# Proof Nets and Explicit Substitutions

##### Citations

36 citations

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

...We are grateful to José Espı́rito Santo for suggesting a simpler termination proof for RE and to the anonymous referees of the current paper and of Di Cosmo et al. (2000) for their contributions to improve the presentation of this document....

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34 citations

32 citations

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

...Relationship with Linear Logic [24] and Relevant Logic [23, 18] provides an insight on the information refinement aspect of non-idempotent intersection types....

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...But calculi with ES can also be interpreted in Linear Logic [22, 28, 26, 5] by implementing another kind of operational semantics: their dynamics is defined using contexts (i.e. terms with holes) that allows the ES to act directly at a distance on single variable occurrences, with no need to commute with any other constructor in between....

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...But calculi with ES can also be interpreted in Linear Logic [22, 28, 26, 5] by implementing another kind of operational semantics: their dynamics is defined using contexts (i....

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31 citations

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

...Also, it can be shown [18] that there is a simple translation from λws into the Proof...

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...1 In contrast to λws with names [17,18], where terms affected by substitutions have a complex format t[x, u, Γ, ∆]...

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30 citations

##### 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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