The paper presents a simple programming language and rewriting system called GENS. It is based on an extension of the λ-calculus called λE-calculus. GENS is a multiparadigm language: it has been used for definition of semantics and for implementation of functional, logical, procedural, and object-oriented languages. It also allows combining different programming paradigm styles in a single programming language.

The purpose of this paper is to define and to introduce the λE-calculus – theoretical foundation of GENS. It will also be shown how the most important language constructs of different programming paradigms can be defined in GENS.