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We introduce Scruff, a new framework for developing AI systems using probabilistic programming. Scruff enables a variety of representations to be included, such as code with stochastic choices, neural networks, differential equations, and constraint systems. These representations are defined implicitly using a set of standardized operations that can be performed on them. General-purpose algorithms are then implemented using these operations, enabling generalization across different representations. Zero, one, or more operation implementations can be provided for any given representation, giving algorithms the flexibility to use the most appropriate available implementations for their purposes and enabling representations to be used in ways that suit their capabilities. In this paper, we explain the general approach of implicitly defined representations and provide a variety of examples of representations at varying degrees of abstraction. We also show how a relatively small set of operations can serve to unify a variety of AI algorithms. Finally, we discuss how algorithms can use policies to choose which operation implementations to use during execution.