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This article is devoted to the presentation of lambda_rex, an explicit substitution calculus with de Bruijn indexes and a simple notation. By being isomorphic to lambda_ex - a recent formalism with variable names -, lambda_rex accomplishes simulation of beta-reduction (Sim), preservation of beta-strong normalization (PSN) and meta-confluence (MC), among other desirable properties. Our calculus is based on a novel presentation of lambda_dB, using a swap notion that was originally devised by de Bruijn. Besides lambda_rex, two other indexed calculi isomorphic to lambda_x and lambda_xgc are presented, demonstrating the potential of our technique when applied to the design of index
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one of the main
In this paper we introduce a typed, concurrent $lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a reducibility t
Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless, we use doma
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking.
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch of differen