What is the syntax: `instance.method::()`?

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This construct is called turbofish. If you search for this statement, you will discover its definition and its usage.

Although the first edition of The Rust Programming Language is outdated, I feel that this particular section is better than in the second book.

Quoting the second edition:

path::<...>, method::<...>
Specifies parameters to generic type, function, or method in an expression; often referred to as turbofish (e.g., "42".parse::<i32>())

You can use it in any kind of situation where the compiler is not able to deduce the type parameter, e.g.

fn main () {
    let a = (0..255).sum();
    let b = (0..255).sum::<u32>();
    let c: u32 = (0..255).sum();
}

a does not work because it cannot deduce the variable type.
b does work because we specify the type parameter directly with the turbofish syntax.
c does work because we specify the type of c directly.

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