We present a quantitative, statistical analysis of random lambda terms in the De Bruijn notation. Following an analytic approach using multivariate generating functions, we investigate the distribution of various combinatorial parameters of random open and closed lambda terms, including the number of redexes, head abstractions, free variables or the De Bruijn index value profile. Moreover, we conduct an average-case complexity analysis of finding the leftmost-outermost redex in random lambda terms showing that it is on average constant. The main technical ingredient of our analysis is a novel method of dealing with combinatorial parameters inside certain infinite, algebraic systems of multivariate generating functions. Finally, we briefly discuss the random generation of lambda terms following a given skewed parameter distribution and provide empirical results regarding a series of more involved combinatorial parameters such as the number of open subterms and binding abstractions in closed lambda terms.
@article{10_37236_8491,
author = {Maciej Bendkowski and Olivier Bodini and Sergey Dovgal},
title = {Statistical properties of lambda terms},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8491},
zbl = {1539.03044},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8491/}
}
TY - JOUR
AU - Maciej Bendkowski
AU - Olivier Bodini
AU - Sergey Dovgal
TI - Statistical properties of lambda terms
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8491/
DO - 10.37236/8491
ID - 10_37236_8491
ER -
%0 Journal Article
%A Maciej Bendkowski
%A Olivier Bodini
%A Sergey Dovgal
%T Statistical properties of lambda terms
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8491/
%R 10.37236/8491
%F 10_37236_8491
Maciej Bendkowski; Olivier Bodini; Sergey Dovgal. Statistical properties of lambda terms. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8491
