[Tried to improve assignment, partly based on student feedback.
Nils Anders Danielsson <nad@cs.chalmers.se>**20050908104013] {
hunk ./CasesAndRecursionAssignment.ws 14
-  p <#>Today you'll work with cases and recursion.</#>
+  p <#>Today you'll work with cases and recursion. Try to follow the
+       method for defining functions proposed in the lecture.</#>
hunk ./CasesAndRecursionAssignment.ws 18
-       follow-up questions, just as before, so you should always read
-       the answers.</b></em></#>
+       follow-up questions and/or useful information, so you should
+       always read the answers.</b></em></#>
hunk ./Rec.hs 28
+even'' :: Integer -> Bool
+even'' 0 = True
+even'' n | n > 0 = not (even'' (n-1))
+even'' n | n < 0 = not (even'' (n+1))
+
+-- Checks if argument is odd.
+odd'' :: Integer -> Bool
+odd'' n = not (even'' n)
+
+prop_even'' :: Integer -> Bool
+prop_even'' n = even'' (2*n)
+
+prop_odd'' :: Integer -> Bool
+prop_odd'' n = odd'' (2*n + 1)
+
+-- Checks if argument is even.
hunk ./Recursion.ws 8
+divisorUrl = "http://en.wikipedia.org/wiki/Divisor"
hunk ./Recursion.ws 38
-            , "prop_factorial n = n >= 0 ==> factorial (n+1) `div` factorial n == n+1"
+            , "prop_factorial n ="
+            , "  n >= 0 ==> factorial (n+1) `div` factorial n == n+1"
hunk ./Recursion.ws 49
-            , "prop_factorial' n = n >= 0 ==> factorial n `divides` factorial (n+1)"
+            , "prop_factorial' n ="
+            , "  n >= 0 ==> factorial n `divides` factorial (n+1)"
hunk ./Recursion.ws 61
-    p <#>The <tt>error</tt> function can be used to signal invalid
-         input. It halts the program and prints the given error message.
-         Try to write understandable error messages.</#>
+      li $ do
+
+        p <#>The <tt>error</tt> function can be used to signal invalid
+             input. It halts the program and prints the given error message.
+             Try to write understandable error messages.</#>
+
+        fixed $ unlines
+          [ "Main> factorial (-3)"
+          , ""
+          , "Program error: factorial: Negative input not allowed."
+          ]
hunk ./Recursion.ws 73
-    fixed $ unlines
-      [ "Main> factorial (-3)"
-      , ""
-      , "Program error: factorial: Negative input not allowed."
-      ]
+      li $ p <#>By putting a function name in backquotes we can use it in an
+                infix style. Writing <tt>m `divides` n</tt> means
+                exactly the same thing as writing <tt>divides m
+                n</tt>. The reason for doing this is that the
+                expression becomes easier to read.</#>
hunk ./Recursion.ws 133
-        p <#>Two ways of solving the problem:</#>
+        p <#>Three ways of solving the problem:</#>
hunk ./Recursion.ws 136
+
+          li $ fixed $ unlines
+            [ "-- Checks if argument is even."
+            , "even :: Integer -> Bool"
+            , "even 0 = True"
+            , "even n | n > 0 = not (even (n-1))"
+            , "even n | n < 0 = not (even (n+1))"
+            , ""
+            , "-- Checks if argument is odd."
+            , "odd :: Integer -> Bool"
+            , "odd n = not (even n)"
+            ]
hunk ./Recursion.ws 178
-  <#>Compute the number of positive divisors of an arbitrary positive
+  p <#>Compute the number of positive <a href=<% divisorUrl
+     %>>divisors</a> of an arbitrary positive
hunk ./Recursion.ws 181
-     arguments.</#> ?> do
+     integer arguments <tt>m</tt> and <tt>n</tt>:</#>
+
+  ul $ do
+
+    li $ p <#><tt>n</tt>: We want to know how many divisors <tt>n</tt>
+              has in the range <tt>1</tt> to <tt>m</tt>.</#>
+
+    li $ p <#><tt>m</tt>: The number next in turn. We should check
+              whether it divides <tt>n</tt> or not.</#>
+
+  <#>If you get stuck, don't hesitate to take a peak at the
+     solution.</#> ?> do
hunk ./Recursion.ws 227
-             functions. The names introduced using <tt>where</tt> are only
-             visible in the current function definition. We could also
-             have written <tt>divisors</tt> as follows:</#>
+             functions. The names introduced using <tt>where</tt> are
+             only visible in the current function definition. We could
+             also have written <tt>divisors</tt> as follows (as
+             proposed in the hint):</#>
}