Your description means they are design patterns: a technique to solve a problem that appears repeatedly. What trips people up is that monad is a 2nd-level pattern, as can be seen in the type. 'List a' is-a pattern for nondeterminism. 'Maybe a' is-a pattern for handling failure. Instancing 'm a' is a pattern
for 'sequencing effects with branching' and
also other patterns for various other applications.
I still wouldn't call them design patterns. At least in haskell, they are not used like design patterns in OOP languages. They are more inherent properties of certain types (Maybe a "is" a monad etc.) and the instances are provided regardless of whether they are needed to solve a problem or not.
In OOP design patterns not only solve a specific problem, they are only used to solve the problem (no need to sprinkle the visitor-pattern all over your classes just because it's possible). Monad/Functor etc. instances are defined where they are possible. I view them as making inherent properties visible and explicit ("this action obeys these laws").
They are used to solve problems, but mainly by making abstract properties directly visible and reminding the programmer that he can just view them as this abstract concept and reuse existing machinery.
