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    <p>There is a very similar function in the <code>List</code> theory in the standard library. That function takes a predicate as an argument, i.e. a function <code>f</code> from the element type to <code>bool</code>, and it returns <code>Some x</code> if a matching element <code>x</code> is found, or <code>None</code> if none is found.</p> <pre><code>Variable A : Type. Fixpoint find (f:A-&gt;bool) (l:list A) : option A := match l with | nil =&gt; None | x :: tl =&gt; if f x then Some x else find tl end. </code></pre> <p>You're looking for an element that's equal to a particular object <code>a</code>. That means your predicate is <code>eq_Interface a</code>, where <code>eq_Interface</code> is the equality you want over the <code>Interface</code>.</p> <p>It's up to you to define an equality function on your type, because there can be many definitions of equality. Coq defines <code>=</code>, which is <a href="http://en.wikipedia.org/wiki/Leibniz%27s_law" rel="nofollow">Leibniz equality</a>: two values are equal iff there is no way to distinguish between them. <code>=</code> is a proposition, not a boolean, because this property is not decidable in general. It's also not always the desirable equality on a type, sometimes you want a coarser equivalence relation, so that two objects can be considered equal if they were constructed in different ways but nonetheless have the same meaning.</p> <p>If <code>Interface</code> is a simple datatype — intuitively, a data structure with no embedded proposition — there's a built-in tactic to build a structural equality function from the type definition. Look up <code>decide equality</code> in the reference manual.</p> <pre><code>Definition Interface_dec : forall x y : Interface, {x=y} + {x &lt;&gt; y}. Proof. decide equality. Defined. Definition Interface_eq x y := if Interface_dec x y then true else false. </code></pre> <p><code>Interface_dec</code> not only tells you whether its arguments are equal, but also comes with a proof that the arguments are equal or that they're different.</p> <p>Once you have that equality function, you can define your <code>find</code> function in terms of the standard library function:</p> <pre><code>Definition Interface_is_in x := if List.find (Interface_eq x) then true else false. </code></pre>
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