Weighted models for higher-order computation

We study a class of quantitative models for higher-order computation: Lafont categories with (infinite) biproducts. Each of these has a complete “internal semiring” and can be enriched over its modules. We describe a semantics of nondeterministic PCF weighted over this semiring in which fixed points are obtained from the bifree algebra over its exponential structure. By characterizing them concretely as infinite sums of approximants indexed over nested finite multisets, we prove computational adequacy.