Map and Reduce Monad for Clojure… What about a Juxt Monad?

Question

Whilst learning Clojure, I\'ve spent ages trying to make sense of monads - what they are and how we can use them.... with not too much success. However, I found an excellent \'M

Answer 1

Your examples are not monads. A monad represents composable computational steps. In the trivial identity monad, the computational step is just an expression evaluation.

In the maybe monad, a step is an expression that may succeed or fail.

In the sequence monad, a step is an expression that produces a variable number of results (the elements of the sequence).

In the writer monad, a computational step is a combination of expression evaluation and log output. In the state monad, a computational step involves accessing and/or modifying a piece of mutable state.

In all these cases, the monad plumbery takes care of correctly combining steps. The m-result function packages a "plain" value to fit into the monadic computation scheme, and the m-bind function feeds the result of one computational step into the next computational step.

In (map + a b), there are no computational steps to be combined. There is no notion of order. It's just nested expression evaluation. Same for reduce.