'equal' ordering.