Boltzmann Samplers for Closed Simply-Typed Lambda Terms

Bendkowski, Maciej; Grygiel, Katarzyna; Tarau, Paul

doi:10.1007/978-3-319-51676-9_8

Cited by 12 publications

(14 citation statements)

References 13 publications

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“…This presentation shares similarity with this of [14,15,4]. Instead of considering the size n and the bound m of free indices like in expressions of the form:…”

Section: Resultsmentioning

confidence: 70%

Quantitative Aspects of Linear and Affine Closed Lambda Terms

Lescanne

2018

ACM Trans. Comput. Logic

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Affine λ-terms are λ-terms in which each bound variable occurs at most once and linear λ-terms are λ-terms in which each bound variable occurs once. and only once. In this paper we count the number of closed affine λ-terms of size n, closed linear λ-terms of size n, affine β-normal forms of size n and linear β-normal forms of size n, for different ways of measuring the size of λ-terms. From these formulas, we show how we can derive programs for generating all the terms of size n for each class. The foundation of all of this is specific data structures, which are contexts in which one counts all the holes at each level of abstractions by λ's.

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“…This presentation shares similarity with this of [14,15,4]. Instead of considering the size n and the bound m of free indices like in expressions of the form:…”

Section: Resultsmentioning

confidence: 70%

Quantitative Aspects of Linear and Affine Closed Lambda Terms

Lescanne

2018

ACM Trans. Comput. Logic

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“…We reported the bug in BugZilla and the error was quickly confirmed and fixed. 5 Internally, SpiderMonkey's Wasm-engine creates a vector of "exported function" objects, each with a (bit-packed) Boolean, indicating whether a function is marked explicitly as exported. In the test program the same function occurs both as a start function and in a table, causing it to occur twice in the vector, with only one occurrence being marked explicitly.…”

Section: Bugs Foundmentioning

confidence: 99%

“…Alternatives to a randomized recursive generator exist, such as enumeration-based program generation in the style of SmallCheck [22] and Bolzmann samplers to generate typed lambda terms of an approximate size [5]. Both these approaches have currently only been attempted on languages with relatively few language constructs.…”

Section: Related Workmentioning

confidence: 99%

Stack-Driven Program Generation of WebAssembly

Perényi

Midtgaard

2020

Programming Languages and Systems

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WebAssembly (Wasm) is a popular portable assembly-like language. Besides browser support in the four most common browsers (Chrome, Firefox, Safari, Edge) a number of standalone Wasm engines are available. With several such independent implementations naturally follows a risk of disagreement between the individual implementations. To help ensure agreement between Wasm implementations, we develop a stackdirected program generator to drive differential testing of the four browsers' Wasm engines. We describe our experimental setup, our development of a stackdirected shrinker for reducing a generated counterexample program, and finally report on a number of disagreements and bugs found. Surprisingly our black-box generator found 2 crashing bugs, despite browser vendor efforts to fuzz test their Wasm engines using a state-of-the-art fuzzer.

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“…However, the concepts of closable and typable skeletons of lambda terms and their uniquely closable and typable variants are new and have not been studied previously. The second author has used extensively Prolog as a metalanguage for the study of combinatorial and computational properties of lambda terms in papers like [16,11] covering different families of terms and properties, but not in combination with the precise analytic methods as developed in this paper.…”

Section: Related Workmentioning

confidence: 99%

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Bodini

Tarau

2018

Logic-Based Program Synthesis and Transformation

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Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size 3n + 1 are in a bijection with binary trees of size n.

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Boltzmann Samplers for Closed Simply-Typed Lambda Terms

Cited by 12 publications

References 13 publications

Quantitative Aspects of Linear and Affine Closed Lambda Terms

Quantitative Aspects of Linear and Affine Closed Lambda Terms

Stack-Driven Program Generation of WebAssembly

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

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