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    <p>To complete 0_'s answer, <code>fibonacci</code> is being instanciated through the apply method of <code>Memo</code>'s companion object, generated automatically by the compiler since <code>Memo</code> is a case class.</p> <p>This means that the following code is generated for you:</p> <pre><code>object Memo { def apply[A, B](f: A =&gt; B): Memo[A, B] = new Memo(f) } </code></pre> <p>Scala has special handling for the <code>apply</code> method: its name needs not be typed when calling it. The two following calls are strictly equivalent:</p> <pre><code>Memo((a: Int) =&gt; a * 2) Memo.apply((a: Int) =&gt; a * 2) </code></pre> <p>The <code>case</code> block is known as pattern matching. Under the hood, it generates a partial function - that is, a function that is defined for some of its input parameters, but not necessarily all of them. I'll not go in the details of partial functions as it's beside the point (<a href="http://nrinaudo.github.io/blog/2013/08/03/partial-functions/" rel="nofollow">this</a> is a memo I wrote to myself on that topic, if you're keen), but what it essentially means here is that the <code>case</code> block is in fact an instance of <a href="http://www.scala-lang.org/api/current/index.html#scala.PartialFunction" rel="nofollow">PartialFunction</a>.</p> <p>If you follow that link, you'll see that <code>PartialFunction</code> extends <a href="http://www.scala-lang.org/api/current/index.html#scala.Function1" rel="nofollow">Function1</a> - which is the expected argument of <code>Memo.apply</code>.</p> <p>So what that bit of code actually means, once desugared (if that's a word), is:</p> <pre><code>lazy val fibonacci: Memo[Int, BigInt] = Memo.apply(new PartialFunction[Int, BigInt] { override def apply(v: Int): Int = if(v == 0) 0 else if(v == 1) 1 else fibonacci(v - 1) + fibonacci(v - 2) override isDefinedAt(v: Int) = true }) </code></pre> <p>Note that I've vastly simplified the way the pattern matching is handled, but I thought that starting a discussion about <code>unapply</code> and <code>unapplySeq</code> would be off topic and confusing.</p>
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    1. POIn Scala, what does "extends (A => B)" on a case class mean?
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    1. USNicolas Rinaudo
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    1. CORight, I didn't read till the end :)
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    2. COI got everything right up and until your last sentence, "The pattern-matching passed to apply is a PartialFunction1, which is an instance of Function1." And there, you lost me. There still appears to be too much assumed about the "= Memo {...}" part; i.e. too many Scala syntax reductions where I am not able to make the "assumption leaps".
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    3. CO@chaotic3quilibrium now that I have access to a proper computer, I've added proper code samples to my explanation. I hope this clarifies things for you, even though _0's answer really is the one you were looking for.
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