Improve Haskell code for a few problems

Haskell/ProjectEuler.hs

@@ -1,5 +1,6 @@
 module ProjectEuler
 ( isPrime
+, lcmm
 , digitSum
 , sumProperDivisors
 , countDivisors
@@ -18,6 +19,11 @@ isPrime n =
     where candidates = [5,11..limit]
           limit = floor(sqrt(fromIntegral n)) + 1
 
+lcmm :: (Integral n) => [n] -> n
+lcmm values
+    | length values == 2    = lcm (head values) (last values)
+    | otherwise             = lcm (head values) (lcmm (tail values))
+
 digitSum :: (Integral a, Show a) => a -> Int
 digitSum n = sum $ map digitToInt $ show n
 

Haskell/p001.hs

@@ -2,11 +2,11 @@
 --
 -- Find the sum of all the multiples of 3 or 5 below 1000.
 
-sumMultiples :: Integer
+sumMultiples :: Int
 sumMultiples = sum $ filter p [1..999]
-                where p n = n `mod` 3 == 0 || n `mod` 5 == 0
+               where p n = n `mod` 3 == 0 || n `mod` 5 == 0
 
-main =  do
+main = do
     let result = sumMultiples
     putStrLn $ "Project Euler, Problem 1\n"
         ++ "Answer: " ++ show result

Haskell/p002.hs

@@ -4,15 +4,15 @@
 --
 -- By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
 
-fib :: Integer -> Integer
+fib :: Int -> Int
 fib 0 = 0
 fib 1 = 1
 fib n = fib (n-1) + fib(n-2)
 
-sumEvenFib :: Integer
+sumEvenFib :: Int
 sumEvenFib = sum $ filter even $ takeWhile (<=4000000) (map fib [0..])
 
-main =  do
+main = do
     let result = sumEvenFib
     putStrLn $ "Project Euler, Problem 2\n"
         ++ "Answer: " ++ show result

Haskell/p003.hs

@@ -3,7 +3,7 @@
 
 import ProjectEuler (isPrime)
 
-maxPrimeFactor :: Integer -> Integer
+maxPrimeFactor :: Int -> Int
 maxPrimeFactor n
     | isPrime n = n         
     | even n    = maxPrimeFactor $ n `div` 2

Haskell/p004.hs

@@ -2,10 +2,10 @@
 --
 -- Find the largest palindrome made from the product of two 3-digit numbers.
 
-isPalindrome :: Integer -> Bool
+isPalindrome :: Int -> Bool
 isPalindrome n = show n == reverse (show n)
 
-maxPalindrome :: Integer
+maxPalindrome :: Int
 maxPalindrome =
     maximum $ filter isPalindrome [ x * y | x <- [100..999], y <- [100..999] ]
 

Haskell/p005.hs

@@ -2,10 +2,7 @@
 --
 -- What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
 
-lcmm :: (Integral n) => [n] -> n
+import ProjectEuler (lcmm)
-lcmm values
-    | length values == 2    = lcm (head values) (last values)
-    | otherwise             = lcm (head values) (lcmm (tail values))
 
 main = do
     let result = lcmm [1..20]

Haskell/p006.hs

@@ -10,8 +10,8 @@
 --
 --Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
 
-sumSquareDiff :: (Integral a) => a -> a
+sumSquareDiff :: Int -> Int
-sumSquareDiff n = (sum [1..n]^2) - sum (map (^2) [1..n])
+sumSquareDiff n = (sum [1..n] ^2) - sum (map (^2) [1..n])
 
 main = do
     let result = sumSquareDiff 100

Haskell/p007.hs

@@ -4,7 +4,7 @@
 --
 import ProjectEuler (isPrime)
 
-nthPrime :: (Integral a) => Int -> a
+nthPrime :: Int -> Int
 nthPrime n = last $ take n [ x | x <- [1..], isPrime x ]
 
 main = do

Haskell/p009.hs

@@ -8,10 +8,10 @@
 --
 -- Find the product abc.
 
-pythagoreanTriplet :: (Integral a) => a -> (a, a, a)
+pythagoreanTriplet :: Int -> (Int, Int, Int)
 pythagoreanTriplet n = head [ (x, y, z) | x <- [1..n], y <- [x..n], z <- [y..n], x + y + z == n, x^2 + y^2 == z^2]
 
-prodTriplet :: (Integral a) => (a, a, a) -> a
+prodTriplet :: (Int, Int, Int) -> Int
 prodTriplet (x, y, z) = x * y * z
 
 main = do

Haskell/p010.hs

@@ -4,7 +4,7 @@
 
 import ProjectEuler (isPrime)
 
-sumPrimes :: (Integral a) => a -> a
+sumPrimes :: Int -> Int
 sumPrimes n = sum [ x | x <- [1..n], isPrime x ]
 
 main = do