From d8341f0c810d3da5226a29314c1edfb37392d0a4 Mon Sep 17 00:00:00 2001 From: Marco Ammon Date: Thu, 4 Oct 2018 18:12:22 +0200 Subject: [PATCH] Induktion, Koinduktion, Aufbau --- merkzettel.pdf | Bin 142496 -> 148394 bytes merkzettel.tex | 28 ++++++++++++++++++++++++++++ 2 files changed, 28 insertions(+) diff --git a/merkzettel.pdf b/merkzettel.pdf index 0cd21c5555c9236846944ad5b2cd72a83ffa7955..bdf2e6ed2a0ab21a03dcd25d9c09d1baaea0fb73 100644 GIT binary patch delta 98485 zcmV)BK*PVF*$AqK39v!|0Xefn0W}2#!Px<@lY9m!0yH&~FOevJ)mm9^+ei|A&#zGO zBmrT&?{3-{EHcO>JDa%>8_2_Cfu%;Y%!xz=B9--IANH?LbvKVD-4rPwyO)UC)F@TCWGmT;?x%rR_hA5Nu zmzQV}F{$Pp_m)%GUoPSt{*Y`I5sffo?&JR)-y%VZs@@hC5&ZhiJl~}7OU*x>n@MJZ zB0}jbl8968zIfsOfiTfC@AcbkQ^KAZ10iATPS_PFqlj^TT`&BvYDi~qF_Lk!wbG5~ z?p~sHzvW&yU!8CzLkzS( zLAW0ln$45K$u}!1L9g5!K3{_R)I428WL}hMNGe()iPe}`;86-uk2-U!e0K{Af&rJI zdBJM6icgz=cbknE3XPHeiy8{U1c?WmiS@>`(sq86EVD8xvt91YCT1`>ab_dJW>dXB zsyfb*()y?j6%tAwQ(I>=l}Ho)aHTw0CtYibC;$)9F+5Nth`bk)f1ex8d@(=LeF3T{ 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auch $\Gamma \vdash s:\alpha$, aber nicht umgekehrt! \satz{3.38}{45} \end{itemize} +\section*{Induktive Datentypen} +\subsection*{Mehrsortigkeit} +\subsection*{Strukturelle Induktion} +\begin{itemize} +\item über einsortige Datentypen \siehe{S. 63} +\begin{itemize} + \item Induktionsanfang: \enquote{Anfangs}-Konstruktor (etwa $Nil$) + \item Induktionsschritt: alle anderen Konstruktoren (etwa $cons$) +\end{itemize} +\item über mehrsortige Datentypen \siehe{S. 64} +\begin{itemize} + \item Funktionen müssen immer auf allen Datentypen definiert werden +\end{itemize} +\end{itemize} +\subsection*{Kodatentypen} +\subsection*{Koinduktion} +\begin{itemize} + \item Bisimulation $R\subseteq A^\omega \times A^\omega$, wenn für alle $(s,t) \in R$ gilt: \defin{4.39}{74} + \begin{align*} + hd\ s &= hd\ t\\ + (tl\ s)\ &R\ (tl\ t) + \end{align*} + \item Wenn $R$ eine Bisimulation ist, gilt $sRt \Rightarrow s=t$ \satz{4.40}{74} +\end{itemize} +\subsection*{Kodatentypen mit Alternativen} +\section*{System F} +\section*{Polymorphie} +\subsection*{ML-Polymorphie} \section*{Unifikationsalgorithmus (Martelli/Montanari)} \begin{align*} &S \cup \lbrace x \pteq x\rbrace &&\rightarrow S &&\text{(delete)}\\