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Monad

{ This is my poor understanding of a monad. I am not actually sure if it's correct lol :D TODO: get back to this. ~drummyfish }

Monad is a mathematical concept which has become useful in functional programming and is one of the very basic design patterns in this paradigm. A monad basically wraps some data type into an "envelope" type and gives a way to operate with these wrapped data types which greatly simplifies things like error checking or abstracting input/output side effects.

A typical example is a maybe monad which wraps a type such as integer to handle exceptions such as division by zero. A maybe monad consists of:

1. The maybe(T) data type where T is some other data type, e.g. maybe(int). Type maybe(T) can have these values:

• just(X) where X is any possible value of T (for int: -1, 0, 1, 2, ...), or
• nothing, a special value that says no value is present

2. A special function return(X) that converts value of given type into this maybe type, e.g. return(3) will return just(3)
3. A special combinator X >>= f which takes a monadic (maybe) values X and a function f and does the following:

• if X is nothing, gives back nothing
• if X is a value just(N), gives back the value f(N) (i.e. unwraps the value and hand it over to the function)

Let's look at a pseudocode example of writing a safe division function. Without using the combinator it's kind of ugly:

divSafe(x,y) = // takes two maybe values, returns a maybe value
  if x == nothing
    nothing else
    if y == nothing
      nothing else
        if y == 0
          nothing else
            just(x / y)

With the combinator it gets much nicer (note the use of lambda expression):

divSafe(x,y) =
  x >>= { a: y >== { b: if b == 0 nothing else a / b } }

Languages will typicall make this even nicer with a syntax sugar such as:

divSafe(x,y) = do
  a <- x,
  b <- y,
  if y == 0 nothing else return(a / b)

TODO: I/O monad TODO: general monad TODO: example in real lang, e.g. haskell

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