ON FORMALIZATION OF NOTION OF $δ$-REDUCTION IN MONOTONIC MODELS OF TYPED $λ$-CALCULUS - Budaghyan, L. E. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2003)
In this paper monotonic models of typed $λ$-calculus are examined. Formal definition of concept of a $δ$-reduction is given. Strong $δ$-normalization and strong $βδ$-normalization of terms are proved. The concept of a natural $δ$-reduction is defined and the necessary and sufficient condition for uniqueness of a $βδ$-normal form for such concept of a $δ$-reduction is resulted.
Keywords: $λ$-calculus; normalization; $δ$-reduction