a-conjecture-of-mine

An exercise on polyglossy: the same problem solved on multiple languages

Diffstat

1 file changed, 54 insertions, 54 deletions

diff --git a/haskell/Main.hs b/haskell/Main.hs
@@ -1,54 +1,54 @@
--- The following program is a simple test for the following conjecture:
-
--- Let S: N -> N be the sum of the digits of a positive integer.
--- For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
-
-module Main where
-
-import Numeric (readDec)
-import Numeric.Natural
-import System.Environment
-import System.Exit
-import Control.Monad (foldM)
-import Data.Vector (Vector, unsafeIndex, generate)
-
-main :: IO Int
-main = do
-    args <- getArgs
-        
-    case readDec <$> head' args of
-        Just [(max, "")] ->
-            if counterexempl max then exitFailure else exitSuccess
-
-        _ -> exitInvalidInput
-    
-    where head' [] = Nothing
-          head' xs = Just (head xs)
-
--- Calculates the sum of the digits of `n`.
-sumDigits :: Int -> Int
-sumDigits = sumDigitsTail 0
-    where sumDigitsTail acc n
-              | n == 0 = acc
-              | otherwise = sumDigitsTail (acc + (n `mod` 10)) (n `div` 10)
-
--- Returns `True` if the if the conjecture holds for pair.
--- Otherwise returns `False`.
-test' :: Vector Int -> (Int, Int) -> Bool
-test' sums (a, b) = diff `mod` 9 == 0
-    where diff = sums !! (a + b) - sums !! a - sums !! b
-          (!!) = unsafeIndex
-
--- Checks if there is any counterexample in
--- [(a, b) | a <- [0..max], b <- [a..max]].
---
--- Returns `True` if a counter example was found.
--- Otherwise returns `False`.
-counterexempl :: Int -> Bool
-counterexempl max =
-    all (test' sums) [(a, b) | a <- [0..max], b <- [a..max]]
-    where sums = generate (2 * max + 1) sumDigits
-
-exitInvalidInput :: IO Int
-exitInvalidInput = exitWith $ ExitFailure 2
-
+-- The following program is a simple test for the following conjecture:
+
+-- Let S: N -> N be the sum of the digits of a positive integer.
+-- For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
+
+module Main where
+
+import Numeric (readDec)
+import Numeric.Natural
+import System.Environment
+import System.Exit
+import Control.Monad (foldM)
+import Data.Vector (Vector, unsafeIndex, generate)
+
+main :: IO Int
+main = do
+    args <- getArgs
+        
+    case readDec <$> head' args of
+        Just [(max, "")] ->
+            if counterexempl max then exitFailure else exitSuccess
+
+        _ -> exitInvalidInput
+    
+    where head' [] = Nothing
+          head' xs = Just (head xs)
+
+-- Calculates the sum of the digits of `n`.
+sumDigits :: Int -> Int
+sumDigits = sumDigitsTail 0
+    where sumDigitsTail acc n
+              | n == 0 = acc
+              | otherwise = sumDigitsTail (acc + (n `mod` 10)) (n `div` 10)
+
+-- Returns `True` if the if the conjecture holds for the pair.
+-- Otherwise returns `False`.
+test' :: Vector Int -> (Int, Int) -> Bool
+test' sums (a, b) = diff `mod` 9 == 0
+    where diff = sums !! (a + b) - sums !! a - sums !! b
+          (!!) = unsafeIndex
+
+-- Checks if there is any counterexample in
+-- [(a, b) | a <- [0..max], b <- [a..max]].
+--
+-- Returns `True` if a counter example was found.
+-- Otherwise returns `False`.
+counterexempl :: Int -> Bool
+counterexempl max =
+    all (test' sums) [(a, b) | a <- [0..max], b <- [a..max]]
+    where sums = generate (2 * max + 1) sumDigits
+
+exitInvalidInput :: IO Int
+exitInvalidInput = exitWith $ ExitFailure 2
+