We describe a novel approach to mathematical description of context-dependent notions of computation and the semantics of corresponding programming languages. Notably, this covers various notions of dataflow computation (stream-based computation) and tree transformations. The approach is based on symmetric monoidal comonads. It is analogous to Moggi's treatment of effects based on strong monads and continues the line of Brookes, Geva and Van Stone's early work on "computational" comonads for intensional semantics. Especially, we pay attention to the precision and theoretical cohesion that for some notions of context-dependence can be achieved by "parametrizing" the appropriate "basic" comonads.