Interaction Improvement
For researchers in linear logic and lambda calculus semantics, this work provides a quantitative refinement of existing qualitative preorders, though it is incremental.
The paper shows that the relational semantics of linear logic refines the contextual preorder by constraining the number of interactions between terms and contexts, using the checkers calculus to provide a quantitative interpretation.
The relational semantics of linear logic is a powerful framework for defining resource-aware models of the $λ$-calculus. However, its quantitative aspects are not reflected in the preorders and equational theories induced by these models. Indeed, they can be characterized in terms of (in)equalities between Böhm trees up to extensionality, which are qualitative in nature. We employ the recently introduced checkers calculus to provide a quantitative and contextual interpretation of the preorder associated to the relational semantics. This way, we show that the relational semantics refines the contextual preorder constraining the number of interactions between the related terms and the context.