[Added some exercises based on arithmetic properties.
Nils Anders Danielsson <nad@cs.chalmers.se>**20050901103350
 Suggested by Andreas Farre.
] {
hunk ./.boring 10
+^MoreProperties\.hs$
addfile ./ArithmeticProperties.hs
hunk ./ArithmeticProperties.hs 1
+import QuickCheck
+
+prop_addCommutative :: Integer -> Integer -> Bool
+prop_addCommutative x y = x + y == y + x
+
+prop_mulCommutative :: Integer -> Integer -> Bool
+prop_mulCommutative x y = x * y == y * x
+
+prop_addAssociative :: Integer -> Integer -> Integer -> Bool
+prop_addAssociative x y z = x + (y + z) == (x + y) + z
+
+prop_mulAssociative :: Integer -> Integer -> Integer -> Bool
+prop_mulAssociative x y z = x * (y * z) == (x * y) * z
+
+prop_mulLeftDistributive :: Integer -> Integer -> Integer -> Bool
+prop_mulLeftDistributive x y z = x * (y + z) == x * y + x * z
hunk ./IntroAssignment.ws 8
+import MoreProperties
hunk ./IntroAssignment.ws 26
+  moreProperties
+
hunk ./Makefile 1
-SOURCE = ArbitraryRatio.hs Commands.ws Intro.ws Pythagoras.ws	\
-Temperature.hs Calculator.ws Functions.ws IntroAssignment.ws	\
-MoreFunctions.ws Question.hs TypeClasses.ws
+SOURCE = ArbitraryRatio.hs Commands.ws Intro.ws MoreProperties.ws	\
+Pythagoras.ws Temperature.hs Calculator.ws Functions.ws			\
+IntroAssignment.ws MoreFunctions.ws Question.hs TypeClasses.ws
addfile ./MoreProperties.ws
hunk ./MoreProperties.ws 1
+module MoreProperties where
+
+import Question
+
+commutativeUrl = "http://en.wikipedia.org/wiki/Commutative"
+associativeUrl = "http://en.wikipedia.org/wiki/Associative"
+distributiveUrl = "http://en.wikipedia.org/wiki/Distributive"
+
+moreProperties :: WithHTML x CGI ()
+moreProperties = do
+
+  <h2>More properties</h2>
+
+  p <#>Let's now practice writing some properties. Recall that a
+       property is a function that should always return <tt>True</tt>.</#>
+
+  ul $ do
+
+    <#>Write a property stating that addition of <tt>Integer</tt>s is
+       <a href=<% commutativeUrl %>>commutative</a> (i.e. x + y = y +
+       x). Test it.</#> .?> do
+
+      fixed $ unlines
+        [ "prop_addCommutative :: Integer -> Integer -> Bool"
+        , "prop_addCommutative x y = x + y == y + x"
+        ]
+
+      prompts "Main>"
+        [ ("quickCheck prop_addCommutative", "OK, passed 100 tests.") ]
+
+    <#>Write a property stating that multiplication of <tt>Integer</tt>s is
+       commutative.</#> .?> do
+
+      fixed $ unlines
+        [ "prop_mulCommutative :: Integer -> Integer -> Bool"
+        , "prop_mulCommutative x y = x * y == y * x"
+        ]
+
+    <#>Write a property stating that addition of <tt>Integer</tt>s is
+       <a href=<% associativeUrl %>>associative</a>.</#> .?> do
+
+      fixed $ unlines
+        [ "prop_addAssociative :: Integer -> Integer -> Integer -> Bool"
+        , "prop_addAssociative x y z = x + (y + z) == (x + y) + z"
+        ]
+
+    <#>Write a property stating that multiplication of <tt>Integer</tt>s is
+       associative.</#> .?> do
+
+      fixed $ unlines
+        [ "prop_mulAssociative :: Integer -> Integer -> Integer -> Bool"
+        , "prop_mulAssociative x y z = x * (y * z) == (x * y) * z"
+        ]
+
+    <#>Write a property stating that multiplication <a href=<%
+       distributiveUrl %>>distributes</a> from the left over addition
+       (for <tt>Integer</tt>s).</#> .?> do
+
+      fixed $ unlines
+        [ "prop_mulLeftDistributive :: Integer -> Integer -> Integer -> Bool"
+        , "prop_mulLeftDistributive x y z = x * (y + z) == x * y + x * z"
+        ]
}