diff --git a/Dockerfile b/Dockerfile index a370790..e8e21c2 100644 --- a/Dockerfile +++ b/Dockerfile @@ -1,4 +1,4 @@ -FROM haskell:buster +FROM docker.io/haskell:buster RUN apt-get update && apt-get install -y haskell-platform diff --git a/code/Angabe5.hs b/code/Angabe5.hs new file mode 100644 index 0000000..8da21b7 --- /dev/null +++ b/code/Angabe5.hs @@ -0,0 +1,183 @@ +module Angabe5 where + +{- 1. Vervollstaendigen Sie gemaess Angabentext! + 2. Vervollständigen Sie auch die vorgegebenen Kommentaranfänge! + 3. Loeschen Sie keine Deklarationen aus diesem Rahmenprogramm, auch nicht die Modulanweisug! + 4. Achten Sie darauf, dass `Gruppe' Leserechte fuer Ihre Abgabedatei hat! +-} + + +type Nat0 = Int + + +-- Die selbstdefinierte Typklasse Menge_von: + +class Eq a => Menge_von a where + leer :: [] a + vereinige :: [] a -> [] a -> [] a + schneide :: [] a -> [] a -> [] a + ziehe_ab :: [] a -> [] a -> [] a + ist_teilmenge :: [] a -> [] a -> Bool + ist_obermenge :: [] a -> [] a -> Bool + ist_element :: a -> [] a -> Bool + ist_leer :: [] a -> Bool + sind_gleich :: [] a -> [] a -> Bool + anzahl :: a -> [] a -> Nat0 + + -- Protoimplementierungen + leer = [] + vereinige xs ys = xs ++ ys + ist_teilmenge xs ys = ist_obermenge ys xs + ist_obermenge xs ys = ist_teilmenge ys xs + ist_element x xs = anzahl x xs >= 1 + ist_leer xs = xs == leer + sind_gleich xs ys = ist_teilmenge xs ys && ist_teilmenge ys xs + + +-- Weitere Typen: + +newtype Paar a b = P (a,b) deriving (Eq,Show) + +data Zahlraum_0_10 = N | I | II | III | IV | V | VI + | VII | VIII | IX | X | F deriving (Eq,Ord,Show) + +newtype Funktion = Fkt { f :: Zahlraum_0_10 -> Zahlraum_0_10 } + +data Baum a = Blatt a | Knoten (Baum a) a (Baum a) deriving (Eq,Show) + +newtype ElemTyp a = ET a + +-- Pseudoheterogene Elementtypen +data PH_ElemTyp a b c d e = A a | B b | C c | D d | E e deriving (Eq,Show) +data PH_ElemTyp' q r s = Q q | R r | S s deriving (Eq,Show) + + +-- Simple helper functions +roman_to_nat :: Zahlraum_0_10 -> Nat0 +roman_to_nat N = 0 +roman_to_nat I = 1 +roman_to_nat II = 2 +roman_to_nat III = 3 +roman_to_nat IV = 4 +roman_to_nat V = 5 +roman_to_nat VI = 6 +roman_to_nat VII = 7 +roman_to_nat VIII = 8 +roman_to_nat IX = 9 +roman_to_nat X = 10 +roman_to_nat F = -1 + +nat_to_roman :: Nat0 -> Zahlraum_0_10 +nat_to_roman 0 = N +nat_to_roman 1 = I +nat_to_roman 2 = II +nat_to_roman 3 = III +nat_to_roman 4 = IV +nat_to_roman 5 = V +nat_to_roman 6 = VI +nat_to_roman 7 = VII +nat_to_roman 8 = VIII +nat_to_roman 9 = IX +nat_to_roman 10 = X +nat_to_roman n + | n > 10 = F + | n < 0 = F + | otherwise = error "Could not recognize input" -- this should not happen + +is_correct_num :: Zahlraum_0_10 -> Bool +is_correct_num n = + case n of + F -> False + _ -> True + +-- Aufgabe A.1 + +instance Num Zahlraum_0_10 where + (+) n n' = add_r n n' + (-) n n' = diff_r n n' + (*) n n' = mult_r n n' + fromInteger n = nat_to_roman (fromInteger n) + +add_r :: Zahlraum_0_10 -> Zahlraum_0_10 -> Zahlraum_0_10 +add_r n n' + | is_correct_num n == False || is_correct_num n' == False = F + | otherwise = nat_to_roman sum_r + where + a = roman_to_nat n + b = roman_to_nat n' + sum_r = a + b + +diff_r :: Zahlraum_0_10 -> Zahlraum_0_10 -> Zahlraum_0_10 +diff_r n n' + | is_correct_num n == False || is_correct_num n' == False = F + | otherwise = nat_to_roman dif_r + where + a = roman_to_nat n + b = roman_to_nat n' + dif_r = a - b + +mult_r :: Zahlraum_0_10 -> Zahlraum_0_10 -> Zahlraum_0_10 +mult_r n n' + | is_correct_num n == False || is_correct_num n' == False = F + | otherwise = nat_to_roman prod_r + where + a = roman_to_nat n + b = roman_to_nat n' + prod_r = a * b + +-- Aufgabe A.2 + +-- instance Eq Funktion where +-- ... + +-- instance Show Funktion where +-- ... + + +-- Aufgabe A.3 + +-- instance Menge_von Int where +-- ... + +-- instance Menge_von Zahlraum_0_10 where +-- ... + +-- instance Menge_von Funktion where +-- ... + + +-- Aufgabe A.4 + +-- instance (Eq a,Eq b) => Menge_von (Paar a b) where +-- ... + +-- instance Eq a => Menge_von (Baum a) where +-- ... + + +-- Aufgabe A.5 + +-- instance Eq a => Eq (ElemTyp a) where +-- ... + +-- instance Show a => Show (ElemTyp a) where +-- ... + + +-- Aufgabe A.6 + +-- instance Eq a => Menge_von (ElemTyp a) where +-- ... + + + +-- Aufgabe A.7 + +-- instance (Eq a,Eq b,Eq c,Eq d,Eq e) => Menge_von (PH_ElemTyp a b c d e) where +-- ... + + +-- Aufgabe A.8 + +-- instance (Eq p,Eq q,Eq r) => Menge_von (PH_ElemTyp' p q r) where ... +