To solve a
cyber-dojo challenge (implement a function/method that returns the prime factors of a number) I decided to implement a somewhat nieve (but workable)
isPrime function in Haskell. Here's the code:
-- Public type-definition
isPrime :: Integer -> Bool
-- Private type-definition
lookForPrimeFrom :: Integer -> Integer -> Bool
isPrime 2 = True
isPrime n
| n < 2 = False
| even n = False
| otherwise = lookForPrimeFrom n 5
lookForPrimeFrom n i
| ceiling (sqrt (fromIntegral n))+1 < i = True
| (n `mod` i) == 0 = False
| otherwise = lookForPrimeFrom n (i+2)
This code (to me at least) seems very self-documenting. The more I'm playing around with Haskell, the more I'm enjoying it and seeing its strength as a functional language. I think if I were to map this algorithm into more mathematical notation it would look like:
\[
\forall n \in \mathbb{N}
\]
\[
p \left( n \right) = \left\{ \begin{array}{lr}
0, & n = 1 \\
1, & n = 2 \\
0, & \text{$n$ is even} \\
1, & \nexists m \in \left\{ x \in \mathbb{N} \, | \, 5 \leq x \leq{\sqrt{n}}, \text{$x$ is odd} \right\}
\end{array} \right.
\]
As you can see, this is somewhat nieve; however, the Haskell code really is quite similar to the mathematical notation.
