  Many effect systems for algebraic effect handlers are designed to guarantee
that all invoked effects are handled adequately. However, respective
researchers have developed their own effect systems that differ in how to
represent the collections of effects that may happen. This situation results in
blurring what is required for the representation and manipulation of effect
collections in a safe effect system.
  In this work, we present a language ${\lambda_{\mathrm{EA}}}$ equipped with
an effect system that abstracts the existing effect systems for algebraic
effect handlers. The effect system of ${\lambda_{\mathrm{EA}}}$ is
parameterized over effect algebras, which abstract the representation and
manipulation of effect collections in safe effect systems. We prove the
type-and-effect safety of ${\lambda_{\mathrm{EA}}}$ by assuming that a given
effect algebra meets certain properties called safety conditions. As a result,
we can obtain the safety properties of a concrete effect system by proving that
an effect algebra corresponding to the concrete system meets the safety
conditions. We also show that effect algebras meeting the safety conditions are
expressive enough to accommodate some existing effect systems, each of which
represents effect collections in a different style. Our framework can also
differentiate the safety aspects of the effect collections of the existing
effect systems. To this end, we extend ${\lambda_{\mathrm{EA}}}$ and the safety
conditions to lift coercions and type-erasure semantics, propose other effect
algebras including ones for which no effect system has been studied in the
literature, and compare which effect algebra is safe and which is not for the
extensions.
