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<h1>EtaExpansion</h1>
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<div class="paragraph"><p>Eta expansion is a simple syntactic change used to work around the
<a href="ValueRestriction">ValueRestriction</a> in <a href="StandardML">Standard ML</a>.</p></div>
<div class="paragraph"><p>The eta expansion of an expression <span class="monospaced">e</span> is the expression
<span class="monospaced">fn z => e z</span>, where <span class="monospaced">z</span> does not occur in <span class="monospaced">e</span>. This only
makes sense if <span class="monospaced">e</span> denotes a function, i.e. is of arrow type. Eta
expansion delays the evaluation of <span class="monospaced">e</span> until the function is
applied, and will re-evaluate <span class="monospaced">e</span> each time the function is
applied.</p></div>
<div class="paragraph"><p>The name "eta expansion" comes from the eta-conversion rule of the
<a href="LambdaCalculus">lambda calculus</a>. Expansion refers to the
directionality of the equivalence being used, namely taking <span class="monospaced">e</span> to
<span class="monospaced">fn z => e z</span> rather than <span class="monospaced">fn z => e z</span> to <span class="monospaced">e</span> (eta
contraction).</p></div>
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