¨Ubungsblatt 1 - Trash.net

Übersetzerbau
22. 4. 2005 Übungsblatt 1
Christoph Leuzinger
Matr.-Nr. 111803
Aufgabe 1.1
extEuclid (n ,0) = (n ,1 ,0)
extEuclid (n,m) = (d,x,y)
where
(d’,x’,y ’) = extEuclid (m , n ‘mod ‘ m)
(d,x,y) = (d ’ , y ’ , x ’ - ( n ‘div ‘m) * y ’)
Aufgabe 1.2
pascal 1 = [1]
pascal n = [1] ++ [ pascal ’ n x | x < - [2 .. (n -1) ]] ++ [1]
where
pascal ’ n x = foldl (+) 0 ( take 2 ( drop (x -2) ( pascal (n
-1) )))
Aufgabe 1.3
1. mapIt f [] = []
mapIt f [x ] = [ x]
mapIt f l = ( head l) : ( mapIt f ( map f ( drop 1 l)))
2. data NestedList a = Empty | Elem a | NestedNestedList (
NestedList a) | Concat ( NestedList a) ( NestedList a)
deriving ( Show )
nestedElem ( Elem x) Empty = False
nestedElem ( Elem x) ( Elem y) = x == y
nestedElem ( Elem x) ( NestedNestedList y) = nestedElem (
Elem x) y
nestedElem ( Elem x) ( Concat y z) = ( nestedElem ( Elem x)
y) || ( nestedElem ( Elem x) z)
Aufgabe 1.3
data Expr = Con Int | Var String | Sum [ Expr ] | Prod [ Expr ]
deriving ( Show ,Eq)
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Übersetzerbau
22. 4. 2005 Übungsblatt 1
Christoph Leuzinger
Matr.-Nr. 111803
simplify ( Con x) = ( Con x)
simplify ( Var x) = ( Var x)
simplify ( Sum [x]) = simplify x
simplify ( Sum (x:xs))
| ( simplify x) == ( Con 0) = simplify ( Sum xs)
| ( simplify ( Sum xs)) == ( Con 0) = simplify x
| otherwise = Sum [ simplify x, simplify ( Sum xs)]
simplify ( Prod [x]) = simplify x
simplify ( Prod (x:xs))
| ( simplify x) == ( Con 0) = Con 0
| ( simplify ( Prod xs)) == ( Con 0) = Con 0
| otherwise = Prod [ simplify x, simplify ( Prod xs)]
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