Mercurial > cpdt > repo
comparison src/Coinductive.v @ 104:32a5ad6e2bb0
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| author | Adam Chlipala <adamc@hcoop.net> |
|---|---|
| date | Sun, 12 Oct 2008 08:44:23 -0400 |
| parents | cde1351d18bb |
| children | df289eb8ef76 |
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| 103:22f111d5cda2 | 104:32a5ad6e2bb0 |
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| 463 | 463 |
| 464 %\item%#<li># %\begin{enumerate}%#<ol># | 464 %\item%#<li># %\begin{enumerate}%#<ol># |
| 465 %\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># | 465 %\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># |
| 466 %\item%#<li># Define a function [everywhere] for building a tree with the same data value at every node.#</li># | 466 %\item%#<li># Define a function [everywhere] for building a tree with the same data value at every node.#</li># |
| 467 %\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># | 467 %\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># |
| 468 %\item%#<li># Define a stream [falses] where every node has the value [false].#</li># | 468 %\item%#<li># Define a tree [falses] where every node has the value [false].#</li># |
| 469 %\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># | 469 %\item%#<li># Define a tree [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># |
| 470 %\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># | 470 %\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># |
| 471 #</ol>#%\end{enumerate}% #</li># | 471 #</ol>#%\end{enumerate}% #</li># |
| 472 | 472 |
| 473 #</ol>#%\end{enumerate}% *) | 473 #</ol>#%\end{enumerate}% *) |