 Observe that the framework of concrete data structures gives the necessary notions to reconstruct a semantical version of sequentiality. Roughly, a monotonic function \(f\) from states of \(M\) to states of \(M'\) is sequential (at state \(x\)) if, for any output cell \(c'\), there is an input cell \(c\) that must be filled in any transition from \(x\) to \(y\) such that the transition from \(f(x)\) to \(f(y)\) fills \(c'\) (if such a \(c'\) does exist) (Curien 1986: Def. 2.4.5). The cell \(c\) is the sequentiality index for \(f\) at \(x\) for \(c'\).