I motivate a variation (due to K. Szlachányi) of monoidal categories called skew-monoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the well-known monoidal case. In my (to my knowledge new) version it becomes a statement of uniqueness of normalizing rewrites. I present a proof of this coherence theorem and also formalize it fully in the dependently typed programming language Agda.