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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Test-ChasingBottoms-Approx.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">ChasingBottoms-1.3.0.6: For testing partial and infinite values.</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>non-portable (GHC-specific)</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Maintainer</th><td>http://www.cse.chalmers.se/~nad/</td></tr><tr><th>Safe Haskell</th><td>None</td></tr></table><p class="caption">Test.ChasingBottoms.Approx</p></div><div id="description"><p class="caption">Description</p><div class="doc empty"> </div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">class</span> <a href="#t:Approx">Approx</a> a <span class="keyword">where</span><ul class="subs"><li><a href="#v:approxAll">approxAll</a> :: <a href="Test-ChasingBottoms-Nat.html#t:Nat">Nat</a> -> a -> a</li><li><a href="#v:approx">approx</a> :: <a href="Test-ChasingBottoms-Nat.html#t:Nat">Nat</a> -> a -> a</li></ul></li></ul></div><div id="interface"><h1>Documentation</h1><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Approx" class="def">Approx</a> a <span class="keyword">where</span><a href="src/Test-ChasingBottoms-Approx.html#Approx" class="link">Source</a></p><div class="doc"><p><code><a href="Test-ChasingBottoms-Approx.html#t:Approx">Approx</a></code> is a class for approximation functions as described
in The generic approximation lemma, Graham Hutton and Jeremy
Gibbons, Information Processing Letters, 79(4):197-201, Elsevier
Science, August 2001, <a href="http://www.cs.nott.ac.uk/~gmh/bib.html">http://www.cs.nott.ac.uk/~gmh/bib.html</a>.
</p><p>Instances are provided for all members of the <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a></code> type class. Due
to the limitations of the <a href="Data-Generics.html">Data.Generics</a> approach to generic
programming, which is not really aimed at this kind of application,
the implementation is only guaranteed to perform correctly, with
respect to the paper (and modulo any bugs), on non-mutually-recursive
sum-of-products datatypes. In particular, nested and mutually
recursive types are not handled correctly with respect to the
paper. The specification below is correct, though (if we assume that
the <code><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a></code> instances are well-behaved).
</p><p>In practice the <code><a href="Test-ChasingBottoms-Approx.html#v:approxAll">approxAll</a></code> function can probably be more useful than
<code><a href="Test-ChasingBottoms-Approx.html#v:approx">approx</a></code>. It traverses down <em>all</em> subterms, and it should be possible
to prove a variant of the approximation lemma which <code><a href="Test-ChasingBottoms-Approx.html#v:approxAll">approxAll</a></code>
satisfies.
</p></div><div class="subs methods"><p class="caption">Methods</p><p class="src"><a name="v:approxAll" class="def">approxAll</a> :: <a href="Test-ChasingBottoms-Nat.html#t:Nat">Nat</a> -> a -> a<a href="src/Test-ChasingBottoms-Approx.html#approxAll" class="link">Source</a></p><div class="doc"><p><code><code><a href="Test-ChasingBottoms-Approx.html#v:approxAll">approxAll</a></code> n x</code> traverses <code>n</code> levels down in <code>x</code> and replaces all
values at that level with bottoms.
</p></div><p class="src"><a name="v:approx" class="def">approx</a> :: <a href="Test-ChasingBottoms-Nat.html#t:Nat">Nat</a> -> a -> a<a href="src/Test-ChasingBottoms-Approx.html#approx" class="link">Source</a></p><div class="doc"><p><code><a href="Test-ChasingBottoms-Approx.html#v:approx">approx</a></code> works like <code><a href="Test-ChasingBottoms-Approx.html#v:approxAll">approxAll</a></code>, but the traversal and
replacement is only performed at subterms of the same monomorphic
type as the original term. For polynomial datatypes this is
exactly what the version of <code>approx</code> described in the paper above
does.
</p></div></div><div class="subs instances"><p id="control.i:Approx" class="caption collapser" onclick="toggleSection('i:Approx')">Instances</p><div id="section.i:Approx" class="show"><table><tr><td class="src"><a href="/usr/share/doc/ghc-doc/html/libraries/base-4.6.0.1/Data-Data.html#t:Data">Data</a> a => <a href="Test-ChasingBottoms-Approx.html#t:Approx">Approx</a> a</td><td class="doc empty"> </td></tr></table></div></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
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