Variable Elimination ( \(\textsf{VE}\) ) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goal is to understand Variable Elimination as an algorithm acting on programs in an idealized probabilistic functional language—a linear simply-typed \(\lambda \) -calculus suffices for our purpose. Precisely, we express \(\textsf{VE}\) as a term rewriting process, which transforms a global definition of a variable into a local definition, by swapping and nesting let-in expressions. We exploit in an essential way linear types.