Counting Environments and Closures

Authors: Maciej Bendkowski and Pierre Lescanne

Paper Information

Title:Counting Environments and Closures
Authors:Maciej Bendkowski and Pierre Lescanne
Proceedings:FSCD Presented Papers
Editor: Helene Kirchner
Keywords:lambda-calculus, combinatorics, functional programming, mathematical analysis, complexity

ABSTRACT. Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environemnts and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size n. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures.

Talk:Jul 10 15:40 (Session 57A: Complexity)