Descriptive variable names are a code smell.

More precisely, if you can name your variables after more descriptive things than f , a , b , and so on, then your code is probably monomorphic.

Monomorphic code is much more likely to be incorrect than polymorphic code, because for every type signature, there are many more possible implementations.

Thus, descriptive variable names are a code smell, indicating your code is overly monomorphic and more likely to be broken.

Fortunately, you can turn this around with a little refactoring process I call, extract polymorphism from monomorphism. While this refactoring does not always eliminate monomorphism, it can defer it, which is an overriding theme of functional programming (defer all the things!).

In the next section, I’ll show you this refactoring in action.

Monomorphism in String Functions

Some functions are maximally monomorphic — which is to say, every type in the signature is concrete, and there are no values in the signature described by type parameters.

For such monomorphic functions, the “number” of possible implementations is exceedingly great: we can implement them in numerous ways that satisfy the type signature, but are horribly broken.

For example, consider how many ways there are to implement the following function:

foo :: List Char -> List Char -> List Char

def foo ( string1 : List [ Char ], string2 : List [ Char ]) : List [ Char ]

There are a huge number of ways to implement the function. The type signature of the function barely constrains it. All we know is that if we feed the function two strings, we’ll get back a string.

The string may or may not be related to either input. It may contain random hard-coded characters. Or it might be empty.

Now consider how many ways there are to implement the following function:

foo :: forall a . List a -> List a -> List a

def foo [ A ]( fst : List [ A ], snd : List [ A ]) : List [ A ]

This function is at least somewhat polymorphic. There are fewer ways we can implement the function. In particular, we can’t just hard-code some elements in a list, because we have no ability to manufacture values of an arbitrary type.

Adding a type parameter to describe the type of the elements in the list has constrained our space of possible solutions!

However, there’s still lots of ways to implement the function: we can return the first list, return the second list, return some mashup of the first and second lists, or return an empty list.

Let’s say we take this one step further and introduce even more polymorphism into the code, hiding the fact that the second parameter and return values are lists:

foo :: forall a b . List a -> ( a -> b ) -> ( b -> b -> b ) -> b -> b

def foo [ A , B ]( as : List [ A ], b : B , ab : A => B , bbb : B => B => B ) : B

There are considerably fewer ways to implement this function. The function can return b (a useless definition, since it doesn’t use the type parameters), or it convert a ’s to b ’s, and smash b ’s together to produce a final b .

If we continued this process to its logical conclusion, and leverage standard type classes, we might end up with the following types:

foo :: forall f a r . ( Foldable f , Semigroup r ) => f a -> ( a -> r ) -> r -> r

def foo [ F [ _ ] : Foldable , A , R: Semigroup ]( fa : F [ A ], ar : A => R , r : R ) : R

This is a sufficiently high degree of polymorphism that our variable names are now totally abstract, named after their types.

It’s high enough I’m betting you can guess what the function foo is supposed to do (let me know if you need a hint!).

Note that in our process of trying to polymorphize this function, we lost the original type signature, which was, presumably, required by a bunch of code.

Our program may not need the original type signature, if we can force the polymorphism higher into the code base.

However, if our code does require the original type signature, then we can recapture the original definition quite simply:

foo0 :: List Char -> List Char -> List Char foo0 l1 l2 = foo l1 pure l2

def foo0 ( l1 : List [ Char ], l2 : List [ Char ]) : List [ Char ] = foo [ List , Char , List [ Char ]]( l1 , List ( _ ), l2 )

While these signatures are the same as the old ones, their implementation is trivial, and very easy to reason about.

In essence, what we’ve done is created a little bubble of polymorphism in which we pushed as much logic as possible, so that the amount of monomorphic code we have to reason about is as small as possible.

Of course, in many cases, you can push the polymorphism even higher, by looking at the functions that require foo and generalizing them.

This is just a toy example, so I’ll briefly run through a real-world example to show how the technique works in the wild.

Real-World Example: Grouping

A few months ago, I was working on a function that had this type signature:

type JoinMap = Map ( Set Data ) ( List Data ) groupByJoinKeys :: List ( List Data -> Data ) -> List Data -> JoinMap

type JoinMap = Map [ Set [ Data ] , List [ Data ]] def groupByJoinKeys ( joinKeys : List [ List [ Data => Data ]], dataset : List [ Data ]) : JoinMap

The purpose of the function was to iterate through a dataset , and apply a bunch of projections to the data (the “join keys”), and then stuff the values of the dataset into a map keyed off the projections.

I don’t recall my first implementation of this function, but I know for a fact it was broken. Totally broken, in fact, and unnecessarily complex.

After a bit of work, I managed to extract out something much more polymorphic:

groupBy :: forall k v . ( Ord k ) => ( v -> k ) -> List v -> Map k ( List v )

def groupBy [ K: Ord , V ]( vk : V => K , vs : List [ V ]) : Map [ K , List [ V ]]

There’s still lots of ways to implement this function, but far fewer than the original definition.

Although I could have taken the technique farther, in this case, I stopped here (the point of diminishing returns). A correct implementation proved straightforward.

Finally, I went back to groupByJoinKeys , and implemented this monomorphic function in terms of the polymorphic groupBy — because in this case, I couldn’t easily push the polymorphism any higher.

The implementation of groupByJoinKeys turned out to be a simple one-liner.

Nothing New Under the Sun

The technique I’ve elaborated here is not unique to functional programming.

In object-oriented programming, we had a saying: require the least powerful interface you need to implement a method.

In other words, if your method only needs to know if a thing is a Shape, then don’t also require it to be a Hexagon (a subtype of Shape).

This technique applies to functional programming, as well, only since we don’t typically have subtyping, we use polymorphism, and when that alone is insufficient, we add type class constraints to provide more structure.

Whether in OOP or FP, the effect is the same: making the code more polymorphic reduces the space of possible implementations.

Summary

Monomorphic type signatures are very concrete. They permit richly descriptive variable names, because you know exactly the types you are working with and what they semantically represent.

The dark side of monomorphic type signatures is that they have far more inhabitants. There are so many ways to implement them, your chances of screwing them up is comparatively high, and it’s harder to reason about their correctness.

Introducing polymorphism can constrain the space of possible implementations and make it simpler to mentally verify correctness of a piece of code. Completely polymorphic type signatures don’t permit descriptive variable names, but they do vastly constrain the space of implementations.

Sometimes we can push the polymorphism very high in the code, and other times we can’t. But even when we need monomorphism, we can push as much functionality as we can into little bubbles of polymorphism.

This lets us apply the technique virtually anywhere, and reduce the total amount of functionality that is implemented monomorphically.

As with all refactoring techniques, it’s possible to over-apply this technique, as I’m sure you can imagine. But in general, I recommend experienced developers look for more ways to polymorphize their code (not fewer).

At least for me, the resulting improvements in code quality have been quite noticeable. If you’ve tried the technique, please share your experiences below!