As probabilistic computation plays an increasing role in diverse fields in computer science, researchers have designed new languages to facilitate the development of probabilistic programs. In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value. The most notable feature of our calculus is that it is founded upon sampling functions, which map the unit

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... erval to probability domains. As a consequence, we achieve a unified representation scheme for all types of probability distributions. In order to support an efficient implementation of the calculus, we also develop a refinement type system which is capable of distinguishing expressions denoting regular values from expressions denoting probability distributions. We use a novel formulation of the intuitionistic modal logic S4 with an intersection connective in the refinement type system. We present preliminary evidence that a probabilistic language based upon our calculus is viable in applications involving massive probabilistic computation.