A coherent differential PCF
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential linear logic are concerned, these models feature finite non-det...
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| Published in: | Logical methods in computer science Vol. 19, Issue 4 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science Association
26.10.2023
Logical Methods in Computer Science e.V |
| Subjects: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online Access: | Get full text |
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| Summary: | The categorical models of the differential lambda-calculus are additive
categories because of the Leibniz rule which requires the summation of two
expressions. This means that, as far as the differential lambda-calculus and
differential linear logic are concerned, these models feature finite
non-determinism and indeed these languages are essentially non-deterministic.
In a previous paper we introduced a categorical framework for differentiation
which does not require additivity and is compatible with deterministic models
such as coherence spaces and probabilistic models such as probabilistic
coherence spaces. Based on this semantics we develop a syntax of a
deterministic version of the differential lambda-calculus. One nice feature of
this new approach to differentiation is that it is compatible with general
fixpoints of terms, so our language is actually a differential extension of PCF
for which we provide a fully deterministic operational semantics. |
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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-19(4:7)2023 |