From 2a58ef985d874f5c5611b6932b173048317a5bdd Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sat, 8 Mar 2014 14:05:57 +0100 Subject: [PATCH] =?UTF-8?q?Beispiel=20hinzugef=C3=BCgt?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../{lambda.tex => Lambda.tex} | 12 ++++++++++-- .../Programmierparadigmen.pdf | Bin 639218 -> 640403 bytes .../Programmierparadigmen.tex | 2 +- 3 files changed, 11 insertions(+), 3 deletions(-) rename documents/Programmierparadigmen/{lambda.tex => Lambda.tex} (91%) diff --git a/documents/Programmierparadigmen/lambda.tex b/documents/Programmierparadigmen/Lambda.tex similarity index 91% rename from documents/Programmierparadigmen/lambda.tex rename to documents/Programmierparadigmen/Lambda.tex index 1267cdb..e8c041f 100644 --- a/documents/Programmierparadigmen/lambda.tex +++ b/documents/Programmierparadigmen/Lambda.tex @@ -47,6 +47,10 @@ Die Funktionsapplikation sei linksassoziativ. Es gilt also: \end{satz} \section{Reduktionen} +\begin{definition}[Redex]\xindex{Redex}% + Eine $\lambda$-Term der Form $(\lambda x. t_1) t_2$ heißt Redex. +\end{definition} + \begin{definition}[$\alpha$-Äquivalenz] Zwei Terme $T_1, T_2$ heißen $\alpha$-Äquivalent, wenn $T_1$ durch konsistente Umbenennung in $T_2$ überführt werden kann. @@ -64,11 +68,15 @@ Die Funktionsapplikation sei linksassoziativ. Es gilt also: \end{beispiel} \begin{definition}[$\beta$-Äquivalenz] - TODO + Eine $\beta$-Reduktion ist die Funktionsanwendung auf einen Redex: + \[(\lambda x. t_1) t_2 \Rightarrow t_1 [x \mapsto t_2]\] \end{definition} \begin{beispiel}[$\beta$-Äquivalenz] - TODO + \begin{defenum} + \item $(\lambda x.x) y \overset{\beta}{\Rightarrow} x[x \mapsto y] = y$ + \item $(\lambda x. x (\lambda x. x)) (y z) \overset{\beta}{\Rightarrow} (x(\lambda x. x))[x \mapsto y z] (y z) (\lambda x. x)$ + \end{defenum} \end{beispiel} \begin{definition}[$\eta$-Äquivalenz] diff --git a/documents/Programmierparadigmen/Programmierparadigmen.pdf b/documents/Programmierparadigmen/Programmierparadigmen.pdf index 9bac72eafc048b1e44c32c9dd0f524ac0307dfee..48ada3175e4d13920dfcf59ff66f0ea127fa6e30 100644 GIT binary patch delta 77392 zcmZs>Q+S|F&@CFFS&As#UeB z9s;S8qN(F0Ksl50)o2nN5COw|6m& z6V@?EqTp7xi@W*El@eQFOc7ORZ&(b~`S_s&NrJRWVu(se91AY3>;Sw#o)$?0OcpJ9 zFf;~RK2FfNkz-oCjQJNY7L*!lysUY?aCniD@yHiN0x~fSIFJZ4Mn!1>w_kLmR!2t( 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