Mercurial > cpdt > repo
changeset 81:f295a64bf9fd
Coinductive exercise description
author | Adam Chlipala <adamc@hcoop.net> |
---|---|
date | Sun, 05 Oct 2008 11:34:09 -0400 |
parents | 506a06118014 |
children | 15e2b3485dc4 |
files | src/Coinductive.v |
diffstat | 1 files changed, 16 insertions(+), 0 deletions(-) [+] |
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--- a/src/Coinductive.v Sat Oct 04 14:58:00 2008 -0400 +++ b/src/Coinductive.v Sun Oct 05 11:34:09 2008 -0400 @@ -455,3 +455,19 @@ (** If we print the proof term that was generated, we can verify that the proof is structured as a [cofix], with each co-recursive call properly guarded. *) Print constFold_ok. + + +(** * Exercises *) + +(** %\begin{enumerate}%#<ol># + +%\item%#<li># %\begin{enumerate}%#<ol># + %\item%#<li># Define a co-inductive type of infinite trees carrying data of a fixed parameter type. Each node should contain a data value and two child trees.#</li># + %\item%#<li># Define a function [everywhere] for building a tree with the same data value at every node.#</li># + %\item%#<li># Define a function [map] for building an output tree out of two input trees by traversing them in parallel and applying a two-argument function to their corresponding data values.#</li># + %\item%#<li># Define a stream [falses] where every node has the value [false].#</li># + %\item%#<li># Define a stream [true_false] where the root node has value [true], its children have value [false], all nodes at the next have the value [true], and so on, alternating boolean values from level to level.#</li># + %\item%#<li># Prove that [true_falses] is equal to the result of mapping the boolean "or" function [orb] over [true_false] and [falses]. You can make [orb] available with [Require Import Bool.]. You may find the lemma [orb_false_r] from the same module helpful. Your proof here should not be about the standard equality [=], but rather about some new equality relation that you define.#</li># +#</ol>#%\end{enumerate}% #</li># + +#</ol>#%\end{enumerate}% *)