One popular example of a monad is a type constructor that extends the given type - a “wrapper”, if you will, where a value can be wrapped in a trivial way (e.g. x -> {x} or x -> x?), and a double wrapping can be trivially unwrapped (“naturally transformed”) into a single one: {{xyz}} -> {xyz}. (Note that unwrapping the last remaining layer will not be always possible - e.g., while {x} -> x does indeed make sense, {x, y, z} -> … or x? -> x do/may not.)
> where a value can be wrapped in a trivial way (e.g. x -> {x} or x -> x?)
> and a double wrapping can be trivially unwrapped (“naturally transformed”) into a single one: {{xyz}} -> {xyz}
You've described the "pure" and "join" operations (in Haskell terms), which are two of the three requirements for a monad. The third and final requirement is that there must be a way to lift an arbitrary function on plain values to work on "wrapped" values: (x → y) → ({x} → {y}).
