Some New Results on Easy lambda-Terms

Abstract Given two closed λ-terms A and B we consider the question whether the equation A = B is consistent with the λβ-calculus. In general the problem is undecidable. However, if A is a 0-term, we can give good sufficient conditions for the consistency of λβ +{ A = B }. This allows us to prove some counterintuitive results such as: (1) there is a closed λ-term X which can be consistently equated to every closed λ-term with the exception of the identity λχ.χ, (2) there is a closed λ-term which can be consistently equated to every closed normal form, but not to the Curry fixed point operator Y .