# Collapsing non-idempotent intersection types

##### Citations

53 citations

### Cites background or methods from "Collapsing non-idempotent intersect..."

...In [30], strong normalization for a call-by-value λ-calculus is characterized by means of intersection types, both idempotent and non-idempotent....

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...Following the same approach, and exploiting in particular the validity of the Taylor formula in the relational model of the λ-calculus and a resource call-by-value λ-calculus presented in [30], [13] provides a characterization of solvability for a call-by-value λ-calculus in terms of non-idempotent IT1....

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50 citations

### Cites background or methods from "Collapsing non-idempotent intersect..."

...Its syntax is defined by the following grammar (the same as in [15]):...

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...We use the relational model of [15], which is also a model of ordinary λ-calculus, unlike the model V of [8]....

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...For more details we refer the reader to [20,15]....

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...The starting points of our work are [7,6,15]....

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...The resource λv -calculus consists of the language rΛ t and the reduction →v: it is the resource CBV λ-calculus of [15] plus the σ1- and σ3-rules....

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43 citations

### Cites background or methods from "Collapsing non-idempotent intersect..."

...Actually, it can be shown that Lemma 7 holds not only for the relational semantics but also for any model of the bang calculus coming from a model of differential LL which satisfies a version of the Taylor formula [17, 18]....

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...1 below) in a purely combinatorial way (along the lines of [10, 17]), without using a reducibility argument....

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...Our definition of Taylor expansion is a generalization of analogous deeply studied notions for CBN [20, 22, 33] and CBV [10, 17] λ-calculi....

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...It can be shown that both call-by-name [21, 22] and call-by-value [10, 17] resource calculi can be embedded in the resource bang calculus....

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...1 is a generalization of System R [14] for CBN λ-calculus and the type system used in [17] for CBV λ-calculus....

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29 citations

### Cites background or methods from "Collapsing non-idempotent intersect..."

...For Plotkin’s original CbV λ-calculus, it has been introduced by Ehrhard [23]....

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...Here we introduce Ehrhard’s multi type system for CbV [23] and show that—with respect to it—the fireball calculus λfire fails the denotational test of the benchmark sketched in Sect....

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...We connect the size of type derivations for a term with its evaluation via rewriting, and the size of elements in its denotation with the size of its normal form, in a model coming from the linear logic interpretation of CbV and presented as a type system: Ehrhard’s relational semantics for CbV [23]....

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...Among them, Ehrhard’s [23], Diaz-Caro, Manzonetto, and Pagani’s [22], Carraro and Guerrieri’s [13], Ehrhard and Guerrieri’s [24], and Guerrieri’s [31] deal with CbV, while de Carvalho’s [14,16], Bernadet and Lengrand’s [8], de Carvalho, Pagani, and Tortora de Falco’s [17], Accattoli, Graham-Lengrand, and Kesner’s [2] provide exact bounds....

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...It recasts in CbV de Carvalho’s work for CbN [14,16], building on a type system introduced by Ehrhard [23] for Plotkin’s original CbV λ-calculus λv [45]....

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27 citations

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