[Added exercise about geometric mean.
Nils Anders Danielsson <nad@cs.chalmers.se>**20050831205349] {
hunk ./Mean.hs 3
-mean2 x y = (x + y)/2
+mean x y = (x + y)/2
hunk ./Mean.hs 7
-  (min x y <= mean2 x y) && (mean2 x y <= max x y)
+  (min x y <= mean x y) && (mean x y <= max x y)
+
+geometricMean :: Floating a => a -> a -> a
+geometricMean x y = sqrt (x * y)
+
+prop_geometricMeanBetween :: Double -> Double -> Property
+prop_geometricMeanBetween x y =
+  x > 0 && y > 0 ==>
+  (min x y <= geometricMean x y) && (geometricMean x y <= max x y)
+
+prop_geometricMeanBetween' :: Double -> Double -> Bool
+prop_geometricMeanBetween' x y =
+  (min x y <= geometricMean x y) && (geometricMean x y <= max x y)
hunk ./MoreFunctions.ws 5
+geometricMeanURL = "http://en.wikipedia.org/wiki/Geometric_mean"
+
hunk ./MoreFunctions.ws 10
-  h2 $ text "More on functions"
+  h2 $ text "More functions"
hunk ./MoreFunctions.ws 128
+
+  <#>Repeat the procedure above, but now with the <a href=<%
+     geometricMeanURL %>><em>geometric</em>
+     mean</a> instead of the arithmetic one.</#> ?> do
+
+    fixed $ unlines
+      [ "geometricMean :: Floating a => a -> a -> a"
+      , "geometricMean x y = sqrt (x * y)"
+      ]
+
+    fixed $ unlines
+      [ "prop_geometricMeanBetween :: Double -> Double -> Bool"
+      , "prop_geometricMeanBetween x y ="
+      , "  (min x y <= geometricMean x y) && (geometricMean x y <= max x y)"
+      ]
+
+    p <#>Let us try out the property. Several things can happen:</#>
+
+    prompts "Main>"
+      [ ( "quickCheck prop_geometricMeanBetween"
+        , unlines [ "Falsifiable, after 2 tests:"
+                  , "-0.2"
+                  , "-0.4"
+                  ]
+        )
+      ]
+
+    prompts "Main>"
+      [ ( "quickCheck prop_geometricMeanBetween"
+        , unlines [ "3"
+                    , "Program error: argument out of range"
+                  ]
+        )
+      ]
+
+    <#>What is the problem?</#> ?> do
+
+      p <#>The geometric mean is only defined for <em>positive</em> numbers. We
+           can restrict the test to positive numbers by using <tt>(==>)</tt>.</#>
+
+      fixed $ unlines
+        [ "prop_geometricMeanBetween :: Double -> Double -> Property"
+        , "prop_geometricMeanBetween x y ="
+        , "  x > 0 && y > 0 ==>"
+        , "  (min x y <= geometricMean x y) && (geometricMean x y <= max x y)"
+        ]
+
+      p <#>Now the test should succeed. Note that we have to change
+           the type of the property when using <tt>(==>)</tt>.</#>
}