solutions for chapter 01

Author: lpalma

ch01/11.hs

@@ -0,0 +1,18 @@
+{-
+ - Give another possible calculation for the result of double (double 2)
+ -}
+
+main = do
+       putStrLn "double (double 2)"
+       putStrLn "{applying the inner double}"
+       putStrLn "double 2 + double 2"
+       putStrLn "{applying the first double}"
+       putStrLn "(2 + 2) + double 2"
+       putStrLn "{applying the second double}"
+       putStrLn "(2 + 2) + (2 + 2)"
+       putStrLn "{applying the first +}"
+       putStrLn "4 + (2 + 2)"
+       putStrLn "{applying the second +}"
+       putStrLn "4 + 4"
+       putStrLn "{applying +}"
+       putStrLn "8"

ch01/12.hs

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+{-
+ - Show that sum [x] = x for any number x.
+ -}
+
+ main = do
+     putStrLn "sum [] = 0"
+     putStrLn "sum (x:xs) = x + sum xs"
+     putStrLn "{given sum [x], applying the second definition}"
+     putStrLn "sum (x:[]) = x + sum []"
+     putStrLn "{applying the first defintion}"
+     putStrLn "sum (x:[]) = x + 0"
+     putStrLn "{simplifying the right side}"
+     putStrLn "sum (x:[]) = x"
+     putStrLn "{simplifying the left side}"
+     putStrLn "sum [x] = x"

ch01/13.hs

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+{-
+ - Define a function product that produces the product of a list of numbers,
+ - and show using your definition that product [2,3,4] = 24
+ -}
+
+recProduct [] = 1
+recProduct (x:xs) = x * product xs
+
+main = print recProduct [2,3,4]

ch01/14.hs

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+{-
+ - How should the definition of the function qsort be modified
+ - so that it produces a sorted reverse version of a list?
+ -}
+
+ rQsort [] = []
+ rQsort (x:xs) = rQsort larger ++ [x] ++ rQsort smaller
+                 where 
+                     larger = [b | b <- xs, b > x]
+                     smaller = [a | a <- xs, a <= x]

ch01/15.hs

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+{-
+ - What would be the effect of replacing <= by < in the original
+ - definition of qsort? Hint: consider the example qsort [2,2,3,1,1].
+ -}
+
+buggyQsort [] = []
+buggyQsort (x:xs) = buggyQsort smaller ++ [x] ++ buggyQsort larger
+                     where
+                         smaller = [a | a <- xs, a < x]
+                         larger = [b | b <- xs, b > x]
+
+main = do
+    putStrLn "using buggyQsort in a list with"
+    putStrLn "duplicate values, such as [2,2,3,1,1]"
+    putStrLn "will remove the duplicate values from"
+    putStrLn "the result sorted list, such as [1,2,3]."