# Proof Nets and Explicit Substitutions

##### Citations

5 citations

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

...It is a leading principle behind, among others, explicit substitution calculi [1, 18, 8, 9, 15, 2], term calculi with strategies or higher-order transformations [14, 3], and sharing graphs in the style of Lamping [17, 4, 21]....

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4 citations

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

...Let us point out that via the Curry-Howard correspondence between MELLP and .µ-calculus this work provides implicit boxes for classical logic....

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...Therefore, non-linear cut-elimination rules can easily be de.ned by duplicating or erasing sub-trees, as in Figure 1.a. Switching to proof nets, the situation radically changes....

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3 citations

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

...Di Cosmo, Kesner and Polonovsky [ 7 ] understood the relation between ¸ws and linear logic and, by using a translation of ¸ws into proof nets, they proved this conjecture....

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...This was proved in [ 7 ] by Di Cosmo & al. by using a translation of ¸ws into the proof nets of linear logic....

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...Theorem 5 below has first been proved in [ 7 ] by Di Cosmo & al. It is of course a trivial consequence of theorem 7 of section 5. However, the proof presented below is interesting in itself because it is purely arithmetical whereas the one of section 5 is not....

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...Note that permutation of rules is also the main ingredient in the proof of [ 7 ]....

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3 citations

3 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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