add image for morphism condition

beamer/lc-beamer/example.tex

@@ -271,23 +271,23 @@ image-write "out.png" im3
 
 \begin{frame}{Coercions: (In-)Coherence with Transitivity}
   \begin{itemize}
-    \item<1-> Common example: coerce  \texttt{Int -> Real}
+    \item<1-> Common example: coerce  \texttt{Int -> Float}
     (subsumption \(\mathbb{N} \subset \mathbb{R}\))
 
       \begin{itemize}
-        \item \texttt{Int -> Real}
+        \item \texttt{Int -> Float}
         \item \texttt{Int -> String}
-        \item \texttt{Real -> String}
+        \item \texttt{Float -> String}
       \end{itemize}
 
     \item<2-> transitivity creates two extensionally \emph{different} coercion paths:
     \begin{itemize}
       \item \texttt{Int -> String}  (3 -> "3")
-      \item \texttt{Int -> Real -> String} (3 -> "3.0")
+      \item \texttt{Int -> Float -> String} (3 -> "3.0")
     \end{itemize}
 
     \item<3-> Subsumptive interpretation is misleading!
-    \item<3-> \texttt{Int -> Real} is not as unambiguous as it might seem.
+    \item<3-> \texttt{Int -> Float} is not as unambiguous as it might seem.
     \begin{itemize}
       \item value ranges (e.g. map int to unit interval [0,1])
       \item multiple quantization functions (linear, exponential, \dots)
@@ -342,17 +342,21 @@ image-write "out.png" im3
 \end{frame}
 
 \begin{frame}{Morphisms}
-\framesubtitle{Coherence}
   \begin{block}{Morphism Condition}
 	Assume\\
 	\(\metavariable{m_\sigma} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_1}  \rightarrow_\text{morph}  \metavariable{\sigma} \sim \metavariable{\sigma_2}}\)\\
 	\(\metavariable{m_\tau} : \typeterminal{\metavariable{\tau} \sim \metavariable{\tau_1}  \rightarrow_\text{morph}  \metavariable{\tau} \sim \metavariable{\tau_2}}\)\\
 	\(\metavariable{f_1} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_1}  \rightarrow  \metavariable{\tau} \sim \metavariable{\tau_1} }\)\\
 	\(\metavariable{f_2} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_2}  \rightarrow  \metavariable{\tau} \sim \metavariable{\tau_2} }\)\\
+	\vskip1cm
 	then it holds that:\\
 	\(\forall x:\typeterminal{\metavariable{\sigma}\sim\metavariable{\sigma_1}},\quad
 	\metavariable{m_\tau}(\metavariable{f_1} x) = \metavariable{f_2} (\metavariable{m_\sigma} x) \)
+
+	\vskip-4.5cm
+	\hfill\includegraphics[width=0.3\textwidth]{morphisms.png}
   \end{block}
+
 \end{frame}
 
 

beamer/lc-beamer/morphisms.dot

@@ -0,0 +1,17 @@
+digraph Morphisms {
+    node [fontcolor=blue];
+    edge [fontcolor=red];
+
+    sigma1 [label="σ ~ σ1", shape=plaintext];
+    sigma2 [label="σ ~ σ2", shape=plaintext];
+    tau1 [label="τ ~ τ1", shape=plaintext];
+    tau2 [label="τ ~ τ2", shape=plaintext];
+
+    sigma1 -> tau1 [label="f_1"];
+    sigma2 -> tau2 [label="f_2"];
+
+    tau1 -> tau2 [label="m_τ"];
+    sigma1 -> sigma2 [label="m_σ"];
+}
+
+