  Stabler proposes an implementation of the Chomskyan Minimalist Program,
Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits a
long linguistic tradition. But the semantic calculus is more easily added if
one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars - MCG,
based on an extension of the Lambek calculus, the mixed logic, were introduced
to provide a theoretically-motivated syntax-semantics interface, Amblard 07. In
this article, we give full definitions of MG with algebraic tree descriptions
and of MCG, and take the first steps towards giving a proof of inclusion of
their generated languages.
