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A natural approach to software quality assurance consists in writing unittests securing programmer-declared code invariants. Throughout the literature agreat body of work has been devoted to tools and techniques automating thislabour-intensive process. A prominent example is the successful use ofrandomness, in particular random typeable $\lambda$-terms, in testingfunctional programming compilers such as the Glasgow Haskell Compiler.Unfortunately, due to the intrinsically difficult combinatorial structure oftypeable $\lambda$-terms no effective uniform sampling method is known, settingit as a fundamental open problem in the random software testing approach. Inthis paper we combine the framework of Boltzmann samplers, a powerful techniqueof random combinatorial structure generation, with today's Prolog systemsoffering a synergy between logic variables, unification with occurs check andefficient backtracking. This allows us to develop a novel sampling mechanismable to construct uniformly random closed simply-typed $\lambda$-terms of upsize 120. We apply our techniques to the generation of uniformly random closedsimply-typed normal forms and design a parallel execution mechanism pushingforward the achievable term size to 140. Under consideration in Theory andPractice of Logic Programming (TPLP).

Random generation of closed simply-typed $\lambda$-terms: a synergy between logic programming and Boltzmann samplers