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Distilling abstract machines
TLDR
We show that many environment-based abstract machines can be seen as strategies in lambda calculi with explicit substitutions (ES). Expand
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Beta reduction is invariant, indeed
TLDR
We show that the length of a leftmost-outermost derivation to normal form in the theory of λ-calculus is an invariant cost model. Expand
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Environments and the complexity of abstract machines
TLDR
We show that local environments admit implementations that are asymptotically faster than global environments, lowering the dependency from the size of the initial term from linear to logarithmic. Expand
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An Abstract Factorization Theorem for Explicit Substitutions
TLDR
We study a simple form of standardization, here called factorization, for explicit substitutions calculi, i.e. lambda-calculi where beta-reduction is decomposed in various rules. Expand
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(Leftmost-Outermost) Beta Reduction is Invariant, Indeed
TLDR
We show that the length of a leftmost-outermost derivation to normal form of lambda-calculus is an invariant cost model. Expand
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Call-by-Value Solvability, Revisited
TLDR
We introduce the value-substitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λ CBV calculus and from Accattoli and Kesner's substitution calculus λ sub . Expand
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A nonstandard standardization theorem
TLDR
This paper focuses on standardization for the linear substitution calculus, a calculus with ES capable of mimicking reduction in lambda-calculus and linear logic proof-nets. Expand
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The Structural lambda-Calculus
TLDR
We introduce an untyped structural λ-calculus, called λj, which combines action at a distance with exponential rules decomposing the substitution by means of weakening, contraction and dereliction. Expand
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Open Call-by-Value
TLDR
The elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. Expand
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Evaluating functions as processes
TLDR
A famous result by Milner is that evaluating a lambda-term in the pi-calculus is like running an environment-based abstract machine, rather than applying ordinary beta-reduction. Expand
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