Traditional proof theory and Post-Turing computability are parts of discrete mathematics, whereas traditional analysis deals with non-discrete objects like real numbers and related topological notions. On the other hand, familiar mathematical proofs very often use methods of (functional) analysis which are compatible with functional formalizations of Post-Turing computability. We elaborate these connections with regard to the polynomial-time computability.
['Lew Gordeew']
Proof Theory and Post-turing Analysis