Adding one to the functional programming list...

I can’t remember where I found it, but there was a brilliant explanation of how functional code maps value. Remember, in a functional program, the basic notation is x → y, that is, for every function, it maps value x to another value y. Things like map() map an array to another array, while reduce() maps a single thing (an array) to another single thing (a value). How does functional programming encode other things?

Well, there’s

x → y

x is mapped to y

x → y∪E

x is mapped to y or Error (Maybe)

x → P(y)

x is mapped to all possible values of y (Random Number Generators)

x → (S -> y ⨯ S)

x is mapped to a function that takes a state and returns a value and a new state (State)

x → Σy

x is mapped to the set of all real-world consequences (IO)

The other day I realized that there’s one missing from this list:

x → ♢y

x is mapped to y eventually (Promises)

I’m not sure what to do with this knowledge, but it’s fun to realize I actually knew one more thing than my teacher.  Note that the first case, x → y, really does cover all sum (union) and product (struct) types, which tells me that the ML-style languages’ internal type discrimination features are orthogonal to their encapsulation of non-linear mappings.

The really weird thing is to realize that the last four are all order-dependent.  They’re all about making sure things happen in the correct sorted order (and temporal order, if that matters).  That leads me to think more about compiler design…