Causal Inference is the statistical discipline that seeks to give quantitative answers to questions about causal relationships (‘does smoking cause cancer?’) and counterfactuals (‘had I not smoked, what is the probability that I would not have got cancer?’). In this talk, we show how to build a typed and compositional causal language with clear semantics on top of a typed probabilistic programming language. In analyzing the causal framework ChiRho, we extract several key abstractions such as grading and applicatives and showcase their power by implementing them as a definitional causal library in Haskell.