Games, mobile processes, and functionss -- alternating, concurrent, and well-bracketed semantics
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| Format: | Preprint |
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2025
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| author | Jaber, Guilhem Sangiorgi, Davide |
| author_facet | Jaber, Guilhem Sangiorgi, Davide |
| contents | We establish a tight connection between two models of the $λ$-calculus, namely Milner's encoding into the $π$-calculus (precisely, the Internal $π$-calculus), and operational game semantics (OGS). We first investigate the operational correspondence between the behaviours of the encoding provided by $π$ and OGS. We do so for various LTSs: the standard LTS for $π$ and a new `concurrent' LTS for OGS; an `output-prioritised' LTS for $π$ and the standard alternating LTS for OGS. We then show that the equivalences induced on $λ$-terms by all these LTSs (for $π$ and OGS) coincide. We also prove that when equivalence is based on complete traces, the `concurrent' and `alternating' variants of OGS also coincide with the `well-bracketed' variant.
These connections allow us to transfer results and techniques between $π$ and OGS. In particular: we import up-to techniques from $π$ onto OGS; we derive congruence and compositionality results for OGS from those of $π$; we transport the notion of complete traces from OGS onto $π$, obtaining a new behavioural equivalence that yields a full abstraction result for the encoding of $λ$-terms with respect to contexts written in a $λ$-calculus extended with store.
The study is illustrated for both call-by-value and call-by-name. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Games, mobile processes, and functionss -- alternating, concurrent, and well-bracketed semantics Jaber, Guilhem Sangiorgi, Davide Logic in Computer Science 68N15, 68Q85, 03B70 We establish a tight connection between two models of the $λ$-calculus, namely Milner's encoding into the $π$-calculus (precisely, the Internal $π$-calculus), and operational game semantics (OGS). We first investigate the operational correspondence between the behaviours of the encoding provided by $π$ and OGS. We do so for various LTSs: the standard LTS for $π$ and a new `concurrent' LTS for OGS; an `output-prioritised' LTS for $π$ and the standard alternating LTS for OGS. We then show that the equivalences induced on $λ$-terms by all these LTSs (for $π$ and OGS) coincide. We also prove that when equivalence is based on complete traces, the `concurrent' and `alternating' variants of OGS also coincide with the `well-bracketed' variant. These connections allow us to transfer results and techniques between $π$ and OGS. In particular: we import up-to techniques from $π$ onto OGS; we derive congruence and compositionality results for OGS from those of $π$; we transport the notion of complete traces from OGS onto $π$, obtaining a new behavioural equivalence that yields a full abstraction result for the encoding of $λ$-terms with respect to contexts written in a $λ$-calculus extended with store. The study is illustrated for both call-by-value and call-by-name. |
| title | Games, mobile processes, and functionss -- alternating, concurrent, and well-bracketed semantics |
| topic | Logic in Computer Science 68N15, 68Q85, 03B70 |
| url | https://arxiv.org/abs/2504.18227 |