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We define sound and adequate denotational and operational semantics for thestochastic lambda calculus. These two semantic approaches build on previouswork that used similar techniques to reason about higher-order probabilisticprograms, but for the first time admit an adequacy theorem relating theoperational and denotational views. This resolves the main issue left open in(Bacci et al. 2018).

Universal Semantics for the Stochastic Lambda-Calculus