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Distilling abstract machines
TLDR
The distillation process unveils that abstract machines in fact implement weak linear head reduction, a notion of evaluation having a central role in the theory of linear logic, and shows that the LSC is a complexity-preserving abstraction of abstract machines.
Environments and the complexity of abstract machines
TLDR
It is shown 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, thus improving the bounds in the literature.
Beta reduction is invariant, indeed
TLDR
The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties, and the first complete positive answer to this long-standing problem of λ-calculus.
Call-by-Value Solvability, Revisited
TLDR
The value-substitution lambda-calculus is introduced, 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 .
(Leftmost-Outermost) Beta Reduction is Invariant, Indeed
TLDR
The main technical contribution of the paper is indeed the definition of useful reductions and the thorough analysis of their properties, and the first complete positive answer to this long-standing problem.
An Abstract Factorization Theorem for Explicit Substitutions
TLDR
A simple form of standardization, here called factorization, for explicit substitutions calculi, i.e. lambda-calculi where beta-reduction is decomposed in various rules, is studied and an abstract theorem deducing factorization from some axioms on local diagrams is developed.
Abstract machines for Open Call-by-Value
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, and relies on Gonthier, Lévy, and Melliès' axiomatic theory for standardization.
On the Invariance of the Unitary Cost Model for Head Reduction (Long Version)
TLDR
Invariance is proved by way of a linear calculus of explicit substitutions, which allows to nicely decompose any head reduction step in the lambda calculus into more elementary substitution steps, thus making the combinatorics of head-reduction easier to reason about.
Open Call-by-Value
TLDR
A detailed comparative study of the operational semantics of four calculi, coming from different areas such as the study of abstract machines, denotational semantics, linear logic proof nets, and sequent calculus, showing that these calculi are all equivalent from a termination point of view.
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