Inital commit

2011-10-26 10:11:42 +02:00
commit c0da376199
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+1b. mod. Menge 	(Haskell Listen)
+2b. mod. Queue	(Haskell Listen)
+3b. mod. Stack	(Haskell Listen)
+4b. mod. Baum	(Haskell Listen)  // erstmal weggelassen
+
+1c. mod. Menge	(Folgen)
+2c. mod. Queue	(Folgen)
+3c. mod. Stack	(Folgen)
+4c. mod. Baum	(Folgen)
+
+	
+1b. Modellierende Spezifikation einer Menge	(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------
+
+Model :			Haskell Listen 
+
+Invariante :	In einer Menge dürfen keine Duplikate vorkommen
+
+Spezifikation:	createM :: [a]
+				create 						= []
+								
+				isEmpty :: [a] -> Bool
+				isEmpty [] 					= True
+				isEmpty (x:xs)  			= False
+				
+				insert :: a -> [a] -> [a]
+				insert x []					= [x]
+				insert y (x:xs)				
+							| y == x 		= (x:xs)
+							| otherwise		= x:(insert y xs)
+				
+				delete :: a -> [a] -> [a]
+				delete x []					= []
+				delete y (x:xs)	
+							| y == x 		= xs
+							| otherwise		= x:(delete y xs)
+				
+				isIn :: a -> [a] -> Bool
+				isIn x []					= False
+				isIn y (x:xs)				
+							| y == x 		= True
+							| otherwise		= x:(isIn y xs)
+							
+
+
+2b. Modellierende Spezifikation einer Schlange	(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------				
+							
+Modell:  Liste in Haskell [t]
+
+Invariante :   length [t] <= MAX
+
+Spezifikation:	createQ :: [t]
+		createQ 					= []
+					
+		enqueue :: t -> [t] -> [t]
+		enqueue x [] 					= [x]
+		enqueue y (x:xs) 				= (x:xs) ++ [y]
+					
+		dequeue :: [t] -> [t]
+		dequeue [] 					= error "Queue leer, Du OpfA"
+		dequeue (x:xs) 					= xs 
+								
+		first :: [t] -> t
+		first [] 					= error "Queue leer, Du OpfA"
+		first (x:xs)  					= x
+				
+				
+3b. Modellierende Spezifikation eines Stacks	(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------				
+
+Modell:  Liste in Haskell [t]
+
+Invariante :   length [t] <= MAX
+
+Spezifikation:	createS :: Stack s
+				createS 				= []
+				
+				isEmpty :: Stack s -> Bool
+				isEmpty []				= True
+				isEmpty xs				= False
+				
+				push	:: e -> Stack s -> Stack s
+				push x []				= [x]
+				push y (x:xs)			= y : (x:xs)
+								
+				pop		:: Stack s -> Stack s
+				pop []					= error "Stack ist leer"
+				pop (x:xs)				= xs
+							
+				top		:: Stack s -> e
+				top [] 					= error "Stack ist leer"
+				top (x:xs)				= x	
+				
+				size	:: Stack s -> int
+				size []					= 0
+				size (x:xs)				= 1 + size (xs)
+				
+
+
+4b. Algebraische Spezifikation eines Baumes   	(Model,Spezifikation,Invariante)
+--------------------------------------------------------------------------------------------------
+
+									folgt
+									
+									
+
+1c. Modellierende Spezifikation einer Menge		(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------
+
+Model : 			Menge = e | (xi)i=1..n , type xi = T , n <- N
+
+Invariante : 		n < N && Alle (xi)i=1..n Exisitiert kein (xj)j=1..n mit xj = xi
+
+Spezifikation :		createM = e 
+					//post	return e
+					
+					isEmpty	Menge
+					//post	if Menge == e return True else return False	
+					
+					//pre	createM && isIn T Menge = False (s. Invariante) && k < N
+					insert	T Menge
+					//post	insert T (xi)i=1..k => (xi)i=1..k+1 && xk+1 = T
+					
+					//pre 	createM
+					delete	T (xi)i=1..k
+					//post	(xi)i=1..k-1 && isIn T Menge = False
+					
+					//pre	createM
+					isIn	T Menge
+					//post	return ( Existiert ein (xi)i=1..k | xi == T )
+					
+					
+				
+
+2c. Modellierende Spezifikation einer Schlange	(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------	
+
+Model : 			Queue = e | (xi)i=1..n , type xi = T , n <- N
+
+Invariante : 		n < N
+
+Spezifikation :		createQ = e 
+					//post	returns e
+					
+					isEmpty (xi)i=1..k
+					//post 	if Queue == e  return True else return False 	
+					
+					//pre 	createQ && k < N
+					enqueue	T Queue
+					//post  enqueue	T (xi)i=1..k => (xi)i=1..k+1 && xk+1 = T
+					
+					//pre   !isEmpty
+					dequeue	Queue
+					//post	dequeue (xi)i=1..k   => (xi)i=2..k  (size = size-1)
+					
+					//pre	!isEmpty
+					first	Queue
+					//post	first (xi)i=1..k 	 => return x1
+					
+
+
+
+3c. Modellierende Spezifikation eines Stacks	(Model,Spezifikation,Invariante)
+---------------------------------------------------------------------------------------------------
+
+Model : 			Stack = e | (xi)i=1..n , type xi = T , n <- N
+
+Invariante : 		n < N
+
+Spezifikation :		createS = e 
+					
+					//pre 	createS
+					isEmpty Stack 
+					//post  Stack == e True else return False
+					
+					//pre 	createS && k < N
+					push	T (xi)i=1..k-1 
+					//post 	push T (xi)i=1..k-1 =>(xi)i=1..k && xk = T
+					
+					//pre	!isEmpty
+					pop		(xi)i=1..n
+					//pre	(xi)i=1..n-1
+					
+					//pre 	!isEmpty
+					top		(xi)i=1..n
+					//post	returns xn
+					
+					//pre 	createS
+					size	(xi)i=1..n-1
+					//post	returns n-1
+				
+				
+4c. Algebraische Spezifikation eines Baumes   	(Model,Spezifikation,Invariante)
+--------------------------------------------------------------------------------------------------
+
+									folgt