There's a common belief floating around that total functions are an essential component of functional programming. I suppose there's growing demand for developing in Turing-incomplete languages.
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I think that is akin to claiming that all recursive functions are total, because they have a finitary representation. One could alter the runtime semantics of so that the program terminates after n recursive calls. But is that a satisfactory definition of totality?
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I don't. Really the best (most detailed/precise) explanation is the paper I linked.
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