Principal types of BCK-lambda-terms

Asymptotics and random sampling for BCI and BCK lambda terms

This paper presents a bijection between combinatorial maps and a class of enriched trees, corresponding to a class of expression trees in some logical systems (constrained lambda terms). Starting from two alternative definitions of combinatorial maps: the classical definition by gluing halfedges, and a definition by non-ambiguous depth-first traversal, we derive non-trivial asymptotic expansion...

Monadic Presentations of Lambda Terms Using Generalized Inductive Types

Almost Affine Lambda Terms

It is proved that a λ-term that has a negatively non-duplicated typing is always βη-equal to an almost affine λ-term.

Separability of Infinite Lambda Terms

Infinite lambda calculi extend finite lambda calculus with infinite terms and transfinite reduction. In this paper we extend some classical results of finite lambda calculus to infinite terms. The first result we extend to infinite terms is Böhm Theorem which states the separability of two finite βη-normal forms. The second result we extend to infinite terms is the equivalence of the prefix rel...

Lambda Terms Definable as Combinators

It is well known that for each l-term there is a corresponding combinatory term formed using the combinators K and S instead of the I-operator. Similarly for every combinatory term there is a i.-term. For weaker sets of combinators such as B, C and K or B, B’, I and W we show how such a correspondence or “translation” can be formulated and we determine in the case of several such sets of combin...