We want to program only using functions. (“functional programming” after all -FP).
-
Then, we have a first big problem. This is a program:
f(x) = 2 * x
g(x,y) = x / y
How can we say what is to be executed first? How can we form an ordered sequence of functions (i.e. a program) using no more than functions?
Solution: compose functions. If you want first g
and then f
, just write f(g(x,y))
. OK, but …
- More problems: some functions might fail (i.e.
g(2,0)
, divide by 0). We have no “exceptions” in FP. How do we solve it?
Solution: Let’s allow functions to return two kind of things: instead of having g : Real,Real -> Real
(function from two reals into a real), let’s allow g : Real,Real -> Real | Nothing
(function from two reals into (real or nothing)).
- But functions should (to be simpler) return only one thing.
Solution: let’s create a new type of data to be returned, a “boxing type” that encloses maybe a real or be simply nothing. Hence, we can have g : Real,Real -> Maybe Real
. OK, but …
- What happens now to
f(g(x,y))
?f
is not ready to consume aMaybe Real
. And, we don’t want to change every function we could connect withg
to consume aMaybe Real
.
Solution: let’s have a special function to “connect”/“compose”/“link” functions. That way, we can, behind the scenes, adapt the output of one function to feed the following one.
In our case: g >>= f
(connect/compose g
to f
). We want >>=
to get g
's output, inspect it and, in case it is Nothing
just don’t call f
and return Nothing
; or on the contrary, extract the boxed Real
and feed f
with it. (This algorithm is just the implementation of >>=
for the Maybe
type).
-
Many other problems arise which can be solved using this same pattern: 1. Use a “box” to codify/store different meanings/values, and have functions like
g
that return those “boxed values”. 2. Have composers/linkersg >>= f
to help connectingg
's output tof
's input, so we don’t have to changef
at all. -
Remarkable problems that can be solved using this technique are:
-
having a global state that every function in the sequence of functions (“the program”) can share: solution
StateMonad
. -
We don’t like “impure functions”: functions that yield different output for same input. Therefore, let’s mark those functions, making them to return a tagged/boxed value:
IO
monad.
-
PS: this answer can be found on SO at this link: https://stackoverflow.com/a/28135478