Programming benefits from a clear separation between pure, mathematical computation and impure, effectful interaction
with the world. Existing approaches to enforce this separation
include monads, type-and-effect systems, and capability systems.
All share a tension between precision and usability, and
each one has non-obvious strengths and weaknesses.
This paper aims to raise the bar in assessing such systems.

First, we propose a semantic definition of purity,
inspired by contextual equivalence, as a baseline for effect soundness
independent of any specific typing discipline.
Second, we propose that expressiveness should be measured by
the degree of completeness, i.e., how many semantically pure terms
can be typed as pure.
Using this measure, we focus on minimal meaningful effect and
capability systems and show that they are incomparable, i.e.,
neither subsumes the other in terms of expressiveness.

Based on this result, we
propose a synthesis and show that \emph{type, ability, and effect systems}
combine their respective strengths while
avoiding their weaknesses.
As part of our formal model, we provide a logical relation
to facilitate proofs of purity and other
properties for different effect typing disciplines.