We consider combinatorial aspects of-terms in the model based on de Bruijn indices where
each building constructor is of size one. Surprisingly, the counting sequence for-terms …

Simply-typed lambda terms are often used in the internal language of compilers and proof
assistants, for which generation of large, uniformly distributed random terms is instrumental …

We investigate various classes of Motzkin trees as well as lambda-terms for which we derive
asymptotic enumeration results. These classes are defined through various restrictions …

John Tromp introduced the so-called'binary lambda calculus' as a way to encode lambda
terms in terms of binary words. Later, Grygiel and Lescanne conjectured that the number of …

Contrary to several other families of lambda terms, no closed formula or generating function
is known and none of the sophisticated techniques devised in analytic combinatorics can …

John Tromp introduced the so-called 'binary lambda calculus' as a way to encode lambda
terms in terms of 0–1-strings using the de Bruijn representation along with a weighting …

We present a quantitative, statistical analysis of random lambda terms in the de Bruijn
notation. Following an analytic approach using multivariate generating functions, we …

A natural approach to software quality assurance consists in writing unit tests securing
programmer-declared code invariants. Throughout the literature, a great body of work has …

It is well known that the length of a beta-reduction sequence of a simply typed lambda-term
of order k can be huge; it is as large as k-fold exponential in the size of the lambda-term in …

It is well known that the length of a β-reduction sequence of a simply typed λ-term of order k
can be huge; it is as large as k-fold exponential in the size of the λ-term in the worst case …