Numeration models of $\lambda$B-Calculus

Numeration models of extensional $\lambda$-calculus have been studied (see [5,7]). In this paper, we study numeration models of $\lambda \beta$-calculus. Engeler's graph algebra construction [3] is applied to the category of numerations and is used as a tool to obtain numeration models of $\lambda \beta$-calculus. Several classes of numeration models are studied and several examples of them are presented.