From 403a19865f1e9d03bffd870fbbd2ad86ab4bab24 Mon Sep 17 00:00:00 2001
From: Stefan Dresselhaus <sdressel@techfak.uni-bielefeld.de>
Date: Sun, 17 Apr 2016 17:18:38 +0200
Subject: [PATCH] =?UTF-8?q?added=20Vorlesung1=20and=20=C3=9Cbungsblatt=201?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Folien/Vorlesung1.pdf       | Bin 0 -> 461858 bytes
 "\303\234bungen/Blatt1.hs"  | 115 ++++++++++++++++++++++++++++++++++++
 "\303\234bungen/Blatt1.lhs" | 112 +++++++++++++++++++++++++++++++++++
 "\303\234bungen/Blatt1.md"  |  93 +++++++++++++++++++++++++++++
 "\303\234bungen/Blatt1.pdf" | Bin 0 -> 145796 bytes
 5 files changed, 320 insertions(+)
 create mode 100644 Folien/Vorlesung1.pdf
 create mode 100644 "\303\234bungen/Blatt1.hs"
 create mode 100644 "\303\234bungen/Blatt1.lhs"
 create mode 100644 "\303\234bungen/Blatt1.md"
 create mode 100644 "\303\234bungen/Blatt1.pdf"

diff --git a/Folien/Vorlesung1.pdf b/Folien/Vorlesung1.pdf
new file mode 100644
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diff --git "a/\303\234bungen/Blatt1.hs" "b/\303\234bungen/Blatt1.hs"
new file mode 100644
index 0000000..2397685
--- /dev/null
+++ "b/\303\234bungen/Blatt1.hs"
@@ -0,0 +1,115 @@
+{-
+Ãœbungsblatt 1
+=============
+
+Typtheorie
+----------
+
+Schreiben sie alle **möglichen** Implementationen der folgenden
+Funktionen. Wozu könnte `fun2` nützlich sein?
+-}
+
+fun1 :: a -> a
+fun1 = _fun1
+
+fun2 :: a -> b -> a
+fun2 = _fun2
+
+fun3 :: (Eq a) => a -> a -> Bool
+fun3 = _fun3
+
+{- Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der
+simpelste hiervon ist `Identity`, der genau gar nichts macht, sondern
+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 = _unIdentity
+
+{- 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 = _mapIdentity
+
+{- **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 sei eine Funktion schreiben, die das `Pred a` wieder
+"auspackt". Definieren sie-}
+
+unPred :: Pred a -> (a -> Bool)
+unPred = _unPred
+
+{- Da Haskell-Funktionen aber "gecurried" sind, 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 :: _fun -> Pred a -> Pred b
+mapPred = _mapPred
+
+{-
+Neue Typen erfinden
+-------------------
+
+In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden
+von eigenen Datentypen. Zur Erinnerung; es gibt 2 Möglichkeiten, die man
+miteinander kombinieren kann: `data Prod a b c = Prod a b c` benötigt
+sowohl `a`, `b` als auch `c` um einen Wert zu erzeugen,
+`data Sum a b = Sum1 a | Sum2 b` 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, der 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 = Exercise
+
+{- 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 = _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?
+-}
diff --git "a/\303\234bungen/Blatt1.lhs" "b/\303\234bungen/Blatt1.lhs"
new file mode 100644
index 0000000..981f582
--- /dev/null
+++ "b/\303\234bungen/Blatt1.lhs"
@@ -0,0 +1,112 @@
+Ãœbungsblatt 1
+=============
+
+Typtheorie
+----------
+
+Schreiben sie alle **möglichen** Implementationen der folgenden
+Funktionen. Wozu könnte `fun2` nützlich sein?
+
+> fun1 :: a -> a
+> fun1 = _fun1
+> 
+> fun2 :: a -> b -> a
+> fun2 = _fun2
+> 
+> fun3 :: (Eq a) => a -> a -> Bool
+> fun3 = _fun3
+
+Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der
+simpelste hiervon ist `Identity`, der genau gar nichts macht, sondern
+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 = _unIdentity
+
+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 = _mapIdentity
+
+**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
+Datentype
+
+> 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 sei eine Funktion schreiben, die das `Pred a` wieder
+"auspackt". Definieren sie
+
+> unPred :: Pred a -> (a -> Bool)
+> unPred = _unPred
+
+Da Haskell-Funktionen aber "gecurried" sind, 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 :: _fun -> Pred a -> Pred b
+> mapPred = _mapPred
+
+Neue Typen erfinden
+-------------------
+
+In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden
+von eigenen Datentypen. Zur Erinnerung; es gibt 2 Möglichkeiten, die man
+miteinander kombinieren kann: `data Prod a b c = Prod a b c` benötigt
+sowohl `a`, `b` als auch `c` um einen Wert zu erzeugen,
+`data Sum a b = Sum1 a | Sum2 b` 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, der 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 = Exercise
+
+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 = _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?
+
+> main = putStrLn "compiles"
diff --git "a/\303\234bungen/Blatt1.md" "b/\303\234bungen/Blatt1.md"
new file mode 100644
index 0000000..39a5e33
--- /dev/null
+++ "b/\303\234bungen/Blatt1.md"
@@ -0,0 +1,93 @@
+# Ãœbungsblatt 1
+
+## Typtheorie
+
+Schreiben sie alle **möglichen** Implementationen der folgenden Funktionen. Wozu könnte `fun2` nützlich sein?
+
+```haskell
+fun1 :: a -> a
+fun1 = _fun1
+
+fun2 :: a -> b -> a
+fun2 = _fun2
+
+fun3 :: (Eq a) => a -> a -> Bool
+fun3 = _fun3
+```
+
+Wir haben in der Vorlesung parametrisierte Typen kennengelernt. Der simpelste hiervon ist `Identity`, der genau gar nichts macht, sondern 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
+
+```haskell
+unIdentity :: Identity a -> a
+unIdentity = _unIdentity
+```
+
+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
+
+```haskell
+mapIdentity :: (a -> b) -> Identity a -> Identity b
+mapIdentity = _mapIdentity
+```
+
+**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 Datentype
+
+```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).
+
+Auch hier können sei eine Funktion schreiben, die das `Pred a` wieder "auspackt". Definieren sie
+
+```haskell
+unPred :: Pred a -> (a -> Bool)
+unPred = _unPred
+```
+
+Da Haskell-Funktionen aber "gecurried" sind, 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
+```
+
+## Neue Typen erfinden
+
+In Haskell ist ein zentraler Vorgehenspunkt das Definieren und Verwenden von eigenen Datentypen. Zur Erinnerung; es gibt 2 Möglichkeiten, die man miteinander kombinieren kann: `data Prod a b c = Prod a b c` benötigt sowohl `a`, `b` als auch `c` um einen Wert zu erzeugen, `data Sum a b = Sum1 a | Sum2 b` 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, der 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
+```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?
+
+
+
+
+
diff --git "a/\303\234bungen/Blatt1.pdf" "b/\303\234bungen/Blatt1.pdf"
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-- 
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