Denotational semantics for languages for inference: semirings, monads, and tensors
CoRR(2023)
摘要
Computational effects are commonly modelled by monads, but often a monad can
be presented by an algebraic theory of operations and equations. This talk is
about monads and algebraic theories for languages for inference, and their
connections to semirings and tensors.
A basic class of examples of algebraic theories comes from considering the
theory of modules for a semiring, e.g. the theory of unnormalized
distributions, where the semiring is that of the non-negative real numbers. We
propose that an interesting perspective is given by studying theories via
semirings, and to this end explore several examples of subtheories of module
theories, mostly relating to probability. Our main contribution concerns the
commutative combination of effects, as studied by Hyland, Plotkin and Power: we
observe that while the semiring tensor does not in general determine the tensor
of subtheories of module theories, it still does in several fundamental
probabilistic examples.
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