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 define a quantitative contextual preorder on $λ$-terms, and demonstrate that it coincides with the preorder associated to the relational semantics.

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