On type-directed genmeration of lambda-terms

We describe a Prolog-based combined lambda term generator and type-inferrer for closed well-typed terms of a given size, in de Bruijn notation. By taking advantage of Prolog's unique bidirectional execution model and sound unification algorithm, our generator can build "customized" closed terms of a given type. This relational view of terms and their types enables the discovery of interesting patterns about frequently used type expressions occurring in well-typed functional programs. Our study uncovers the most "popular" types that govern function applications among a about a million small-sized lambda terms and hints toward practical uses to combinatorial software testing. It also shows the effectiveness of Prolog as a meta-language for modeling properties of lambda terms and their types. KEYWORDS: lambda calculus, de Bruijn notation, type inference, generation of lambda terms, logic programming as a meta-language

Counting and Generating Terms in the Binary Lambda Calculus (Extended version)

In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent lambda terms and derive results from their generating functions, especially that the number of terms of size n grows roughly like 1.963447954. .. n. In a second part we use this approach to generate random lambda terms using Boltzmann samplers.Comment: extended version of arXiv:1401.037

Random Testing For Language Design

Property-based random testing can facilitate formal verification, exposing errors early on in the proving process and guiding users towards correct specifications and implementations. However, effective random testing often requires users to write custom generators for well-distributed random data satisfying complex logical predicates, a task which can be tedious and error prone. In this work, I aim to reduce the cost of property-based testing by making such generators easier to write, read and maintain. I present a domain-specific language, called Luck, in which generators are conveniently expressed by decorating predicates with lightweight annotations to control both the distribution of generated values and the amount of constraint solving that happens before each variable is instantiated. I also aim to increase the applicability of testing to formal verification by bringing advanced random testing techniques to the Coq proof assistant. I describe QuickChick, a QuickCheck clone for Coq, and improve it by incorporating ideas explored in the context of Luck to automatically derive provably correct generators for data constrained by inductive relations. Finally, I evaluate both QuickChick and Luck in a variety of complex case studies from programming languages literature, such as information-flow abstract machines and type systems for lambda calculi