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> Math can't deal with imperfect input and/or side effects without turning into something else.

It very much can though.

Not in any sense that matters here, no.

There's no math equation for reading from a socket. Code is not math and math is not code. It's possible to sort of hide the fact by stacking enough abstractions on top, but in the end it's going to be the same old code that makes it happen.

Linear types and session types can enforce protocols for reading from a socket.

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