Abstract
Differential dataflow is a recent approach to incremental computation that relies on a partially ordered set of differences. In the present paper, we aim to develop its foundations. We define a small programming language whose types are abelian groups equipped with linear inverses, and provide both a standard and a differential denotational semantics. The two semantics coincide in that the differential semantics is the differential of the standard one. Möbius inversion, a well-known idea from combinatorics, permits a systematic treatment of various operators and constructs.
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Abadi, M., McSherry, F., Plotkin, G.D. (2015). Foundations of Differential Dataflow. In: Pitts, A. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2015. Lecture Notes in Computer Science(), vol 9034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46678-0_5
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DOI: https://doi.org/10.1007/978-3-662-46678-0_5
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