Abstract
From a programming language viewpoint, the \(\lambda \)-calculus formalises several features of the modern description of computation and its implementation. We present a denotational semantics for the untyped calculus that captures a basic feature of probabilistic programming languages, namely probability distributions as both the objects and the result of a computation.
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Notes
- 1.
We can show that this indeed defines a inner product.
- 2.
It can be shown that a linear mapping is continuous if and only if it is bounded. For a proof see Theorem 1.5.7 of [2].
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Di Pierro, A. (2017). A Probabilistic Semantics for the Pure \(\lambda \)-Calculus. In: Hung, D., Kapur, D. (eds) Theoretical Aspects of Computing – ICTAC 2017. ICTAC 2017. Lecture Notes in Computer Science(), vol 10580. Springer, Cham. https://doi.org/10.1007/978-3-319-67729-3_5
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DOI: https://doi.org/10.1007/978-3-319-67729-3_5
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