From ae9eade752fc54f53ec64311b881dd62a98cfa21 Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Mon, 2 May 2016 15:50:29 +0200 Subject: [PATCH 1/5] cleanup at GZI --- Übungen/Blatt1.md | 144 +++++++++++++++++++++--------------- Übungen/Blatt1.solution.hs | 128 ++++++++++++++++++++++++++++++++ 2 files changed, 213 insertions(+), 59 deletions(-) create mode 100644 Übungen/Blatt1.solution.hs diff --git a/Übungen/Blatt1.md b/Übungen/Blatt1.md index dd0ccf7..707bf2d 100644 --- a/Übungen/Blatt1.md +++ b/Übungen/Blatt1.md @@ -1,90 +1,116 @@ -# Übungsblatt 1 +-- Übungsblatt 1 +-- ============= +-- +-- Typtheorie +-- ---------- +-- +-- Schreiben Sie alle **möglichen** Implementationen der folgenden +-- Funktionen. Wozu könnte `fun2` nützlich sein? -## Typtheorie - -Schreiben Sie alle **möglichen** Implementationen der folgenden Funktionen. Wozu könnte `fun2` nützlich sein? - -```haskell fun1 :: a -> a -fun1 = _fun1 +fun1 a = a + +-- id fun2 :: a -> b -> a -fun2 = _fun2 +fun2 a _ = a fun3 :: (Eq a) => a -> a -> Bool -fun3 = _fun3 -``` +fun3 _ _ = True +fun3 _ _ = False +fun3 = (==) +fun3 = (/=) -Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der simpelste hiervon ist `Identity`, der nur einen anderen Typen einpackt. +-- Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der +-- simpelste hiervon ist `Identity`, der nur einen anderen Typen einpackt. -```haskell data Identity a = Identity a -``` -Diese Definition stellt uns automatisch den Konstruktor `Identity :: a -> Identity a` zur Verfügung, der ein `a` einpackt. Schreiben Sie die Funktion +-- Diese Definition stellt uns automatisch den Konstruktor +-- `Identity :: a -> Identity a` zur Verfügung, der ein `a` einpackt. +-- Schreiben Sie die Funktion -```haskell unIdentity :: Identity a -> a -unIdentity = _unIdentity -``` +unIdentity (Identity a) = a -welche diesen Vorgang wieder rückgängig macht. +-- welche diesen Vorgang wieder rückgängig macht. +-- +-- Angenommen, Sie hätten nun ein Wert vom Typen `Identity a` und eine +-- Funktion mit dem Typen `a -> b`. Wie wenden Sie diese auf das `a` +-- "innerhalb" des `Identity` an um ein `Identity b` herzustellen? +-- Schreiben Sie also eine Funktion -Angenommen, Sie hätten nun ein Wert vom Typen `Identity a` und eine Funktion mit dem Typen `a -> b`. Wie wenden Sie diese auf das `a` "innerhalb" des `Identity` an um ein `Identity b` herzustellen? Schreiben Sie also eine Funktion - -```haskell mapIdentity :: (a -> b) -> Identity a -> Identity b -mapIdentity = _mapIdentity -``` +mapIdentity f a = Identity . f . unIdentity -**Hinweis:** Es gibt *zwei* prinzipielle Vorgehen dieses zu implementieren. Kommen Sie auf beide? +--mapIdentity f (Identity a) = Identity (f a) +-- **Hinweis:** Es gibt *zwei* prinzipielle Vorgehen dieses zu +-- implementieren. Kommen Sie auf beide? +-- +-- Funktionen sind auch nur Typen +-- ------------------------------ +-- +-- Datentypen können auch Funktionen enthalten. Sehen Sie sich einmal den +-- Datentypen -## Funktionen sind auch nur Typen - -Datentypen können auch Funktionen enthalten. Sehen Sie sich einmal den Datentypen - -```haskell data Pred a = Pred (a -> Bool) -``` -an. Hier wird ein Prädikat definiert, welches (gegeben einen Datentyp `a`) eine Funktion gespeichert hat, die `a` in einen `Bool` umwandeln kann (etwa um irgendwas zu filtern/selektieren/löschen/..., wenn man dies an eine weitere Funktion übergibt). +-- an. Hier wird ein Prädikat definiert, welches (gegeben einen Datentyp +-- `a`) eine Funktion gespeichert hat, die `a` in einen `Bool` umwandeln +-- kann (etwa um irgendwas zu filtern/selektieren/löschen/..., wenn man +-- dies an eine weitere Funktion übergibt). +-- +-- Auch hier können Sie eine Funktion schreiben, die das `Pred a` wieder +-- "auspackt". Definieren Sie -Auch hier können Sie eine Funktion schreiben, die das `Pred a` wieder "auspackt". Definieren Sie +unPred :: Pred a -> a -> Bool +unPred (Pred a) = a -```haskell -unPred :: Pred a -> (a -> Bool) -unPred = _unPred -``` +-- Da Haskell-Funktionen aber "gecurried" sind (mehr dazu in der +-- Vorlesung), können Sie die Klammern hinten in der Signatur auch +-- weglassen und erhalten `unPred :: Pred a -> a -> Bool`, was man zugleich +-- als "wende `Pred a` an, wenn du ein `a` bekommst" lesen kann. In der Tat +-- sind beide Funktionen identisch (wieso?). +-- +-- Bonus +-- +-- Was für eine Funktion bräuchten Sie um ein `Pred a` in ein `Pred b` +-- umzuwandeln? Können Sie diese implementieren? -Da Haskell-Funktionen aber "gecurried" sind (mehr dazu in der Vorlesung), können Sie die Klammern hinten in der Signatur auch weglassen und erhalten `unPred :: Pred a -> a -> Bool`, was man zugleich als "wende `Pred a` an, wenn du ein `a` bekommst" lesen kann. -In der Tat sind beide Funktionen identisch (wieso?). - -### Bonus - -Was für eine Funktion bräuchten Sie um ein `Pred a` in ein `Pred b` umzuwandeln? Können Sie diese implementieren? - -```haskell mapPred :: _fun -> Pred a -> Pred b -mapPred = _mapPred -``` +mapPred f (Pred a) = _mapPred -## Neue Typen erfinden +-- Neue Typen erfinden +-- ------------------- +-- +-- In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden +-- von eigenen Datentypen. Zur Erinnerung; es gibt zwei Möglichkeiten, die +-- man miteinander kombinieren kann: `data Prod a b c = Prod a b c` +-- (Produkttyp) benötigt sowohl `a`, `b` als auch `c` um einen Wert zu +-- erzeugen, `data Sum a b = Sum1 a | Sum2 b` (Summentyp) braucht entweder +-- ein `a` um durch den Konstruktor `Sum1` ein `Sum a b` zu erzeugen oder +-- ein `b` um durch den Konstruktor `Sum2` ein `Sum a b` zu erzeugen. +-- +-- Definieren Sie einen Datentypen `Vielleicht a`, der zwei Konstruktoren +-- besitzt: Einen Konstruktor, mit dem durch ein `a` ein `Vielleicht a` +-- konstruiert wird und ein zweiter Konstruktor, der keinen Wert nimmt, +-- sondern die "Abwesenheit eines `a`" symbolisieren soll. -In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden von eigenen Datentypen. Zur Erinnerung; es gibt zwei Möglichkeiten, die man miteinander kombinieren kann: `data Prod a b c = Prod a b c` (Produkttyp) benötigt sowohl `a`, `b` als auch `c` um einen Wert zu erzeugen, `data Sum a b = Sum1 a | Sum2 b` (Summentyp) braucht entweder ein `a` um durch den Konstruktor `Sum1` ein `Sum a b` zu erzeugen oder ein `b` um durch den Konstruktor `Sum2` ein `Sum a b` zu erzeugen. +data Vielleicht a = Exercise -Definieren Sie einen Datentypen `Vielleicht a`, der zwei Konstruktoren besitzt: Einen Konstruktor, mit dem durch ein `a` ein `Vielleicht a` konstruiert wird und ein zweiter Konstruktor, der keinen Wert nimmt, sondern die "Abwesenheit eines `a`" symbolisieren soll. +-- Können Sie hier eine Funktion schreiben, die das `a` extrahiert? Wenn +-- ja, implementieren Sie diese; wenn nein, geben Sie eine kurze +-- Begründung. +-- +-- Wie würden Sie mittels einer Funktion `a -> b` ein `Vielleicht a` in ein +-- `Vielleicht b` wandeln? Implementieren Sie -Können Sie hier eine Funktion schreiben, die das `a` extrahiert? Wenn ja, implementieren Sie diese; wenn nein, geben Sie eine kurze Begründung. - -Wie würden Sie mittels einer Funktion `a -> b` ein `Vielleicht a` in ein `Vielleicht b` wandeln? Implementieren Sie -```haskell mapVielleicht :: (a -> b) -> Vielleicht a -> Vielleicht b mapVielleicht = _mapVielleicht -``` - -### Bonus - -Man kann Typen natürlich auch Schachteln. Worin liegt eigentlich der Unterschied zwischen einem `Pred (Vielleicht a)` und einem `Vielleicht (Pred a)`? Oder sind diese identisch? - +-- Bonus +-- +-- Man kann Typen natürlich auch Schachteln. Worin liegt eigentlich der +-- Unterschied zwischen einem `Pred (Vielleicht a)` und einem +-- `Vielleicht (Pred a)`? Oder sind diese identisch? diff --git a/Übungen/Blatt1.solution.hs b/Übungen/Blatt1.solution.hs new file mode 100644 index 0000000..28d9df2 --- /dev/null +++ b/Übungen/Blatt1.solution.hs @@ -0,0 +1,128 @@ +-- Übungsblatt 1 +-- ============= +-- +-- Typtheorie +-- ---------- +-- +-- Schreiben Sie alle **möglichen** Implementationen der folgenden +-- Funktionen. Wozu könnte `fun2` nützlich sein? + +fun1 :: a -> a +fun1 a = a + +-- id + +fun2 :: a -> b -> a +fun2 a _ = a + +fun3 :: (Eq a) => a -> a -> Bool +fun3 _ _ = True +--fun3 _ _ = False +--fun3 = (==) +--fun3 = (/=) + +-- Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der +-- simpelste hiervon ist `Identity`, der nur einen anderen Typen einpackt. + +data Identity a = Identity a + +-- Diese Definition stellt uns automatisch den Konstruktor +-- `Identity :: a -> Identity a` zur Verfügung, der ein `a` einpackt. +-- Schreiben Sie die Funktion + +unIdentity :: Identity a -> a +unIdentity (Identity a) = a + +-- welche diesen Vorgang wieder rückgängig macht. +-- +-- Angenommen, Sie hätten nun ein Wert vom Typen `Identity a` und eine +-- Funktion mit dem Typen `a -> b`. Wie wenden Sie diese auf das `a` +-- "innerhalb" des `Identity` an um ein `Identity b` herzustellen? +-- Schreiben Sie also eine Funktion + +mapIdentity :: (a -> b) -> Identity a -> Identity b +mapIdentity f = Identity . f . unIdentity + +--mapIdentity f (Identity a) = Identity (f a) + +-- **Hinweis:** Es gibt *zwei* prinzipielle Vorgehen dieses zu +-- implementieren. Kommen Sie auf beide? +-- +-- Funktionen sind auch nur Typen +-- ------------------------------ +-- +-- Datentypen können auch Funktionen enthalten. Sehen Sie sich einmal den +-- Datentypen + +data Pred a = Pred (a -> Bool) + +-- an. Hier wird ein Prädikat definiert, welches (gegeben einen Datentyp +-- `a`) eine Funktion gespeichert hat, die `a` in einen `Bool` umwandeln +-- kann (etwa um irgendwas zu filtern/selektieren/löschen/..., wenn man +-- dies an eine weitere Funktion übergibt). +-- +-- Auch hier können Sie eine Funktion schreiben, die das `Pred a` wieder +-- "auspackt". Definieren Sie + +unPred :: Pred a -> a -> Bool +unPred (Pred a) = a + +-- Da Haskell-Funktionen aber "gecurried" sind (mehr dazu in der +-- Vorlesung), können Sie die Klammern hinten in der Signatur auch +-- weglassen und erhalten `unPred :: Pred a -> a -> Bool`, was man zugleich +-- als "wende `Pred a` an, wenn du ein `a` bekommst" lesen kann. In der Tat +-- sind beide Funktionen identisch (wieso?). +-- +-- Bonus +-- +-- Was für eine Funktion bräuchten Sie um ein `Pred a` in ein `Pred b` +-- umzuwandeln? Können Sie diese implementieren? + +mapPred :: (b -> a) -> Pred a -> Pred b +mapPred f (Pred a) = Pred (a . f) + +-- Neue Typen erfinden +-- ------------------- +-- +-- In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden +-- von eigenen Datentypen. Zur Erinnerung; es gibt zwei Möglichkeiten, die +-- man miteinander kombinieren kann: `data Prod a b c = Prod a b c` +-- (Produkttyp) benötigt sowohl `a`, `b` als auch `c` um einen Wert zu +-- erzeugen, `data Sum a b = Sum1 a | Sum2 b` (Summentyp) braucht entweder +-- ein `a` um durch den Konstruktor `Sum1` ein `Sum a b` zu erzeugen oder +-- ein `b` um durch den Konstruktor `Sum2` ein `Sum a b` zu erzeugen. +-- +-- Definieren Sie einen Datentypen `Vielleicht a`, der zwei Konstruktoren +-- besitzt: Einen Konstruktor, mit dem durch ein `a` ein `Vielleicht a` +-- konstruiert wird und ein zweiter Konstruktor, der keinen Wert nimmt, +-- sondern die "Abwesenheit eines `a`" symbolisieren soll. + +data Vielleicht a = Etwas a + | Nichts + +-- Können Sie hier eine Funktion schreiben, die das `a` extrahiert? Wenn +-- ja, implementieren Sie diese; wenn nein, geben Sie eine kurze +-- Begründung. +-- +-- Wie würden Sie mittels einer Funktion `a -> b` ein `Vielleicht a` in ein +-- `Vielleicht b` wandeln? Implementieren Sie + +mapVielleicht :: (a -> b) -> Vielleicht a -> Vielleicht b +mapVielleicht f (Etwas a) = Etwas (f a) +mapVielleicht f Nichts = Nichts + +-- Bonus +-- +-- Man kann Typen natürlich auch Schachteln. Worin liegt eigentlich der +-- Unterschied zwischen einem `Pred (Vielleicht a)` und einem +-- `Vielleicht (Pred a)`? Oder sind diese identisch? + +fun4 :: Pred (Vielleicht a) -> x +fun4 (Pred a) = undefined + +fun5 :: Vielleicht (Pred a) -> x +fun5 (Etwas (Pred a)) = undefined +fun5 Nichts = undefined + + +main = putStrLn "compiles" From cb8456060e21e501e7505278a7a3de146e6fc287 Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Mon, 2 May 2016 15:50:59 +0200 Subject: [PATCH 2/5] added Blatt3 --- Übungen/Blatt3.hs | 113 ++++++++++++++++++++++++++++++++++++++++++++ Übungen/Blatt3.lhs | 113 ++++++++++++++++++++++++++++++++++++++++++++ Übungen/Blatt3.md | 101 +++++++++++++++++++++++++++++++++++++++ Übungen/Blatt3.pdf | Bin 0 -> 126462 bytes 4 files changed, 327 insertions(+) create mode 100644 Übungen/Blatt3.hs create mode 100644 Übungen/Blatt3.lhs create mode 100644 Übungen/Blatt3.md create mode 100644 Übungen/Blatt3.pdf diff --git a/Übungen/Blatt3.hs b/Übungen/Blatt3.hs new file mode 100644 index 0000000..1f946ed --- /dev/null +++ b/Übungen/Blatt3.hs @@ -0,0 +1,113 @@ +-- Übungsblatt 3 +-- ============= +-- +-- Throat-Clearing +-- --------------- +-- +-- a.k.a. Imports, damit der Code funktioniert. + +module MonadExercise where +import Control.Applicative +import Control.Monad +import Data.Monoid + +-- Vorwort +-- ------- +-- +-- Die Typklassen, die auf diesem Zettel implementiert werden sollen sind +-- teilweise nicht eindeutig. Ein gutes *Indiz* für eine falsche +-- implementation kann sein, dass Informationen "weggeschmissen" werden - +-- allerdings muss man bei anderen Implementationen genau dies machen. +-- +-- Applicative +-- ----------- +-- +-- Nachdem wir uns letzte Woche ausführlich mit der Typklasse `Functor` +-- beschäftigt haben, bauen wir nun darauf auf und definieren die +-- Applicative-Instanz. Zur Erinnerung: +-- +-- class Functor f => Applicative f where +-- pure :: a -> f a +-- <*> :: f (a -> b) -> f a -> f b +-- +-- Nehmen sie an, sie hätten folgende Datentypen mit ihren +-- `Functor`-Instanzen gegeben. Schreiben sie jeweils die +-- Applicative-Instanz: + +data Identity a = Identity { unIdentity :: a } + deriving (Show, Eq) + +instance Functor Identity where + fmap f (Identity a) = Identity (f a) + +data Vielleicht a = Etwas a + | Nichts + deriving (Show, Eq) + +instance Functor Vielleicht where + fmap f (Etwas a) = Etwas (f a) + fmap _ Nichts = Nichts + +data EntwederOder b a = Entweder a + | Oder b + deriving (Show, Eq) + +instance Functor (EntwederOder b) where + fmap f (Entweder a) = Entweder (f a) + fmap _ (Oder b) = Oder b + +data List a = Cons a (List a) + | Nil + deriving (Show, Eq) + +instance Functor List where + fmap f (Cons a r) = Cons (f a) (fmap f r) + fmap _ Nil = Nil + +instance Monoid (List a) where + mempty = Nil + mappend Nil bs = bs + mappend (Cons a as) bs = Cons a (mappend as bs) + +data V3 a = V3 a a a + +instance Functor V3 where + fmap f (V3 x y z) = V3 (f x) (f y) (f z) + +-- Monad +-- ----- +-- +-- Zu welchen der oben aufgeführten Typen gibt es eine Monaden-Instanz? Wie +-- sieht diese aus? Schreiben sie diese (falls möglich). +-- +-- Bonus +-- ----- + +data Account = Account +data Inbox = Inbox +data Mail = Mail + +-- Seien folgende Funktionen gegeben: + +login :: Maybe Account +login = undefined + +getInbox :: Account -> Maybe Inbox +getInbox = undefined + +getMails :: Inbox -> [Mail] +getMails = undefined + +safeHead :: [a] -> Maybe a +safeHead = undefined + +-- Schreiben sie eine Funktion: + +getFirstMail :: Maybe Mail +getFirstMail = undefined + +-- welche die oben genannten 4 Funktionen nutzt um die erste Mail aus dem +-- gegebenen Account zurückzuliefern, sofern alles erfolgreich war. +-- +-- Können sie beide Varianten (einmal mittels `do`-notation und einmal mit +-- `>>=`) schreiben? diff --git a/Übungen/Blatt3.lhs b/Übungen/Blatt3.lhs new file mode 100644 index 0000000..6448e12 --- /dev/null +++ b/Übungen/Blatt3.lhs @@ -0,0 +1,113 @@ +Übungsblatt 3 +============= + +Throat-Clearing +--------------- + +a.k.a. Imports, damit der Code funktioniert. + +> module MonadExercise where +> import Control.Applicative +> import Control.Monad +> import Data.Monoid + +Vorwort +------- + +Die Typklassen, die auf diesem Zettel implementiert werden sollen sind +teilweise nicht eindeutig. Ein gutes *Indiz* für eine falsche +implementation kann sein, dass Informationen "weggeschmissen" werden - +allerdings muss man bei anderen Implementationen genau dies machen. + +Applicative +----------- + +Nachdem wir uns letzte Woche ausführlich mit der Typklasse `Functor` +beschäftigt haben, bauen wir nun darauf auf und definieren die +Applicative-Instanz. Zur Erinnerung: + + class Functor f => Applicative f where + pure :: a -> f a + <*> :: f (a -> b) -> f a -> f b + +Nehmen sie an, sie hätten folgende Datentypen mit ihren +`Functor`-Instanzen gegeben. Schreiben sie jeweils die +Applicative-Instanz: + +> data Identity a = Identity { unIdentity :: a } +> deriving (Show, Eq) +> +> instance Functor Identity where +> fmap f (Identity a) = Identity (f a) +> +> data Vielleicht a = Etwas a +> | Nichts +> deriving (Show, Eq) +> +> instance Functor Vielleicht where +> fmap f (Etwas a) = Etwas (f a) +> fmap _ Nichts = Nichts +> +> data EntwederOder b a = Entweder a +> | Oder b +> deriving (Show, Eq) +> +> instance Functor (EntwederOder b) where +> fmap f (Entweder a) = Entweder (f a) +> fmap _ (Oder b) = Oder b +> +> data List a = Cons a (List a) +> | Nil +> deriving (Show, Eq) +> +> instance Functor List where +> fmap f (Cons a r) = Cons (f a) (fmap f r) +> fmap _ Nil = Nil +> +> instance Monoid (List a) where +> mempty = Nil +> mappend Nil bs = bs +> mappend (Cons a as) bs = Cons a (mappend as bs) +> +> data V3 a = V3 a a a +> +> instance Functor V3 where +> fmap f (V3 x y z) = V3 (f x) (f y) (f z) + +Monad +----- + +Zu welchen der oben aufgeführten Typen gibt es eine Monaden-Instanz? Wie +sieht diese aus? Schreiben sie diese (falls möglich). + +Bonus +----- + +> data Account = Account +> data Inbox = Inbox +> data Mail = Mail + +Seien folgende Funktionen gegeben: + +> login :: Maybe Account +> login = undefined +> +> getInbox :: Account -> Maybe Inbox +> getInbox = undefined +> +> getMails :: Inbox -> [Mail] +> getMails = undefined +> +> safeHead :: [a] -> Maybe a +> safeHead = undefined + +Schreiben sie eine Funktion: + +> getFirstMail :: Maybe Mail +> getFirstMail = undefined + +welche die oben genannten 4 Funktionen nutzt um die erste Mail aus dem +gegebenen Account zurückzuliefern, sofern alles erfolgreich war. + +Können sie beide Varianten (einmal mittels `do`-notation und einmal mit +`>>=`) schreiben? diff --git a/Übungen/Blatt3.md b/Übungen/Blatt3.md new file mode 100644 index 0000000..7423b69 --- /dev/null +++ b/Übungen/Blatt3.md @@ -0,0 +1,101 @@ +# Übungsblatt 3 + +## Throat-Clearing + +a.k.a. Imports, damit der Code funktioniert. + +```haskell +import Control.Applicative +import Control.Monad +import Data.Monoid +``` + +## Vorwort + +Die Typklassen, die auf diesem Zettel implementiert werden sollen sind teilweise nicht eindeutig. Ein gutes *Indiz* für eine falsche implementation kann sein, dass Informationen "weggeschmissen" werden - allerdings muss man bei anderen Implementationen genau dies machen. + +## Applicative + +Nachdem wir uns letzte Woche ausführlich mit der Typklasse `Functor` beschäftigt haben, bauen wir nun darauf auf und definieren die Applicative-Instanz. +Zur Erinnerung: + + class Functor f => Applicative f where + pure :: a -> f a + <*> :: f (a -> b) -> f a -> f b + +Nehmen sie an, sie hätten folgende Datentypen mit ihren `Functor`-Instanzen gegeben. Schreiben sie jeweils die Applicative-Instanz: + +```haskell +data Identity a = Identity { unIdentity :: a } + deriving (Show, Eq) + +instance Functor Identity where + fmap f (Identity a) = Identity (f a) + +data Vielleicht a = Etwas a + | Nichts + deriving (Show, Eq) + +instance Functor Vielleicht where + fmap f (Etwas a) = Etwas (f a) + fmap _ Nichts = Nichts + +data EntwederOder b a = Entweder a + | Oder b + deriving (Show, Eq) + +instance Functor (EntwederOder b) where + fmap f (Entweder a) = Entweder (f a) + fmap _ (Oder b) = Oder b + +data List a = Cons a (List a) + | Nil + deriving (Show, Eq) + +instance Functor List where + fmap f (Cons a r) = Cons (f a) (fmap f r) + fmap _ Nil = Nil + +instance Monoid List where + mempty = Nil + mappend Nil bs = bs + mappend (Cons a as) bs = Cons a (mappend as bs) + +data V3 a = V3 a a a + +instance Functor V3 where + fmap f (V3 x y z) = V3 (f x) (f y) (f z) +``` + +## Monad + +Zu welchen der oben aufgeführten Typen gibt es eine Monaden-Instanz? Wie sieht diese aus? Schreiben sie diese (falls möglich). + + +## Bonus + +Seien folgende Funktionen gegeben: + +```haskell +login :: Maybe Account +login = undefined + +getInbox :: Account -> Maybe Inbox +getInbox = undefined + +getMails :: Inbox -> [Mail] +getMails = undefined + +safeHead :: [a] -> Maybe a +safeHead = undefined +``` + +Schreiben sie eine Funktion: + +```haskell +getFirstMail :: Maybe Mail +``` + +welche die oben genannten 4 Funktionen nutzt um die erste Mail aus dem gegebenen Account zurückzuliefern, sofern alles erfolgreich war. + +Können sie beide Varianten (einmal mittels `do`-notation und einmal mit `>>=`) schreiben? diff --git a/Übungen/Blatt3.pdf b/Übungen/Blatt3.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c8463197c3f9f552334a24cd3aba2744723ae7e9 GIT binary patch literal 126462 zcma&NQukGs;;or0Zd*@F zqoRS*#Gd3y)nUFPrxL|%-rZcS_}*;?O~b8=Mp!Asg@*nd~jsYAGr02@98Vq~#k z-Ug*KbL!F`{g4T}&@H-Dg%os5#~8X=V|QXhrU*Q=}*%o(+>?Nu`7o!dq0~ 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a/Übungen/Blatt2.solution.hs b/Übungen/Blatt2.solution.hs new file mode 100644 index 0000000..fdb115f --- /dev/null +++ b/Übungen/Blatt2.solution.hs @@ -0,0 +1,125 @@ +-- # Übungsblatt 2 +-- +-- ## Throat-Clearing +-- +-- a.k.a. Imports, damit der Code funktioniert. + +import Control.Monad +import Data.Functor +import Data.Monoid + +-- ## Functor +-- +-- Sie haben in der Vorlesung die Typklasse `Functor` kennengelernt. Zur Erinnerung: +-- +-- class Functor f where +-- fmap :: (a -> b) -> f a -> f b +-- +-- Nehmen sie an, sie hätten folgende Datentypen gegeben, für die alle eine `Functor`-Instanz existiert und eindeutig ist: + +data Identity a = Identity { unIdentity :: a } + +instance Functor Identity where + fmap f (Identity a) = Identity (f a) + +data Vielleicht a = Etwas a + | Nichts + +instance Functor Vielleicht where + fmap f (Etwas a) = Etwas (f a) + fmap f Nichts = Nichts + +data EntwederOder b a = Entweder a + | Oder b + +instance Functor (EntwederOder c) where + fmap f (Entweder a) = Entweder (f a) + fmap _ (Oder b) = Oder b + +data GameVector b a = V3 a a a + | VStrange [a] + | Neighbours [GameVector b a] + | EntwederOder b (GameVector b a) + +instance Functor (GameVector c) where + fmap f (V3 x y z) = V3 (f x) (f y) (f z) + fmap f (VStrange l) = VStrange (f <$> l) + fmap f (Neighbours l) = Neighbours (fmap f <$> l) + fmap f (EntwederOder b v) = EntwederOder b (f <$> v) + +-- Schreiben sie hierzu die jeweiligen `Functor`-Instanzen. +-- +-- ## Besser und allgemeiner +-- +-- Vereinfachen und verallgemeinern sie folgenden Ausdrücke so weit wie möglich und geben die sie dadurch entstehenden Typsignaturen an. +-- Bedenken sie, dass wenn sie auf eine Typklasse abstrahieren, sie die gesamten Gesetze der Typklasse benutzen können. +-- +-- Kann die Funktion nachher mehr als vorher? +-- +-- *Bonus*: Hat sich an der Laufzeit etwas verändert? + +mystery1 :: [[a]] -> [[a]] +mystery1 = map (++[]) + +-- List is Functor => fmap instead of map +mystery1' :: Functor f => f [a] -> f [a] +mystery1' = fmap (++[]) + +-- List is a Monoid => ++ == <> && [] == mempty +mystery1'' :: (Functor f, Monoid m) => f m -> f m +mystery1'' = fmap (<> mempty) + +-- Monoid-Law: (<> mempty) == id +mystery1''' :: Functor f => f a -> f a +mystery1''' = fmap id + +-- Functor-Law: fmap id == id +mystery1'''' :: a -> a +mystery1'''' = id + +mystery2 :: (Eq a) => a -> a -> a -> Bool +mystery2 x y z + | x == y || y == z = True + | otherwise = False + +mystery3 :: (MonadPlus f, Eq a) => (a -> a) -> a -> f a -> f a +mystery3 f a l = mfilter (==a) (f <$> l) + +mystery3' :: Eq a => (a -> a) -> a -> [a] -> [a] +mystery3' f a l = filter (==a) (f <$> l) + -- post a l' + -- where + -- l' = map f l + -- post a (x:xs) + -- | a == x = x : post a xs + -- | otherwise = post a xs + -- post _ [] = [] + +mystery4 :: (Int -> Bool) + -> Vielleicht (EntwederOder String Int) + -> Vielleicht (EntwederOder String Bool) +mystery4 f (Etwas (Entweder a)) = Etwas . Entweder . f $ a +mystery4 _ (Etwas (Oder b)) = Etwas (Oder b) +mystery4 _ Nichts = Nichts + +mystery4'' :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b) +mystery4'' f ve = fmap (fmap f) ve + +mystery4' :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b) +mystery4' = fmap . fmap + +-- ## Bonus +-- +-- Es gibt von dem bekannten Spiel 2048 eine Haskell-Implementation für die Kommandozeile in unter 100 Zeilen. Diese ist zu finde unter +-- https://github.com/gregorulm/h2048/blob/master/h2048.hs +-- +-- Sie können diesen Code mit `GHC` kompilieren oder im `ghci` ausführen (`main` ist die Start-Funktion). +-- +-- Was für Prinzipielle Vorgehenspunkte können sie erkennen? +-- Eine kleine Erklärung gibt es im Blog der Erstellers: http://gregorulm.com/2048-in-90-lines-haskell/ +-- +-- Keine Angst, sie müssen dies noch nicht verstehen, aber es soll verdeutlichen, wie viel man mit extrem wenig erreichen kann. Viele der Abgabeprojekte werden in dieser Größenordnung liegen (aber meist noch so etwas wie ein GUI o.ä. benötigen). Versuchen sie einfach den Code kaputtzuspielen (z.b. Tasten ändern, Siegbedingung ändern, Cheats einbauen, ...). +-- +-- Viel Spass beim Spielen! :) + +main = putStrLn "compiles" From 1d19a7803689055969fb129b2ed743683758619b Mon Sep 17 00:00:00 2001 From: Stefan Dresselhaus Date: Mon, 9 May 2016 12:02:48 +0200 Subject: [PATCH 5/5] =?UTF-8?q?added=20Folien=20und=20=C3=9Cbungen=20f?= =?UTF-8?q?=C3=BCr=20Vorlesung=204?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Folien/vorlesung4.pdf | Bin 0 -> 275537 bytes Übungen/Blatt4.md | 155 +++ Übungen/Blatt4.pdf | Bin 0 -> 120569 bytes Übungen/Blatt4_data/CSV_Dummy_hard.csv | 1001 +++++++++++++++++ .../Blatt4_data/CSV_Dummy_problematic.csv | 11 + Übungen/Blatt4_data/CSV_Dummy_simple.csv | 11 + 6 files changed, 1178 insertions(+) create mode 100644 Folien/vorlesung4.pdf create mode 100644 Übungen/Blatt4.md create mode 100644 Übungen/Blatt4.pdf create mode 100644 Übungen/Blatt4_data/CSV_Dummy_hard.csv create mode 100644 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In den praktischen Übungen soll es weniger um das "erfinden" eines neuen Parser-Kombinators gehen, als um die Anwendung. + +## Set-Up + +Da wir nun zum ersten mal mit externen dependencies arbeiten, müssen wir diese zunächst installieren. Dies ist ein sehr wichtiger Schritt, da nahezu alle weiteren Übungszettel dieses Vorgehen voraussetzen. + +Als erstes sollten Sie die Quellen von `stack` mit einem `stack update` aktualisieren. Anschließend erstellen sie ein neues Stack-Projekt mittels `stack new `. Sie erhalten ein Verzeichnis mit dem Projektnamen, in dem ein kleines "Hello World" liegt. Als erstes sollte man immer über die `projektname.cabal` drüber schauen. Hier werden nachher auch alle dependencies eingetragen. + +Bei mir sieht das z.B. so aus (Projekt heisst "parser"): + +``` +name: parser +version: 0.1.0.0 +synopsis: Initial project template from stack +description: Please see README.md +homepage: https://github.com/githubuser/parser#readme +license: BSD3 +license-file: LICENSE +author: Author name here +maintainer: example@example.com +copyright: 2016 Author name here +category: Web +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: Lib + build-depends: base >= 4.7 && < 5 + default-language: Haskell2010 + +executable parser-exe + hs-source-dirs: app + main-is: Main.hs + ghc-options: -threaded -rtsopts -with-rtsopts=-N + build-depends: base + , parser + default-language: Haskell2010 + +test-suite parser-test + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Spec.hs + build-depends: base + , parser + ghc-options: -threaded -rtsopts -with-rtsopts=-N + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/githubuser/parser +``` + +Generell sollte man hier ordentliche Angaben machen, da viele tools dieses automatisch lesen und überall eintragen. Insbesondere sollte man nicht seine private Email-Adresse nehmen, sondern z.b. die Techfak-Adresse, die Studiumsbezogen ist. + +Wir haben hier 3 Bereiche: `library`, `parsers-exe` und `test-suite`. Library ist das, was wir meistens schreiben - eine Sammlung von Funktionen, die das eigentlich tun. Dann haben wir die executable; diese enthält die `main` und ruft meist in wenig Code unsere library auf, nachdem sie z.b. Parameter/Dateien/... gelesen hat und kümmert sich um die Ausgabe. Somit können wir für spätere Zwecke (Projekte) die Library 1:1 wiederverwenden. +Die test-suite ignorieren wir für den Moment. Wir kommen in einer separaten Vorlesung noch einmal auf Tests zu sprechen. + +Eine editierte Variante könnte etwa so aussehen: + +``` +name: parser +version: 0.1.0.0 +synopsis: A little parser for generic CSV-Files +description: Please see README.md +homepage: https://github.com/Drezil/FFPiHaskell_parser#readme +license: BSD3 +license-file: LICENSE +author: Stefan Dresselhaus +maintainer: sdressel@techfak.uni-bielefeld.de +copyright: 2016 Stefan Dresselhaus +category: Tool +build-type: Simple +-- extra-source-files: +cabal-version: >=1.10 + +library + hs-source-dirs: src + exposed-modules: Lib + build-depends: base >= 4.7 && < 5 + , attoparsec + default-language: Haskell2010 + +executable parser-exe + hs-source-dirs: app + main-is: Main.hs + ghc-options: -threaded -rtsopts -with-rtsopts=-N + build-depends: base + , parser + default-language: Haskell2010 + +test-suite parser-test + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Spec.hs + build-depends: base + , parser + ghc-options: -threaded -rtsopts -with-rtsopts=-N + default-language: Haskell2010 + +source-repository head + type: git + location: https://github.com/Drezil/FFPiHaskell_parser +``` + +Änderungen die gemacht wurden: + +- Daten ausgefüllt +- attoparsec als dependency der library hinzugefügt +- github-links angepasst (sofern man github verwendet) + +Nachdem man das ganze nun gespeichert hat, reicht ein `stack build` um alle dependencies herunterzuladen, kompilieren und installieren. Anschließend kann man mit `stack exec parser-exe` das Programm ausführen. + +## Ein simpler CSV-Parser + +Sie sollten aus ihrem Studium bereits die EBNF kennen. Eine (simple) CSV-Datei besitzt folgende EBNF: + +``` +csv-file = { row } +row = field-list, eol +field-list = field, [ ",", field-list ] +field = [ whitespace ], field-value, [ whitespace ] +field-value = quoted-string | bare-string +quoted-string = '"', quoted-content, '"' +quoted-content = { quoted-char } +quoted-char = (any char except '"' or eol) +bare-string = { bare-char } +bare-char = (any char except ',' or eol without whitespace at beginning/end) +whitespace = space-char, { space-char } +space-char = " " | "\t" +eol = "\n" +``` + +Kurzes recap: `{ .. }` bedeutet 1 oder mehr, `[ .. ]` sind optional, `A | B` heißt, entweder A oder B, `A, B, C` bedeutet zunächst A, dann B, dann C. + +### Datenstrukturen + +Überlegen sie sich zunächst, wie eine Datenstruktur aussehen könnte und definieren sie diese. Inhalt sind vorerst nur Strings. Sie brauchen keine Zahlen/Daten/... zu erkennen. + +### Parser + +Schreiben sie einen Parser, der einen CSV-String in diese Datenstruktur parsed und geben sie diese aus (`deriving Show` auf der Datenstruktur reicht). Ein paar Testbeispiele für CSV-Dateien finden sie auf github/im Lernraum. + +### Bonus + +Natürlich ist das nur ein simpler CSV-Parser. Folgende Features wären für einen echten Einsatz noch Wünschenswert: + +- sicherstellen, dass alle "rows" gleich lang sind und ggf. mit Fehlermeldung abbrechen +- einen "Header" mit einlesen, der die einzelnen Spalten beschreibt +- Quotation nicht nur als "blabla'bla", sondern auch als 'blabla"bla' zulassen, "bla \" bla" auch entsprechend parsen. diff --git a/Übungen/Blatt4.pdf b/Übungen/Blatt4.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9e1ea69b4b079ccd74da9359057fee7fc7944635 GIT binary patch literal 120569 zcma&NL$EMR(4~28+qP}nwr$(idu`jcZQHhOW4@S~p3UD8)49sZsC7P>=Twm@h=|cL z(y>C3&M%LwLoqWGFc8=qSrPE?K+(&X+L^mp5HPZ`auWRC0YxunY2#w*L_jZQW9VWk zVrpz}VhY8_2j%SIWNK&&<*^x~zGJ_|hTwmvZ)hMu2#hQ&xvXA~D!mGGvkJSBSOY(W zXA#xVA(1SoB%9Rd=gu=}sYJdmTuAJ>_q~Jb>-BMYUY1SIGytV|5;b)ts)kZsn<=Ua zwYqw8*r@%Tqk|f%A!~M|*7NL_f##YKal)U*pX4&S*$A`flWK%o6A)#1#x`vD z4E8e+Y?&V{Cl*Vc>kP`bNv#I~eA_Q3CN7ng4?Y~7X-0fjj&vkikeuy*>8ab0I(GdR 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