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You are probably looking for declarative programming. There are various sorts, but most of them are (mostly) atemporal in the sense that there is no notion of order of execution. Probably the best main-stream example is Haskell. Programs are not "sequences of instructions" but rather systems of equations. When programming in Haskell, we do not ...


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It depends on exactly what you mean I can see three possibilities for what you might be asking about here. If the problem is that, in a language like C for instance, it's not possible to write things like this: int f(int x) { return g(x + 1); } int g(int x) { return x + 1; } because the compiler will complain that it doesn't know what g is during the ...


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Instead of starting with the properties of $\mathrm{Y}$, start with a term that explicitly refers to itself: $$\textbf{letrec }f = \ldots f \ldots f \ldots \textbf{ in } f$$ and consider how it could be expressed without $\textbf{letrec}$. You can get an equivalent term by passing $f$ as an argument to itself at each call site: $$\textbf{let }f f' = \ldots f'...


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