Mercurial > cpdt > repo
changeset 37:c9ade53b27aa
TVL and constant-folding exercises
author | Adam Chlipala <adamc@hcoop.net> |
---|---|
date | Fri, 12 Sep 2008 15:30:59 -0400 |
parents | 9e46ade5af21 |
children | 95e24b629ad9 |
files | src/InductiveTypes.v |
diffstat | 1 files changed, 10 insertions(+), 0 deletions(-) [+] |
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--- a/src/InductiveTypes.v Fri Sep 12 14:59:08 2008 -0400 +++ b/src/InductiveTypes.v Fri Sep 12 15:30:59 2008 -0400 @@ -1091,3 +1091,13 @@ reflexivity. Qed. + +(** * Exercises *) + +(** %\begin{enumerate}%#<ol># + +%\item%#<li># Define an inductive type [truth] with three constructors, [Yes], [No], and [Maybe]. [Yes] stands for certain truth, [False] for certain falsehood, and [Maybe] for an unknown situation. Define "not," "and," and "or" for this replacement boolean algebra. Prove that your implementation of "and" is commutative and distributes over your implementation of "or."#</li># + +%\item%#<li># Modify the first example language of Chapter 1 to include variables, where variables are represented with [nat]. Extend the syntax and semantics of expressions to accommodate the change. Your new [expDenote] function should take as a new extra first argument a value of type [var -> nat], where [var] is a synonym for naturals-as-variables, and the function assigns a value to each variable. Define a constant folding function which does a bottom-up pass over an expression, at each stage replacing every binary operation on constants with an equivalent constant. Prove that constant folding preserves the meaning of expressions.#</li># + +#</ol>#%\end{enumerate}% *)