Here's another trivial convenience function:

divides? : int → int → boolean
divides? a b = mod b a == 0

This makes divisibility tests read more like the mathematical a | b notation:

prime? n = n ≥ 2 && not (some (2 .. isqrt n) (divides? _ n))

Argument order and name are debatable. (I find the ? suffix surprisingly uncomfortable, perhaps because divides? is a binary mathematical predicate, so I expect it to be a single-character infix operator like < ≤ ∈ ⊂, not an “ordinary” function.)

I initially wrote divides? off as a feature useful only in toy problems. It certainly comes up a lot in Project Euler problems, since those (as befits their name) are heavy on number theory. But even in real code, many (most?) uses of mod are divisibility tests. So divides? may be worth having, because it expresses this directly rather than via a slightly awkward use of mod.

(Real-world divisibility tests, incidentally, are often used to do something every nth iteration, e.g. updating a progress indicator, flushing a buffer, updating a cache. This pattern is so common that it might deserve an abstraction of its own. However, it's often a mistake — many periodic operations should be periodic in time, not number of iterations. So there's another useful operation: periodically interval timer.)


  1. Sorry, I can never remember. Which kind of integer division were you talking about: floor, ceiling, truncating, or rounding?

  2. None of them. We're testing for divisibility, not pretending it's always possible.


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