2025/06/27 by Enqvist, Sebastian
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2506.22206
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the computational content of this system, in particular we introduce a notion of computability and show that every valid proof is computable. As a consequence, we obtain a normalization result for proofs of what we call finitary formulas. A special case of this result is that every proof of a sequent of the appropriate form represents a unique function on natural numbers. Finally, we derive a categorical model from the proof system and show that least and greatest fixpoint formulas correspond to initial algebras and final coalgebras respectively.