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A Natural Counting of Lambda Terms
TLDR
We study the sequences of numbers corresponding to lambda terms of given sizes, where the size is this of lambda terms with de Bruijn indices in a very natural model where all the operators have size 1. Expand
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Boltzmann Samplers for Closed Simply-Typed Lambda Terms
TLDR
We advance Boltzmann samplers to term sizes interesting not only for correctness but also for scalability tests, by deriving Boltzmillers returning in a few seconds simply-typed random lambda terms of size 120 and above. Expand
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Polynomial tuning of multiparametric combinatorial samplers
TLDR
In this paper, we propose an efficient polynomial-time, with respect to the number of tuned parameters, tuning algorithm based on convex optimisation techniques for Boltzmann samplers. Expand
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Combinatorics of λ-terms: a natural approach
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On the likelihood of normalization in combinatory logic
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Normal-order reduction grammars
TLDR
We present an algorithm which, for given $n$, generates an unambiguous regular tree grammar defining the set of combinatory logic terms, over the set $\{S,K\}$ of primitive combinators, requiring exactly $n$ normal-order reduction steps to normalize. Expand
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Random generation of closed simply typed λ-terms: A synergy between logic programming and Boltzmann samplers
TLDR
We combine the framework of Boltzmann samplers, a powerful technique of random combinatorial structure generation, with today’s Prolog systems offering a synergy between logic variables, unification with occurs check and efficient backtracking. Expand
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Combinatorics of Explicit Substitutions
TLDR
We investigate the combinatorial properties of λν focusing on the quantitative aspects of substitution resolution. Expand
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Asymptotic Properties of Combinatory Logic
TLDR
We present a quantitative analysis of random combinatory logic terms. Expand
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Combinatorics of $$\lambda$$-terms: a natural approach
TLDR
We consider combinatorial aspects of $\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Expand
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