## Primality test in Haskell

**Problem:** Implement a primality test in Haskell. Below is the code. The first implementation of the function divides uses a homemade function for finding the remainder when an integer is divided by another integer.

-- The remainder when a is divided by b. remainder :: Integer -> Integer -> Integer remainder a b | a < b = a | a == b = 0 | otherwise = remainder (a - b) b -- Whether d divides n. divides :: Integer -> Integer -> Bool divides d n = remainder n d == 0

The second implementation of divides uses the built-in function rem to find the remainder upon division by an integer.

-- Whether d divides n. A more efficient version that uses the built-in -- function rem. divides :: Integer -> Integer -> Bool divides d n = rem n d == 0

The full primality test follows:

-- Whether d divides n. A more efficient version that uses the built-in -- function rem. divides :: Integer -> Integer -> Bool divides d n = rem n d == 0 -- The least divisor of n that is at least k. ldf :: Integer -> Integer -> Integer ldf k n | divides k n = k | k^2 > n = n | otherwise = ldf (k + 1) n -- The least divisor of n. ld :: Integer -> Integer ld n = ldf 2 n -- Primality test. prime :: Integer -> Bool prime n | n < 1 = error "must be a positive integer" | n == 1 = False | otherwise = ld n == n

## Haskell snippet

Just some snippet of Haskell code today to return the last but one element of a list. The first implementation uses the built-in functions `last`

and `take`

.

-- Return the last but one element of a list. This implementation uses -- last and take. penlast :: [a] -> a penlast xs = if null xs || length xs <= 2 then head xs else last (take ((length xs) - 1) xs)

The second implementation below uses the built-in functions `head`

and `drop`

.

-- Return the penultimate element of a list. This implementation uses -- head and drop. penhead :: [a] -> a penhead xs = if null xs || length xs <= 2 then head xs else head (drop ((length xs) - 2) xs)

## Haskell mode spews junk on first load

I’m using Haskell mode version 2.8.0 with Emacs 23.1.1 under Ubuntu 10.04.1 LTS. After loading a Haskell file, I would get the following garbage:

#[nil "\300C\207" [t] 2]

Here’s what it looks like:

Acting on a tip from the ArchLinux community, I grep’d through all the Emacs Lisp files in the source distribution of Haskell mode 2.8.0 and found that the garbage in question is output by the following function in haskell-mode.el:

(eval-when-compile ;; Emacs 21 defines `values' as a (run-time) alias for list. ;; Don't maerge this with the pervious clause. (if (string-match "values" (pp (byte-compile (lambda () (values t))))) (defsubst values (&rest values) values)))

The culprit is the line

(pp (byte-compile (lambda () (values t)))))

I commented out that whole function and the junk is no longer seen when I first load a Haskell file.