From bee9e3d3599389dcafab90a2b0ae9ceedc30de97 Mon Sep 17 00:00:00 2001
From: Camil Staps <info@camilstaps.nl>
Date: Mon, 2 Mar 2015 13:58:22 +0100
Subject: [PATCH] 6.3

---
 files/practicum/StdSet.icl | 24 +++++++++++--
 week4/camil/StdSet.dcl     | 25 ++++++++++++++
 week4/camil/StdSet.icl     | 70 ++++++++++++++++++++++++++++++++++++++
 3 files changed, 117 insertions(+), 2 deletions(-)
 create mode 100644 week4/camil/StdSet.dcl
 create mode 100644 week4/camil/StdSet.icl

diff --git a/files/practicum/StdSet.icl b/files/practicum/StdSet.icl
index b152f37..6cad7f1 100644
--- a/files/practicum/StdSet.icl
+++ b/files/practicum/StdSet.icl
@@ -1,5 +1,25 @@
-implementation module StdSet
+definition module StdSet
 
-import StdEnv
+import StdClass
 
 ::	Set a
+
+toSet			:: [a]             -> Set a | Eq a
+fromSet			:: (Set a)         -> [a]
+
+isEmptySet		:: (Set a)         -> Bool
+isDisjoint		:: (Set a) (Set a) -> Bool  | Eq a
+isSubset		:: (Set a) (Set a) -> Bool  | Eq a
+isStrictSubset	:: (Set a) (Set a) -> Bool  | Eq a
+memberOfSet		:: a       (Set a) -> Bool  | Eq a
+union           :: (Set a) (Set a) -> Set a | Eq a
+intersection	:: (Set a) (Set a) -> Set a | Eq a
+nrOfElements	:: (Set a) -> Int
+without			:: (Set a) (Set a) -> Set a | Eq a
+
+product			:: (Set a) (Set b) -> Set (a,b)
+
+instance zero (Set a)
+instance ==   (Set a) | Eq a
+
+powerSet		:: (Set a)         -> Set (Set a)
diff --git a/week4/camil/StdSet.dcl b/week4/camil/StdSet.dcl
new file mode 100644
index 0000000..6cad7f1
--- /dev/null
+++ b/week4/camil/StdSet.dcl
@@ -0,0 +1,25 @@
+definition module StdSet
+
+import StdClass
+
+::	Set a
+
+toSet			:: [a]             -> Set a | Eq a
+fromSet			:: (Set a)         -> [a]
+
+isEmptySet		:: (Set a)         -> Bool
+isDisjoint		:: (Set a) (Set a) -> Bool  | Eq a
+isSubset		:: (Set a) (Set a) -> Bool  | Eq a
+isStrictSubset	:: (Set a) (Set a) -> Bool  | Eq a
+memberOfSet		:: a       (Set a) -> Bool  | Eq a
+union           :: (Set a) (Set a) -> Set a | Eq a
+intersection	:: (Set a) (Set a) -> Set a | Eq a
+nrOfElements	:: (Set a) -> Int
+without			:: (Set a) (Set a) -> Set a | Eq a
+
+product			:: (Set a) (Set b) -> Set (a,b)
+
+instance zero (Set a)
+instance ==   (Set a) | Eq a
+
+powerSet		:: (Set a)         -> Set (Set a)
diff --git a/week4/camil/StdSet.icl b/week4/camil/StdSet.icl
new file mode 100644
index 0000000..01c854b
--- /dev/null
+++ b/week4/camil/StdSet.icl
@@ -0,0 +1,70 @@
+implementation module StdSet
+
+import StdEnv
+import StdClass
+
+::	Set a :== [a]
+
+toSet			:: [a]             -> Set a | Eq a
+toSet l = toSet` l []
+where 
+    toSet` [] s = s
+    toSet` [x:xs] s = toSet` xs (join x s)
+    where
+        join :: a (Set a) -> Set a | Eq a
+        join e s
+            | memberOfSet e s = s
+            | otherwise = s ++ [e]
+
+fromSet			:: (Set a)         -> [a]
+fromSet s = s
+
+isEmptySet		:: (Set a)         -> Bool
+isEmptySet [] = True
+isEmptySet _ = False
+
+isDisjoint		:: (Set a) (Set a) -> Bool  | Eq a
+isDisjoint s1 s2 = length (intersection s1 s2) == 0
+
+isSubset		:: (Set a) (Set a) -> Bool  | Eq a
+isSubset s1 s2 = nrOfElements (intersection s1 s2) == nrOfElements s1
+
+isStrictSubset	:: (Set a) (Set a) -> Bool  | Eq a
+isStrictSubset s1 s2 = isSubset s1 s2 && s1 <> s2
+
+memberOfSet		:: a       (Set a) -> Bool  | Eq a
+memberOfSet e [] = False
+memberOfSet e [x:xs] 
+    | e == x = True
+    | otherwise = memberOfSet e xs
+
+union           :: (Set a) (Set a) -> Set a | Eq a
+union s1 s2 = toSet (s1 ++ s2)
+
+intersection	:: (Set a) (Set a) -> Set a | Eq a
+intersection s1 s2 = [e \\ e <- s1 | memberOfSet e s2]
+
+nrOfElements	:: (Set a) -> Int
+nrOfElements s = length (fromSet s)
+
+without			:: (Set a) (Set a) -> Set a | Eq a
+without s1 s2 = [e \\ e <- s1 | (memberOfSet e s2) == False]
+
+product			:: (Set a) (Set b) -> Set (a,b)
+product s1 s2 = [(e1,e2) \\ e1 <- s1, e2 <- s2]
+
+instance zero (Set a)
+where zero = []
+
+instance ==   (Set a) | Eq a 
+where (==) s1 s2 = isSubset s1 s2 && isSubset s2 s1
+
+powerSet		:: (Set a)         -> Set (Set a)
+powerSet [] = [zero]
+powerSet [e:es] = map ((++) [e]) (powerSet es) ++ powerSet es
+
+powerSet` :: (Set a) -> [Int]
+powerSet` s = [0 .. 2^(nrOfElements s) - 1]
+
+takeMod :: (Set a) Int -> Set a
+takeMod s m = [e \\ e <- s & k <- [0..] | k rem m == 0]
-- 
2.20.1