Interpreting Lambda Calculus in Domain-Valued Random Variables

We develop Boolean-valued domain theory and show how the lambdacalculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of equality has to be interpreted in the Boolean algebra and when we say that an equation is valid in the model we mean that its interpretation is the top element of the Boolean algebra.

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