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When giving talks on Scala I'm almost always certain I'll be asked "but when would you use a Closure?" Typically I say "wait until I show you a for comprehension" and then I show how the for comprehension can be boiled down to using flatMap/map + closures.
This example does help, however it's tough for me to explain a general "this is when you'd recognize when to use a closure". It's one of those things you "just get used to" in functional programming, you almost do it without thinking.
Typically I'm talking to Java devs when I speak about Scala, and one analogy that comes to mind is "you know when you create an anonymous inner class that needs to access a variable somewhere above where the class was defined? That's like a closure". So I use event call-back processing as one particular example (as inevitably you use anonymous inner classes in that scenario).
Considering the audience (no experience, or limited experience with FP) I don't go on to discuss terms like Monads, these people are typically looking for concrete/pragmatic examples they can relate to.
Question: Anyone have their own way of successfully explaining closures that really hits home for Java (or other OO language) developers?