# Proof Nets and Explicit Substitutions

##### Citations

1 citations

### Cites background or methods from "Proof Nets and Explicit Substitutio..."

...In establishing this property, we adopt the method used in [Curien et al. 1996] to demonstrate that the λσ-calculus is confluent....

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...However, straightforward additions to the rule set suffice to regain this property [Curien et al. 1996]; see also [Dowek et al. 2000] for a system closer in form to the one discussed in this paper....

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...The following lemma, proved in [Curien et al. 1996], is a critical part of the argument....

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1 citations

### Cites background from "Proof Nets and Explicit Substitutio..."

...On the basis of this observation, close relations have been established between normalisation of some ES calculi and cut elimination in Linear Logic’s proof nets by translating typable terms from the former into nets of the latter [52, 80, 78]....

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...It has yielded normalisation proofs for existing explicit substitution calculi [51, 52] as well as aided the development of new calculi with some or all of the properties of preservation of strong normalisation (PSN), open confluence, and full composition of substitutions [80, 78]....

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1 citations

### Cites background from "Proof Nets and Explicit Substitutio..."

...5 λwsn-calculus In [8] a named version of λws was proposed....

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..., see for example [8, 10]), sometimes SN proofs uses PSN (see for example [4])....

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##### References

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2,304 citations

### "Proof Nets and Explicit Substitutio..." refers background or methods in this paper

...In this paper we refine the simulation technique introduced in [10] to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets [13]....

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...While we refer the interested reader to [13] for more details on linear logic in general, we give here a one-sided presentation of the sequent calculus for MELL:...

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1,480 citations

577 citations

### "Proof Nets and Explicit Substitutio..." refers background in this paper

...The pioneer calculus with explicit substitutions, λσ, was introduced in [1] as a bridge between the classical λ-calculus and concrete implementations of functional programming languages....

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321 citations

### "Proof Nets and Explicit Substitutio..." refers methods in this paper

...1 Using various translations of the λ-calculus into proof nets, new abstract machines have been proposed, exploiting the Geometry of Interaction and the Dynamic Algebras [14, 2, 5], leading to the works on optimal reduction [15, 17]....

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