An appropriate framework is put forward for the construction of
λ-models with ∞-groupoid structure, which we call
\textit{homotopic λ-models} through the use of an ∞-bicategory
with cartesian closure and enough points. With this, we establish the start of
a project of generalization of Domain Theory and λ-calculus, in the
sense that the concept of proof (path) of equality of λ-terms is raised
to \textit{higher proof} (homotopy)