An encoding of the $$\lambda $$-calculus in the String MultiSet Rewriting calculus

Abstract

In this paper, we present an encoding of the $$\lambda $$ λ -calculus in a multiset rewriting system and provide a few applications of the construction. For this purpose, we choose the calculus named String MultiSet Rewriting, which was introduced in Barbuti et al. (Electron Notes Theor Comput Sci 194:19–34, 2008) by Barbuti et al. With the help of our encoding, we give alternative proofs for the standardization and the finiteness of developments theorems in the $$\lambda $$ λ -calculus.