We present a Curry–Howard correspondence for Gödel logic based on a simple natural deduction reformulating the hypersequent calculus for this logic. The resulting system extends simply typed λ-calculus by a symmetric higher-order communication mechanism between parallel processes. The normalization proof employs reductions that implement forms of code mobility. We consider this result from a broader perspective and, following A. Avron's 1991 thesis on the connection between hypersequents and parallelism, we discuss the generalisation of the employed techniques for other intermediate logics.