• Monad

Monad

P.S: Just Rough Notes - WIP - Will have to Develop to a readable content :)

Monad, M[T], is an amplification (or considered as a wrapper) of a generic type T such that

1. Any Monad, M[T] can be created by applying a creation function on T x: T => M[T]

2. It provides a mechanism to for applying a function which takes T and gives out Monad of the resultant type

   (x: M[T], fn: T => M[Z]) => M[Z]

These two featurs must obey the following 3 Monadic law : -

1. If you apply the Monad creation function to an any existing Monadic instnace then it should give out a logical equivalent Monad

   monad1 = M[T] monad2 = creationFn(monad1)

   monad 1 and monad2 should be same

2. Appying a function to the result of applying the construction function should always produce a logically equivalent Monad if we apply that function directly on the value

3. Composition rule :

	val f = (X) => M[Y]
	val g = (Y) => M[Z]
	M[X] mx = f;
	val my : M[Y] = monadicFunction(mx, f)
	val mz1 : M[Z]  = monadicFunction(my, g)

	val h: M[Z] = monadicCompose(f, g);
	val mz2 = monadicFunction(mx, h);

Applying to a value a first function followed by applying to the result a second function should produce a logically identical Monad if you applying a composition function to the origial value.