
Counting Environments and Closures
Environments and closures are two of the main ingredients of evaluation ...
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On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms
Uniquely closable skeletons of lambda terms are Motzkintrees that prede...
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Asymptotic Distribution of Parameters in Trivalent Maps and Linear Lambda Terms
Structural properties of large random maps and lambdaterms may be glean...
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Tuning as convex optimisation: a polynomial tuner for multiparametric combinatorial samplers
Combinatorial samplers are algorithmic schemes devised for the approxima...
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Rectangular Young tableaux with local decreases and the density method for uniform random generation (short version)
In this article, we consider a generalization of Young tableaux in which...
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Polynomial tuning of multiparametric combinatorial samplers
Boltzmann samplers and the recursive method are prominent algorithmic fr...
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Average sampling and average splines on combinatorial graphs
In the setting of a weighted combinatorial finite or infinite countable ...
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Statistical properties of lambda terms
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 averagecase complexity analysis of finding the leftmostoutermost 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.
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