Kotlin: Use a lambda in place of a functional interface?

Assuming below that you really need EventHandler as a separate interface (e.g. for Java interop). If you don't, you can simply use a type alias (since Kotlin 1.1):

typealias EventHandler<T> = (T) -> Unit

In this case a simple lambda will work right away.

But if you don't want to use a type alias, the issue still stands. It is that Kotlin only does SAM-conversion for functions defined in Java. Since Events.handler is defined in Kotlin, SAM-conversions do not apply to it.

To support this syntax:

Events.handler(Handshake::class, EventHandler<Handshake> { println(it.sent) })

You can define a function named EventHandler:

fun <T> EventHandler(handler: (T) -> Unit): EventHandler<T> 
    = object : EventHandler<T> { 
        override fun handle(event: T) = handler(event) 
    }

To support this syntax:

Events.handler(Handshake::class, { println(it.sent) })

or this:

Events.handler(Handshake::class) { println(it.sent) }

You need to overload the handler function to take a function instead of EventHandler:

fun <T> Events.handler(eventType: Class<T>, handler: (T) -> Unit) = EventHandler(handler)

A lot of nice things has happened to Kotlin since @andrey-breslav posted the answer. He mentions:

It is that Kotlin only does SAM-conversion for functions defined in Java. Since Events.handler is defined in Kotlin, SAM-conversions do not apply to it.

Well, that's no longer the case for Kotlin 1.4+. It can use SAM-conversion for Kotlin functions if you mark an interface as a "functional" interface:

// notice the "fun" keyword
fun interface EventHandler<T> {
    fun handle(event: T)
}

You can read the YouTrack ticket here: https://youtrack.jetbrains.com/issue/KT-7770. There's also an explanation why Kotlin needs a marker for such interfaces unlike Java (@FunctionalInterface is only informational and has no effect on the compiler).