The call-by-value λ-calculus: a semantic investigation

Pravato, Alberto; Rocca, Simona Ronchi Della; Roversi, Luca

doi:10.1017/s0960129598002722

Cited by 18 publications

(14 citation statements)

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“…Call-by-value. Following [28,13], models of the CbV λ -calculus can be defined using Girard's "boring" CbV translation of the intuitionistic implication into LL. It is enough to find an object X in L satisfying !X !X X (or equivalently, !…”

Section: The Bang Calculus With Respect To Cbn and Cbv λ -Calculi Sementioning

confidence: 99%

“…We plan to investigate whether the (syntactic) logical relations introduced by Pitts in [26] can give an inspiration to define semantic logical relations in the untyped setting. Another source of inspiration might be the study of other concrete LL based models of the CbV λ -calculus, such as Scott domains and coherent semantics [28,13]. 6 Relational semantics interprets terms in the object U -defined in (2), where a α denotes the ordered pair (a, α) -of the category Rel of sets and relations.…”

Section: The Bang Calculus With Respect To Cbn and Cbv λ -Calculi Sementioning

confidence: 99%

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The Bang Calculus and the Two Girard's Translations

Guerrieri

Manzonetto

2019

Electron. Proc. Theor. Comput. Sci.

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We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value λ -calculi to be encoded in. We investigate how the bang calculus subsumes both call-by-name and call-by-value λ -calculi from a syntactic and a semantic viewpoint.1 Actually the full symmetry of such a category is not really essential as far as the λ -calculus is concerned, it is however quite natural from the LL viewpoint: LL restores the classical involutivity of negation in a constructive setting.2. From a semantic viewpoint, we show in §4 that every LL-based model U of the bang calculus (as categorically defined in [16]) provides a model for both this was done only for the special case of relational semantics). Moreover, given a λ -term t, we investigate the relation between its interpretations |t| n in CbN (resp. |t| v in CbV) and the interpretation · of its translation t n (resp. t v ) into the bang calculus. We prove that the diagram below on the left (for CbN) commutes, whereas we give a counterexample (in the relational semantics) to the commutation of the diagram below on the right (for CbV). We conjecture that there still exists a relationship in CbV between |t| v and t v , but it should be more sophisticated than in CbN.In order to achieve these results in a clearer and simpler way, we have slightly modified (see §2) the syntax and operational semantics of the bang calculus with respect to its original formulation in [16].

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Section: The Bang Calculus With Respect To Cbn and Cbv λ -Calculi Sementioning

confidence: 99%

Section: The Bang Calculus With Respect To Cbn and Cbv λ -Calculi Sementioning

confidence: 99%

The Bang Calculus and the Two Girard's Translations

Guerrieri

Manzonetto

2019

Electron. Proc. Theor. Comput. Sci.

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“…Intersection types can be viewed also as a restriction of the domain theory in logical form, see [1], to the special case of modelling pure lambda calculus by means of -algebraic complete lattices. Intersection types have been used as a powerful tool both for the analysis and the synthesis of -models, see e.g., [3], [8], [2], [17], [16], [25], [21], [26]. On the one hand, intersection type disciplines provide finitary inductive definitions of interpretation of -terms in models.…”

Section: Jaap Van Oosten Geometric Aspects Of the Effective Toposmentioning

confidence: 99%

2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08

Wilkie¹

2009

Bull. symb. log

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The program included three tutorial courses, twelve invited plenary lectures, and sixteen invited lectures in four special sessions corresponding to the four main topics. There were about eighty contributed papers and 170 participants from twenty-eight countries. Sixteen students and recent Ph.D's were assisted by local grants (for example, by the Swiss Academy of Sciences) and a further eight by the ASL.

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“…, was qualified as boring by Girard and received little attention in the literature [32,35,15,17,18,31]. Usually, it is said to represent Plotkin's call-by-value (CBV) λ βv -calculus [34].…”

Section: Introductionmentioning

confidence: 99%

Proof nets and the call-by-value λ-calculus

Accattoli

2015

Theoretical Computer Science

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Please cite this article in press as: B. Accattoli, Proof nets and the call-by-value λ-calculus, Theoret. Comput. Sci. (2015), http://dx. AbstractThis paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize an isomorphism between the two systems: every single rewriting step on the calculus maps to a single step on proof nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets. Moreover, we provide a simple correctness criterion for our proof nets, which employ boxes in an unusual way, and identify a subcalculus that is shown to be as expressive as the full calculus.

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The call-by-value λ-calculus: a semantic investigation

Cited by 18 publications

References 18 publications

The Bang Calculus and the Two Girard's Translations

The Bang Calculus and the Two Girard's Translations

2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08

Proof nets and the call-by-value λ-calculus

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