From a66c299e8800d3f3e0d2fa701fd5d56e5a5211de Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jonah=20Br=C3=BCchert?= <jbb@kaidan.im>
Date: Fri, 19 Jan 2024 15:51:16 +0100
Subject: [PATCH] 12: add slides

---
 12/tut12.md  |  77 +++++++++++++++++++++++++++++++++++++++++++++++++++
 12/tut12.pdf | Bin 0 -> 150036 bytes
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 create mode 100644 12/tut12.md
 create mode 100644 12/tut12.pdf

diff --git a/12/tut12.md b/12/tut12.md
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--- /dev/null
+++ b/12/tut12.md
@@ -0,0 +1,77 @@
+---
+theme: metropolis
+aspectratio: 169
+header-includes: |
+    \usepackage{qrcode}
+    \include{hyperref}
+    \include{amsmath}
+---
+
+# Überleitung
+
+```Haskell
+add3 a b c = a + b + c
+```
+\
+**Auswertung**:
+```Haskell
+add3 1 2 3
+(\a -> \b -> \c -> a + b + c) 1 2 3
+(\b -> \c -> 1 + b + c) 2 3
+(\c -> 1 + 2 + c) 3
+1 + 2 + 3
+```
+
+# Lambda-Kalkül
+
+weniger Formal korrekte, aber vielleicht leichter verständliche Zusammenfassung
+
+# Variablen
+
+* Variablennamen bestehen nur aus einem Buchstaben
+
+**Beispiel**:
+
+* $(\lambda xyz.xyz)$ hat drei Argumente
+
+# Bindung
+
+\begin{center}
+\huge{($\lambda$ $V.E$)}
+\end{center}
+
+* Eine Variable ist gebunden, wenn sie in V und in E vorkommt
+* E kann wieder ein weiterer Lambda-Ausdruck sein, dann sind Variablen mit dem gleichen Namen auch darin gebunden
+* In einem Ausdruck mit mehreren Teilausdrücken ist eine Variable gebunden, wenn sie in einem Teilausdruck gebunden ist.
+
+**Beispiele**:
+
+* $(\lambda x.x)$ - x ist gebunden
+* $(\lambda x.y)$ - y ist nicht gebunden
+* $(\lambda x.(\lambda y.x))$ - x ist gebunden
+
+
+# $\beta$-Reduktion (Funktionsanwendung)
+
+\begin{center}
+\huge{($\lambda$ $x.E$) y}
+\end{center}
+
+* Der Ausdruck in Klammern hat ein Argument, $x$
+* Bei der Auswertung mit einem übergebenen Argument ($y$), wird der Wert von $y$ für $x$ eingesetzt
+
+**Beispiel**:
+
+* $(\lambda x.x)y \equiv_{\beta} y$
+
+# $\alpha$-Konversion (Umbenennung)
+
+\begin{center}
+\huge{($\lambda$ $V.E$) x}
+\end{center}
+
+Wenn $x$ in $E$ gebunden wäre, muss $x$ in V und E umbenannt werden, bevor $x$ eingesetzt werden kann.
+
+**Beispiel**:
+
+* $(\lambda xy.x) y \equiv_{\alpha} (\lambda xt.x) y$
diff --git a/12/tut12.pdf b/12/tut12.pdf
new file mode 100644
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-- 
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