Can an extra operation help explain things?

```haskell
appEval :: forall a (b :: TYPE rep).
(a -> b) -> Eval a -> b
appEval f (Eval (IO m)) =
case runRW# m of
(# _, a #) -> f a
```

Ignoring levity polymorphism, this could be implemented

```haskell
appEval f m = runEval (f <$> m)
```

Moreover,

```haskell
runEval = appEval id
```

But what makes this interesting, I think, is its relationship with `>>=`: aside from arity wibbles,

```haskell
m >>= f = appEval f m
```

This strikes me as a really pleasant property.

Start by reviewing the existing Eval, runEval, and appEval definitions, along with the relationship to >>= described in the issue. Determine whether the proposed operation has a concrete API role and how its semantics would be validated; done means an agreed design with corresponding tests or documentation.

Written by the indexing model from the issue text.