What does a Kotlin function signature with T.() mean?

Question

T.() -> Unit is an extension function type with receiver.

Besides ordinary functions, Kotlin supports extension functions. Such function differs from an ordinary one in that it has a receiver type specification. Here it’s a generic T. part.

The this keyword inside an extension function corresponds to the receiver object (the one that is passed before the dot), so you can call its methods directly (referring to this from parent scopes is still possible with qualifiers).

Function with is a standard one, yes. It’s current code:

/**
 * Calls the specified function [block] with the given [receiver] as its receiver and returns its result.
 *
 * For detailed usage information see the documentation for [scope functions](https://kotlinlang.org/docs/reference/scope-functions.html#with).
 */
public inline fun <T, R> with(receiver: T, block: T.() -> R): R = receiver.block()

So it’s a generic function for T and R, with first argument “receiver” of type T and second, f of extension function type, which extends T, returning type R which in turn returned by the with.

For example, you can use it like this:

val threadInfoString = with (Thread.currentThread()) {
    // isDaemon() & getPriority() are called with new property syntax for getters & setters
    "${getName()}[isDaemon=$isDaemon,priority=$priority]"
}

See documentation for extension functions here:
kotlinlang.org/docs/reference/lambdas.html#extension-function-expressions
kotlinlang.org/docs/reference/scope-functions.html#with
kotlinlang.org/docs/reference/extensions.html

Added:

So the only valid f would be any 0-argument function defined for T?

Not really. In Kotlin function types and extension function types are unified, so that they can be used interchangeably. For example, we can pass String::length where a function (String) -> Int is expected.

// map() expects `(String) -> Int`
// argument has type `String.() -> Int`
strings.map(String::length)

Types like Thread.() -> String & (Thread) -> String are the same from the background side – receiver, in fact, is the first argument.

So any of the following functions is suitable for Thread.() -> String argument:

fun main(args: Array<String>) {
    val f1 = fun Thread.(): String = name
    val f2 = fun Thread.() = name
    val f3: Thread.() -> String = { name }
    val f4: (Thread) -> String = { it.name }
    val f5 = { t: Thread -> t.name }
    val f6: (Thread) -> String = Thread::getNameZ
    val f7: Thread.() -> String = Thread::getNameZ
    val f8 = Thread::getNameZ
}

fun Thread.getNameZ() = name

Or you can simply use function literal ({}) as in the example with threadInfoString, but it works only when the receiver type can be inferred from the context.

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