### changeset 115:f6eb1ed8048c

itree exercise
author Adam Chlipala Tue, 14 Oct 2008 14:58:33 -0400 2f97c8177172 7163cc09270f src/DataStruct.v 1 files changed, 13 insertions(+), 0 deletions(-) [+]
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--- a/src/DataStruct.v	Tue Oct 14 14:49:51 2008 -0400
+++ b/src/DataStruct.v	Tue Oct 14 14:58:33 2008 -0400
@@ -819,3 +819,16 @@
end; crush).
Qed.
(* end thide *)
+
+
+(** * Exercises *)
+
+(** Some of the type family definitions from this chapter are duplicated in the [DepList] module of the book source.  Only the recursive versions of length-indexed and heterogeneous lists are included, and they are renamed without the [f] prefixes, e.g., [ilist] in place of [filist].
+
+%\begin{enumerate}%#<ol>#
+
+%\item%#<li># Define a tree analogue of [hlist].  That is, define a parameterized type of binary trees with data at their leaves, and define a type family [itree] indexed by trees.  The structure of an [itree] mirrors its index tree, with the type of each data element (which only occur at leaves) determined by applying a type function to the corresponding element of the index tree.  Define a type standing for all possible paths from the root of a tree to leaves and use it to implement a function [tget] for extracting an element of an [itree] by path.  Define a function [itmap2] for "mapping over two trees in parallel."  That is, [itmap2] takes in two [itree]s with the same index tree, and it forms a new [itree] with the same index by applying a binary function pointwise.
+
+  Repeat this process so that you implement each definition for each of the three definition styles covered in this chapter: inductive, recursive, and reflexive.#</li>#
+
+#</ol>#%\end{enumerate}% *)