Relational semantics for linear logic is a form of non-idempotent
intersection type system, from which several informations on the execution of a
proof-structure can be recovered. An element of the relational interpretation
of a proof-structure R with conclusion Γ acts thus as a type (refining
Γ) having R as an inhabitant. We are interested in the following
type-checking question: given a proof-structure R, a list of formulae Γ,
and a point x in the relational interpretation of Γ, is x in the
interpretation of R? This question is decidable. We present here an algorithm
that decides it in time linear in the size of R, if R is a proof-structure in
the multiplicative fragment of linear logic. This algorithm can be extended to
larger fragments of multiplicative-exponential linear logic containing
λ-calculus