We develop Boolean-valued domain theory and show how the lambda-calculus 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.

翻译：我们发展了布尔值域理论，并展示了如何利用域值随机变量解释lambda演算。本文侧重于自反域构造而非语言及其语义学。等式的概念必须在布尔代数中解释，当我们说某个等式在模型中有效时，意味着其解释是布尔代数的最大元。