From Differential Linear Logic to Coherent Differentiation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914654158061568 |
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| author | Ehrhard, Thomas |
| author_facet | Ehrhard, Thomas |
| contents | In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are compatible with determinism. Indeed, due to the Leibniz rule of the differential calculus, differential linear logic and the differential lambda-calculus feature an operation of addition of proofs or terms operationally interpreted as a strong form of nondeterminism. The main idea of coherent differentiation is that these sums can be controlled and kept in the realm of determinism by means of a notion of summability, upon enforcing summability restrictions on the derivatives which can be written in the models and in the syntax. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Differential Linear Logic to Coherent Differentiation Ehrhard, Thomas Logic in Computer Science In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are compatible with determinism. Indeed, due to the Leibniz rule of the differential calculus, differential linear logic and the differential lambda-calculus feature an operation of addition of proofs or terms operationally interpreted as a strong form of nondeterminism. The main idea of coherent differentiation is that these sums can be controlled and kept in the realm of determinism by means of a notion of summability, upon enforcing summability restrictions on the derivatives which can be written in the models and in the syntax. |
| title | From Differential Linear Logic to Coherent Differentiation |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2401.14834 |