Positive Sharing and Abstract Machines
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908518785744896 |
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| author | Accattoli, Beniamino Coen, Claudio Sacerdoti Wu, Jui-Hsuan |
| author_facet | Accattoli, Beniamino Coen, Claudio Sacerdoti Wu, Jui-Hsuan |
| contents | Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown.
In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quadratic slowdown somehow reappears when analyzing the cost of the machine. We then design an optimized machine for the positive $λ$-calculus, which we prove efficient. The optimization is based on a new slicing technique which is dual to the standard structure of machine environments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive Sharing and Abstract Machines Accattoli, Beniamino Coen, Claudio Sacerdoti Wu, Jui-Hsuan Logic in Computer Science Programming Languages Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quadratic slowdown somehow reappears when analyzing the cost of the machine. We then design an optimized machine for the positive $λ$-calculus, which we prove efficient. The optimization is based on a new slicing technique which is dual to the standard structure of machine environments. |
| title | Positive Sharing and Abstract Machines |
| topic | Logic in Computer Science Programming Languages |
| url | https://arxiv.org/abs/2506.14131 |