Enumeration of Generalized $BCI$ Lambda-terms

Enumeration of Generalized BCI Lambda-terms

We investigate the asymptotic number of elements of size n in a particular class of closed lambda-terms (so-called BCI(p)-terms) which are generalizations of lambdaterms related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved asymptotically. We derive differential ...

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.

Generalized Lambda Distribution and its Properties

‎Generalized Lambda Distribution is an extension of Tukey's lambda distribution‎, ‎that is very flexible in modeling information and statistical data‎. ‎In this paper‎, ‎We introduced two parameterization of this distribution‎. ‎Then We estimate parameters by moment matching‎, ‎percentile‎, ‎starship and maximum likelihood methods and compare two parameterization and parameter estimation method...