Proofs are Programs – 19th Century Logic and 21st Century Computing (2000) [pdf]
That&#x27;s certainly a very language-and-logic perspective on things. But one of the reasons Church missed the general concept of computation whereas Turing didn&#x27;t was precisely because Church was stuck in the formalism of logic, and couldn&#x27;t recognize that computation extends well beyond it. So proofs are programs, but so are, say, metabolic networks, neuron networks, and just about <i>any</i> discrete dynamical system. But are metabolic networks <i>proofs</i>? That&#x27;s not so clear, and therefore it&#x27;s not so clear that there is a universal equivalence here.