in Programming, Haskell

There are a number of errors made in putative Monad tutorials in languages other than Haskell. Any implementation of monadic computations should be able to implement the equivalent of the following in Haskell:

minimal :: Bool -> [(Int, String)] minimal b = do x <- if b then [1, 2] else [3, 4] if x `mod` 2 == 0 then do y <- ["a", "b"] return (x, y) else do y <- ["y", "z"] return (x, y)

This should yield the local equivalent of:

Prelude> minimal True [(1,"y"),(1,"z"),(2,"a"),(2,"b")] Prelude> minimal False [(3,"y"),(3,"z"),(4,"a"),(4,"b")]

At the risk of being offensive, you, ahhh... really ought to understand *why* that's the result too, without too much effort... or you really shouldn't be writing a Monad tutorial. *Ahem.*

In particular:

- Many putative monadic computation solutions only work with a "container" that contains zero or one elements, and therefore do not work on lists.
`>>=`is allowed to call its second argument (`a -> m b`) an*arbitrary*number of times. It may be once, it may be dozens, it may be none. If you can't do that, you don't have a monadic computation. - A monadic computation has the ability to examine the intermediate results of the computation, and make decisions, as shown by the if statement. If you can't do that, you don't have a monadic computation.
- In statically-typed languages, the type of the inner value is not determined by the incoming argument. It's
`a -> m b`, not`a -> m a`, which is quite different. Note how`x`and`y`are of different types. - The monadic computation builds up a namespace as it goes along; note we determine
`x`, then somewhat later use it in the`return`, regardless of which branch we go down, and in both cases, we do not use it right away. Many putative implementations end up with a pipeline, where each stage can use the previous stage's values, but can not refer back to values before that. - Monads are not "about effects". The monadic computation I show above is in fact perfectly pure, in every sense of the term. And yes, in practice monad notation is used this way in real Haskell all the time, it isn't just an incidental side-effect.

A common misconception is that you can implement this in Javascript or similar languages using "method chaining". I do not believe this is possible; for monadic computations to work in Javascript at all, you *must* be nesting functions within calls to bind within functions within calls to bind... basically, it's impossibly inconvenient to use monadic computations in Javascript, and a number of other languages. A mere implementation of method chaining is not "monadic", and libraries that use method chaining are not "monadic" (unless they really do implement the rest of what it takes to be a monad, but I've so far never seen one).

If you *can* translate the above code correctly, and obtain the correct result, I don't guarantee that you have a proper monadic computation, but if you've got a bind or a join function with the right type signatures, and you can do the above, you're probably at least on the right track. This is the approximately minimal example that a putative implementation of a monadic computation ought to be able to do.