fixed point computation

git-svn-id: https://slps.svn.sourceforge.net/svnroot/slps@739 ab42f6e0-554d-0410-b580-99e487e6eeb2

topics/exercises/README.txt

@@ -1,5 +1,6 @@
-b2/hutton - examples from Graham Hutton's "Programming in Haskell"
+*/hutton - examples from Graham Hutton's "Programming in Haskell"
 haskell1 - simple exercises solved in Haskell
+fixed    - fixed point computation by iteration in Haskell
 
 while1	 - a DCG parser for a fragment of While
 while2	 - a DCG parser for While
@@ -9,20 +10,21 @@ while5   - typed While in Prolog
 while6   - While evaluation in Haskell (incomplete)
 while7   - While evaluation in Haskell (complete, big step operational)
 while8   - While execution in Haskell (complete, denotational)
+ewhile   - Extended While execution in Haskell (complete, denotational)
 
 xml1	 - a DCG parser for XML subset (elements only)
 xml2	 - a DCG parser for XML subset (elements and attributes)
 
 b1       - abstract syntax for B in Prolog
 b2       - parsing B in Haskell
 b3       - folding over expressions for B in Haskell
-nb1	 - abstract syntax for NB in Prolog
-nb2	 - semantics and types for NB in Prolog
+nb1      - abstract syntax for NB in Prolog
+nb2      - semantics and types for NB in Prolog
 nb3      - parsing and folding NB in Haskell
 
 lambda1	 - lambda calculus abstract and concrete syntax in Prolog
 lambda2	 - lambda caclulus with Church numbers
 lambda3  - lambda calculus abstract syntax, free variables, substitution, evaluation
 lambda4	 - untyped lambda calculus with alpha conversion & fixed point combinator
-lambda5  - typed lambda calculus with alpha conversion
+lambda5  - typed lambda calculus with alpha conversion in Prolog
 lambda6  - typed lambda calculus with alpha conversion & fixed point operator

topics/exercises/fixed/Makefile

@@ -0,0 +1,5 @@
+all:
+	runhaskell fixedPoint.hs
+
+clean:
+	rm -f *~ *.hi *.o

topics/exercises/fixed/fixedPoint.hs

@@ -0,0 +1,24 @@
+-- Explicitly recursive functorial function
+fac x = if x == 0 then 1 else x * fac (x-1)
+
+-- Recursion by means of fixed point combinator
+fac' = fix f
+	where
+		-- Functional for factorial
+		f g x = if x == 0 then 1 else x * g (x-1)
+		-- Fixed point combinator based on fixed point condition
+		fix f = f (fix f)
+
+-- Fixed point computation based on iteration
+fac'' x = head (dropWhile (==Nothing) [ f'i n x | n <- [0..] ])
+	where
+		f g x = if x == 0 then Just 1 else maybe Nothing (Just . (x*)) (g (x-1))
+		f'i 0 = const Nothing
+		f'i n = f (f'i (n-1))
+
+-- Test functions
+main =
+	do
+		print $ fac 5 -- prints 120
+		print $ fac' 5 -- ditto
+		print $ fac'' 5 -- prints Just 120