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    <p>QuickCheck looks for <em>counterexamples</em>. So you need to provide a negation of the property you seek:</p> <pre><code>prop1 f g x = not $ (f . g) x == (g . f) x </code></pre> <p>This particular property don't specify function type - any function of <code>a -&gt; a</code> could work. So you need to specify types for <code>f</code> and <code>g</code>, or for whole function <code>prop1</code>.</p> <ol> <li><p>You cannot compare <code>f . g</code> and <code>g . f</code> for equality because they are both functions and you cannot have a sensible definition of <code>Eq</code> for functions with infinite domains in Haskell. You need to randomly generate the argument too and compare the <code>f . g</code> and <code>g . f</code> functions by comparing their results by passing a random argument to both.</p></li> <li><p>Read the <a href="http://hackage.haskell.org/packages/archive/QuickCheck/2.4.1.1/doc/html/Test-QuickCheck-Function.html%20documentation" rel="nofollow">documentation</a> on the type of <code>Fun _ f</code>. <code>f</code> there is a <em>monomorphic</em> function. QuickCheck cannot generate random functions of different types - it can only generate functions of some particular type. But <code>.</code> is <em>polymorphic</em>, so the particular type of f cannot be inferred from the context. So you need to choose some arbitrary types for <code>f</code> and <code>g</code> and specify it in the type signature for your property.</p></li> </ol> <p>Also, you don't need <code>let</code> for top-level definitions. Let can be only used inside of expressions in the form of <code>let..in</code> and inside <code>do</code> blocks without <code>in</code>.</p>
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