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authorChloe Brown <chloe.brown.00@outlook.com>2025-06-24 18:42:46 +0100
committerChloe Brown <chloe.brown.00@outlook.com>2025-06-24 18:42:46 +0100
commitbfb81aaad3aebf7415acd64550c66a0ed1fe0ded (patch)
treed5ca2674732bec47344632388c784a546d2b15bf /sec
parent788b26b2d2a913eefe62110dbf76b60ab4f8f112 (diff)
Fix 240--257.
Diffstat (limited to 'sec')
-rw-r--r--sec/systemt.ltx33
1 files changed, 14 insertions, 19 deletions
diff --git a/sec/systemt.ltx b/sec/systemt.ltx
index c43223e..f887328 100644
--- a/sec/systemt.ltx
+++ b/sec/systemt.ltx
@@ -308,25 +308,20 @@ a triple of a \emph{recursive depth}, a \emph{root index}, and an
\(I\)-indexed \emph{heap} of values. Instead of storing recursive
values ``in-line'', one stores an index to its place in the heap.
-Consider the binary tree
-\(\mathsf{branch}(\mathsf{branch}(\mathsf{leaf}(1), \mathsf{leaf}(2)),
-\mathsf{branch}(\mathsf{leaf}(3), \mathsf{branch}(\mathsf{leaf}(4),
-\mathsf{leaf}(5))))\), depicted diagramatically in
-\cref{fig:box-pointer:tree}. The recursive depth of the tree is four,
-as there are at most four nested constructors (e.g.\ the path from
-root to the value five). \Cref{fig:box-pointer:heap} gives a
-representation of the heap used to store this tree. Each constructor
-has its own place in the heap. Leaves store the value of the leaf;
-branches store the indices of the two inductive components. Like
-Church encodings, this encoding relies on having an encoding for sums
-in order to store the data for different constructors within a single
-type.
-
-\TODO{
- \begin{itemize}
- \item create box-and-pointer diagram
- \end{itemize}
-}
+Consider the binary tree depicted in \cref{fig:box-pointer:tree}. The
+recursive depth of the tree is four, as there are at most four nested
+constructors (e.g.\ the path from root to the value
+five). \Cref{fig:box-pointer:heap} gives a representation of the heap
+used to store this tree. Each constructor has its own place in the
+heap. Leaves store the value of the leaf; branches store the indices
+of the two inductive components. Like Church encodings, this encoding
+relies on having an encoding for sums in order to store the data for
+different constructors within a single type.
+
+\begin{figure}
+ \caption{\TODO{create box-and-pointer diagram}}%
+\label{fig:box-pointer:tree}\label{fig:box-pointer:heap}
+\end{figure}
The recursive depth is essential for the fold operation. We
iteratively construct a heap of values; the recursive depth is an