What language functions cannot be defined in terms of lambda?

Question

It seems that lambda can be used for almost anyone (even if it seems more complicated), but has its limitations.

What are some uses not covered by lambda?

Answer 1

Lambda (i.e. function) in itself is not very interesting. Here's the function in JavaScript:

function id(x) {
    return x;
}

Run code

What does this JavaScript program do? Nothing.

However, functions have the dangerous property of being invokable.

When called, the function can potentially do something (conditions apply):

authorize_nuclear_attack(launch_codes); // oops

Hence, trivially, lambda can do something.

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In other words, it is impossible to write a function Hsuch that H(P) = trueif it Pstops at all inputs, H(P) = falseotherwise. If you manage to write a function H, then it will always be incorrect for the following program:

function P(x) {
    return H(P) ? P(x) : x;
}

If he Hthinks he Palways stops, then he Pgoes into an endless cycle.

If he Hbelieves that he Pdoes not always stop, he always stops.

What are some uses not covered by lambda?

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