  Lambek Grammars (LG) are a computational modelling of natural language, based
on non-commutative compositional types. It has been widely studied, especially
for languages where the syntax plays a major role (like English). The goal of
this internship report is to demonstrate that every Lambek Grammar can be, not
entirely but efficiently, expressed in Abstract Categorial Grammars (ACG). The
latter is a novel modelling based on higher-order signature homomorphisms
(using $\lambda$-calculus), aiming at uniting the currently used models. The
main idea is to transform the type rewriting system of LGs into that of
Context-Free Grammars (CFG) by erasing introduction and elimination rules and
generating enough axioms so that the cut rule suffices. This iterative approach
preserves the derivations and enables us to stop the possible infinite
generative process at any step. Although the underlying algorithm was not fully
implemented, this proof provides another argument in favour of the relevance of
ACGs in Natural Language Processing.
