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Computation, Proof, Machine by Marion Roman, Pierre Guillot, Gilles Dowek

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Chapter Four From the Decision Problem to Church’s Theorem

AT THE BEGINNING OF THE TWENTIETH CENTURY, two theories about computation developed almost simultaneously: the theory of computability and the theory of constructivity. In a perfect world, the schools of thought that produced these theories would have recognized how their work was connected and cooperated in a climate of mutual respect. Sadly, this was not the case, and the theories emerged in confusion and incomprehension. Not until the middle of the century would the links between computability and constructivity finally be understood.

To this day, there are traces of the old strife in the sometimes excessively ideological way in which these theories are expounded, both of which deserve ...

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