The variety of lambda abstraction algebras does not admit n-permutable congruences for all n

ION ALGEBRAS DOES NOT ADMIT N-PERMUTABLE CONGRUENCES FOR ALL N Antonino Salibra Dipartimento di Matematica Applicata ed Informatica Universit`a Ca' Foscari di Venezia Via Torino 155, 30173 Venezia, Italy fax: +39 41 2908419, email: [email protected] April 7, 1998 1. Lambda Abstraction Algebras: Basic Notions and Notation In this section we summarize definitions and results concerning the lambda calculus and the theory of lambda abstraction algebras. Our main references will be [10] and [11] for lambda abstraction algebras and Barendregt's book [1] for lambda calculus. Lambda calculus. The untyped lambda calculus was introduced by Church as a foundation for logic. Although the appearance of paradoxes caused the program to fail, a consistent part of the theory turned out to be successful as a theory of "functions as rules" (formalized as terms of the lambda calculus) that stresses the computational process of going from argument to value. Every object is at the same time a function..