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- Beniamino Accattoli
- TERMGRAPH
- 2013

A famous result by Milner is that the λ -calculus can be simulated inside the π-calculus. This simulation, however, holds only modulo strong bisimilarity on processes, i.e. there is a slight mismatch between β -reduction and how it is simulated in the π-calculus. The idea is that evaluating a λ -term in the π-calculus is like running an environment-based… (More)

- Beniamino Accattoli, Ugo Dal Lago
- CSL-LICS
- 2014

Slot and van Emde Boas' weak invariance thesis states that <i>reasonable</i> machines can simulate each other within a polynomially overhead in time. Is λ-calculus a reasonable machine? Is there a way to measure the computational complexity of a λ-term? This paper presents the first complete positive answer to this long-standing problem. Moreover,… (More)

- Beniamino Accattoli, Ugo Dal Lago
- ArXiv
- 2014

Slot and van Emde Boas’ weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is l-calculus a reasonable machine? Is there a way to measure the computational complexity of a l-term? This paper presents the first complete positive answer to this long-standing problem. Moreover, our answer is… (More)

- Beniamino Accattoli
- RTA
- 2012

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. These calculi, despite being non-terminating and non-orthogonal, have a key feature: each rule terminates when considered separately. It is well-known that the study of rewriting… (More)

- Beniamino Accattoli, Ugo Dal Lago
- RTA
- 2012

The λ-calculus is a widely accepted computational model of higher-order functional programs, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing λ-terms to their normal form is typically studied by reasoning on concrete implementation algorithms. In this paper, we show that when… (More)

- Beniamino Accattoli, Luca Paolini
- FLOPS
- 2012

In the call-by-value lambda-calculus solvable terms have been characterised by means of call-by-name reductions, which is disappointing and requires complex reasonings. We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman’s call-by-value λCBV calculus and from Accattoli and Kesner’s substitution… (More)

- Beniamino Accattoli
- CPP
- 2012

In 1994 Gerard Huet formalized in Coq the cube property of λ-calculus residuals. His development is based on a clever idea, a beautiful inductive definition of residuals. However, in his formalization there is a lot of noise concerning the representation of terms with binders. We re-interpret his work in Abella, a recent proof assistant based on… (More)

- Beniamino Accattoli
- LSFA
- 2012

This paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize a strong bisimulation between the two systems: every single rewriting step on the calculus maps to a single step on the nets, and viceversa. In this way, we… (More)

- Beniamino Accattoli
- RTA
- 2013

Strong normalization for linear logic requires elaborated rewriting techniques. In this paper we give a new presentation of MELL proof nets, without any commutative cut-elimination rule. We show how this feature induces a compact and simple proof of strong normalization, via reducibility candidates. It is the first proof of strong normalization for MELL… (More)

Inspired by a recent graphical formalism for λ-calculus based on Linear Logic technology, 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. Firstly, we prove fundamental properties such as confluence and… (More)