Cyclic proofs, system t, and the power of contraction

We study a cyclic proof system C over regular expression types, inspired by linear logic and non-wellfounded theory. Proofs in can be seen as strongly typed goto programs. show that they denote computable total functions we analyse the relative strength of Gödel’s T. In general case, prove two systems capture same on natural numbers. affine i.e., when contraction is removed, precisely primitive recursive functions—providing an alternative more result Dal Lago, about version Without contraction, manage to give direct uniform encoding into T, analysing cycles translating them explicit recursions. Whether such translation from T given presence remains open. obtain upper bounds expressivity using different technique: formalise weak normalisation small step reduction semantics subsystems second-order arithmetic: ACA 0 RCA .