Differentials and distances in probabilistic coherence spaces
| Autor: | Ehrhard, Thomas |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Logical Methods in Computer Science, Volume 18, Issue 3 (August 8, 2022) lmcs:6511 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.46298/lmcs-18(3:2)2022 |
| Popis: | In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of "local" differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful. Comment: extended version of arXiv:1902.04836 . Improved redaction of the proof of the main result of Section 2 (expectation of computation time) |
| Databáze: | arXiv |
| Externí odkaz: |
|