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As cody observed, the problem with that strategy is that definable relations need not be computable. For example, the Halting Problem is definable in $(\mathbb{N}; +,\times)$ (see Kleene's $T$-predicate). That said, a relativized form of the incomputability of the Halting Problem, applied to iterates of the Turing jump, does do the job: First, we show that ...


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(I might be wrong, but this is my understanding.) Callbacks, especially as seen in JS, are analogous to a semantic model known as Continuation-passing style (CPS). In CPS, a program’s flow is modeled as a series of functions, each of which takes in a continuation, and calls the continuation with the function’s result when finished. As stated, this is also ...


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Yes, callbacks belong to to the family of Higer-order functions. Because they're one of the simplest members of the family, they're often encountered in practice.


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