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Environments and closures are two of the main ingredients of evaluation inlambda-calculus. A closure is a pair consisting of a lambda-term and anenvironment, whereas an environment is a list of lambda-terms assigned to freevariables. In this paper we investigate some dynamic aspects of evaluation inlambda-calculus considering the quantitative, combinatorial properties ofenvironments and closures. Focusing on two classes of environments andclosures, namely the so-called plain and closed ones, we consider the problemof their asymptotic counting and effective random generation. We provide anasymptotic approximation of the number of both plain environments and closuresof size $n$. Using the associated generating functions, we construct effectivesamplers for both classes of combinatorial structures. Finally, we discuss therelated problem of asymptotic counting and random generation of closedenvironemnts and closures.

On the enumeration of closures and environments with an application to random generation