# Evaluating functions as processes

##### Citations

77 citations

### Cites background or methods from "Evaluating functions as processes"

...Explicit substitutions (ES) have been connected to linear logic by Kesner and co-authors in a sequence of works [26, 32, 33], culminating in the linear substitution calculus (LSC), a new formalism with ES behaviorally isomorphic to proof nets (introduced in [6], developed in [1, 3, 4, 7, 10], and bearing similarities with calculi by De Bruijn [25], Nederpelt [42], and Milner [41])....

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...The presentation in use here has already appeared in [3, 10] (see also [1, 4]) as the weak head strategy of the linear substitution calculus (which is obtained by considering all contexts as evaluation contexts), and it avoids many technicalities of the original one....

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...The strategies modularly encoding the various machines (generically noted ⊸ and parametric in a fixed notion of evaluation contexts) are in fact call-byname/value/need versions of weak linear head reduction (WLHR), a fundamental notion in the theory of linear logic [3, 18, 21, 27, 40]....

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...Evaluation as Communication: we implicitly establish a link between the KAM/MAM and the π-calculus, given that the evaluation of a term via WLHR is isomorphic to evaluation via Milner’s encoding in the π-calculus [3]....

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61 citations

### Cites background or methods from "Evaluating functions as processes"

...This notion of reduction is deterministic and tightly related to the π-calculus [3] and Krivine Abstract Machine [7, 14]....

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...Linear logic and concurrency: it is tightly connected with the translations of λ-calculus into linear logic [4] and the πcalculus [3]....

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...The alternative approach used here, already in use in [2, 3, 5], improves the original presentation in several aspects: there is no need to work with virtual redexes, there is a one-to-one correspondence between LHR in proof-nets and LHR in λlsub, and LHR can be seen as a strategy of λlsub although it is not a strategy of β-reduction....

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...A new generation of calculi with ES at a distance, having very simple meta-theories and conceived as behaviorally equivalent copies of graphical languages such as linear logic proof-nets, have recently been introduced by Accattoli and Kesner in [6] (see also [2, 3, 5])....

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...Linear head reduction (LHR): given the deep connection between λlsub and proof-nets [4], our calculus naturally expresses linear head reduction, a notion of evaluation for proof nets that is connected with other fundamental models [3, 5, 14, 15, 17, 29]....

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36 citations

### Cites background or methods from "Evaluating functions as processes"

...In the literature, (TCBN is known as weak linear head reduction, and it has been shown to be the strategy implemented by both the KAM [15, 4] and the πcalculus [3]....

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...Note that such a definition is not ad-hoc, as it matches CBV weak linear head reduction as in [3], where it is defined by mimicking evaluation in the π-calculus (according to a CBV translation)....

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34 citations

### Cites background or result from "Evaluating functions as processes"

...[5] Beniamino Accattoli, Pablo Barenbaum & Damiano Mazza (2014): Distilling abstract machines....

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...[1] Beniamino Accattoli (2011): Jumping around the box: graphical and operational studies on λ-calculus and Linear Logic....

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...[4] Beniamino Accattoli (2013): Evaluating functions as processes....

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...[6] Beniamino Accattoli & Claudio Sacerdoti Coen (2014): On the Value of Variables....

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...[10] Beniamino Accattoli & Luca Paolini (2012): Call-by-Value Solvability, Revisited....

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32 citations

### Cites background or methods from "Evaluating functions as processes"

...Partial substitution allows to express linear-head reduction [19, 35], a notion of evaluation of proof nets that is strongly related to significant aspects of computer science [32, 2, 4]....

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...It was recently used in different investigations of computer science [4, 2, 3]....

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##### References

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### "Evaluating functions as processes" refers background in this paper

...This reformulation is justified by the following lemma, whose proof is along the one of the harmony lemma in [38] (p....

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...Nowadays, it takes a relevant part in the standard reference for the π-calculus [38], and in any introductory course about it....

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1,240 citations

### "Evaluating functions as processes" refers background in this paper

...In particular, Milner showed that Plotkin’s call-byname and call-by-value strategies [35] can be both faithfully represented....

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