merge homework8

Author: Nigma-Ks

grammar.pdf

@@ -0,0 +1,108 @@
+\documentclass[12pt]{article}
+\title{Definition Homework}
+\usepackage {amsmath}
+\usepackage {amssymb}
+\usepackage{enumerate}
+\usepackage{cmap}
+\usepackage{mathtext} 			
+\usepackage[T2A]{fontenc}			
+\usepackage[utf8]{inputenc}			
+\usepackage[english,russian]{babel}
+\usepackage{indentfirst}
+
+\setlength{\textwidth}{7.0in}
+\setlength{\oddsidemargin}{-0.35in}
+\setlength{\topmargin}{-0.5in}
+\setlength{\textheight}{9.0in}
+\setlength{\parindent}{0.3in}
+\usepackage{alltt}
+\begin{document}
+\indent   
+\section{Определение грамматики}
+\begin{enumerate} 
+    \item $\Sigma = \{[a-zA-Z],.,\backslash, let, =, (, ),\backslash n\}$
+    \item $N = \{application, definition, defname, term, lambda-abstraction, variable, input\}$
+    \item $S = input$
+    \item $P:$ 
+        \begin{enumerate} [1)]
+            \item $<definition> ::= let <defname> = <term>$.
+            \item $<defname> ::= A | B | ... | Z  \{a | b | ... | z | A | B | ... | Z \}$.
+            \item $<term> ::= <application> | (<term>) | <lambda-abstraction> | <variable> | <~defname>$
+            \item $<variable> ::= a | b | ... | z \{a | b | ... | z | A | B | ... | Z \}$
+            \item $<lambda-abstraction> = \backslash<variable>\{<variable>\}.<term>$
+            \item $<application> = <term> <term>$
+            \item $<input> = \{<definition> \backslash n\} <term>$.
+        \end{enumerate}
+\end{enumerate}
+\section{Пример}
+    \begin{verbatim}
+        let S = \ x y z.x z (y z)
+        let K = \ x y.x
+        S K K
+    \end{verbatim}
+    $$<input> \Rightarrow <definition> \backslash n \{<definition> \backslash n\} <term> \Rightarrow$$
+    Первое $definition$:
+            \begin{eqnarray}
+            <definition>\Rightarrow \\
+            let <termname> = <term> \Rightarrow \\
+            let\ S = <term> \Rightarrow \\
+            let \  S = <lambda-abstraction> \Rightarrow \\
+            let \  S = \backslash<variable>\{<variable>\}.<term> \Rightarrow \\
+            let \  S = \backslash<variable><variable><variable>.<term> \Rightarrow \\
+            let \  S = \backslash x <variable><variable>.<term> \Rightarrow \\
+            let \  S = \backslash x y <variable>.<term> \Rightarrow \\
+            let \  S = \backslash x y z.<term> \Rightarrow \\
+            let \  S = \backslash x y z.<application> \Rightarrow \\
+            let \  S = \backslash x y z.<term> <term> \Rightarrow \\
+            let \  S = \backslash x y z.<application> <term> \Rightarrow \\
+            let \  S = \backslash x y z.<term> <term> <term> \Rightarrow \\
+            let \  S = \backslash x y z.<variable> <term> <term> \Rightarrow \\
+            let \  S = \backslash x y z.x <term> <term> \Rightarrow \\
+            let \  S = \backslash x y z.x <variable> <term> \Rightarrow \\
+            let \  S = \backslash x y z.x z <term> \Rightarrow \\
+            let \  S = \backslash x y z.x z (<term>) \Rightarrow \\
+            let \  S = \backslash x y z.x z (<application>) \Rightarrow \\
+            let \  S = \backslash x y z.x z (<term> <term>) \Rightarrow \\
+            let \  S = \backslash x y z.x z (<variable> <term>) \Rightarrow \\
+            let \  S = \backslash x y z.x z (y <term>) \Rightarrow \\
+            let \  S = \backslash x y z.x z (y z) \Rightarrow
+        \end{eqnarray}
+    Итог:
+        \begin{verbatim}
+            let S = \ x y z.x z (y z)
+        \end{verbatim}
+    Второе $definition$:
+        \begin{eqnarray}
+            <definition>\Rightarrow \\
+            let <termname> = <term> \Rightarrow \\
+            let \  K = <term> \Rightarrow \\
+            let \  K = <lambda-abstraction> \Rightarrow \\
+            let \  K = \backslash<variable>\{<variable>\}.<term> \Rightarrow \\
+            let \  K = \backslash<variable><variable>.<term> \Rightarrow \\
+            let \  K = \backslash x <variable>.<term> \Rightarrow \\
+            let \  K = \backslash x y.<term> \Rightarrow \\
+            let \  K = \backslash x y z.<variable> \Rightarrow \\
+            let \  K = \backslash x y z.x \Rightarrow
+        \end{eqnarray}
+    Итог:
+        \begin{verbatim}
+            let S = \ x y z.x z (y z)
+            let K = \ x y.x
+        \end{verbatim}
+    $term$:
+        \begin{eqnarray}
+            <term>\Rightarrow \\
+            <application> \Rightarrow \\
+            <term> <term> \Rightarrow \\
+            <application> <term>\Rightarrow \\
+            <term> <term> <term> \Rightarrow \\
+            <defname> <defname> <defname> \Rightarrow \\
+            S K K \Rightarrow
+        \end{eqnarray}
+    Итог:
+        \begin{verbatim}
+            let S = \ x y z.x z (y z)
+            let K = \ x y.x
+            S K K
+        \end{verbatim}
+\end{document}