Does not compute

One of the most basic ways to think about a computer program is that it is a device which takes in integers as inputs and spits out integers as outputs. The C# compiler, for example, takes in source code strings, and those source code strings are essentially nothing more than enormous binary numbers. The output of the compiler is either diagnostic text, or strings of IL and metadata, which are also just enormous binary numbers.  Because the compiler is not perfect, in some rare cases it terminates abnormally with an internal error message. But those fatal error messages are also just big binary numbers. So let’s take this as our basic model of a computer program: a computer program is a device that either (1) runs forever without producing output, or (2) computes a function that maps one integer to another.
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