  Wadler and Thiemann unified type-and-effect systems with monadic semantics
via a syntactic correspondence and soundness results with respect to an
operational semantics. They conjecture that a general, "coherent" denotational
semantics can be given to unify effect systems with a monadic-style semantics.
We provide such a semantics based on the novel structure of an indexed monad,
which we introduce. We redefine the semantics of Moggi's computational
lambda-calculus in terms of (strong) indexed monads which gives a one-to-one
correspondence between indices of the denotations and the effect annotations of
traditional effect systems. Dually, this approach yields indexed comonads which
gives a unified semantics and effect system to contextual notions of effect
(called coeffects), which we have previously described.
