8 September 2022 — by Christopher Harrison
Functional Python, Part I: Typopædia Pythonica

Tweagers have an engineering mantra — Functional. Typed. Immutable. — that begets composable software which can be reasoned about and avails itself to static analysis. These are all “good things” for helping us build robust software, which inevitably lead us to using languages such as Haskell, OCaml and Rust. However, it would be remiss of us to snub languages that don’t enforce the same disciplines, but are nonetheless popular choices in industry. Ivory towers are lonely places, after all.

In this series of articles, I will discuss how some of the principles and techniques learnt from typed functional languages can be applied to Python1 to achieve the same results. We’ll see that, while Python famously eschews the functional paradigm, we can build pythonic(ish) equivalents relatively easily.

First up, I’ll look at typing discipline in Python.

Quickly. Tell me the type signature of the following function:

def mystery(a, b):
return a / b

You may be tempted to say that a and b are numeric… and that’s probably true. However, Python is dynamically typed, so without further documentation, the only thing we can actually say for sure is that a must implement the __truediv__ interface at runtime (or b implements __rtruediv__). For instance:

>>> mystery(pathlib.Path("/foo/bar"), "quux")
PosixPath("/foo/bar/quux")

This is a fairly well-behaved (if not contrived) example. However, I’m sure you can relate to the shenanigans that some Python engineers get up to; constructing opaque dictionaries where we’re lucky if we know the keys without mentally running through the code in our heads. Impenetrable. Unmaintainable. Chaos.

Fortunately for our (and future maintainers’) sanity, since Python 3.5, syntax for type hinting has been introduced and continues to improve in each subsequent release. We can thus annotate our function as a form of standardised documentation:

def not_so_mysterious(a: float, b: float) -> float:
return a / b

Python is still dynamically typed; these are just annotations and you are free to flaunt them with reckless abandon. Presuming, however, that you’re an upstanding citizen, this is an approach known as “gradual typing”, which is a pragmatic solution to allow engineers to annotate their code piecemeal, without the friction that comes from the expectations of “all-or-nothing”.

So what’s the point, if it’s transparent to the Python interpreter?

Well, type checkers exist, such as:

Any of these can (and should) be incorporated into an engineer’s setup, or integrated into a project in much the same way as formatters, linters and test runners. The more you annotate your code, the more leverage you gain; type checkers can infer the type of code that isn’t annotated when they have enough information. Having your editor scream at you, or your CI fail if your code doesn’t type check is an easy win in the fight against bugs.

Now, much ink has been spilt on the merits of typing — and I would encourage you to read Python’s and mypy’s documentation — so I won’t go into any more detail about the specifics. Instead, we’ll see how we can use this to implement a keystone of functional programming languages while reassuring ourselves of its correctness.

## Algebraic Data Types

Algebraic data types are structures formed by composition in predictable, well-defined ways.2 Moreover, they can be nested, allowing you to build up complex data structures from well-understood parts. Why is this useful? While the concept may seem abstract, modelling everyday data structures — both algorithmic and for business logic — in this way turns out to be rather natural, where the same arguments that favour modular code, which can be put together into a more-meaningful whole, apply.

Data structures are at the heart of the software we write. For functional programmers, it’s common to start implementing new functionality by thinking about what types will be needed and how they will interact with each other.

With that in mind, rather than waxing poetic, let’s get down to the business of applying the same practice to our Python code. I’ll start with “product types” as they’re simpler, both conceptually and in terms of their Python implementation.

### Product Types

A point on a plane can be represented, for example, by its $x$ and $y$ coordinates relative to some origin. These two values can range independently to cover the entire plane. This is known as the Cartesian product, which directly corresponds to a “product type”. In the plane example, this would be expressed by its two numeric components. However, nothing precludes you from having more components, fewer components, or even heterogeneous components.

At its simplest, this can be represented by the juxtaposition of (zero or more) types. In Python, this is a tuple, which is straightforwardly annotated3 by its component types. For example:

point: tuple[float, float] = (3, 4)

sql_statement: tuple[str, tuple] = (
"select * from foo where bar > ? and quux = ?",
(0, True)
)

Furthermore, tuples are immutable in Python, which ensures that unexpected changes — that can cause bugs and are hard to track down — cannot happen. Less favourably, however, is that their component access is positional, which elides useful information from the engineer. This can lead to meaningless code:

do_something(point[0])

# Destructuring helps, but is at best just a proxy
stmt, params = sql_statement

To resolve this, the fields can be named; a so-called “record type”, or a struct in C and Rust. Before Python 3.7, a record type could be implemented using a named tuple; which gained type annotation support in Python 3.6. Since Python 3.7, data classes4 were introduced which supplant this role. At first blush, the two may seem equivalent, but an important distinction — that will become necessary in the next episode — is that named tuples don’t support multiple inheritance.

The implementation is facilitated through a class decorator, which computes the type’s interface (e.g., constructor, equality matching, etc.) at runtime. It therefore offers a lot of flexibility, such as specifying default values and setting immutability; instantiation is like a normal Python class and field access is through the familiar “dotted-attribute” pattern:

from dataclasses import dataclass

@dataclass(frozen=True)
class ProgrammingLanguage:
name: str
strongly_typed: bool
statically_typed: bool

python = ProgrammingLanguage("Python", True, False)

assert haskell.statically_typed != python.statically_typed

In this example, I use the anti-pattern of Boolean arguments, which gives no clue as to what each argument refers. From Python 3.10 this situation can be improved slightly — at the expense of verbosity — by forcing the use of keyword arguments. However, perhaps there is a better way…

### Sum Types

Sum types can express a variety of types, but only one at a time. The most common example of this is probably a Boolean: it’s either True or False. That can be extended to an arbitrary number of simple branches with an Enum, introduced in Python 3.4. While somewhat pointless5 beyond its illustrative power, we could thus amend our previous example like so:

from dataclasses import dataclass
from enum import Enum, auto

class TypingDiscipline(Enum):
StrongStatic = auto()
StrongDynamic = auto()
WeakStatic = auto()
WeakDynamic = auto()

@dataclass(frozen=True)
class ProgrammingLanguage:
name: str
type_discipline: TypingDiscipline

javascript = ProgrammingLanguage("JavaScript", TypingDiscipline.WeakDynamic)

While this is now clearer, it has limited utility. What would be useful is a mixture of branch types, where individual components can carry information besides their name. For example, say we wanted a Shape type which encoded different metrics for different types of shape (e.g., side lengths for rectangles, radius for circles, etc.). That can’t be done with an Enum.

In object orientated programming languages, like Python, this pattern is a class hierarchy: a root superclass, with any number of child classes representing the branches. From Python 3.8, we can also make use of the typing.final decorator to get the type checker involved in enforcing the correct structure. As for carrying data, we’ve already covered that with product types:

from dataclasses import dataclass
from typing import final

class Shape: ...

@final
@dataclass(frozen=True)
class Rectangle(Shape):
width: float
height: float

@final
@dataclass(frozen=True)
class Circle(Shape):
radius: float

This is approximately equivalent to a true sum type that can be defined in functional languages. We’ve constructed it from smaller, well-understood types to enable us to express data that is more than the sum of its parts (pun intended). However, there are some caveats which must be observed:

• The Shape parent class is a bona fide type. This is perfect for type annotating, but care should be taken not to mistakenly instantiate it. Conversely, the subclasses are also bona fide types, but they’re less useful for type annotation, yet should be instantiated.

• Nothing prevents further subclassing of Rectangle or Circle besides the final decorator, which would only fail the type checker. Deeper subclassing is meaningless with respect to the simulated sum type, but will still type check against the root class.

The instantiation and subclassing problems could be enforced with some metaclass trickery, but this does more to paint you into a corner than provide value. Not recommended. Instead, this is where the judgement of the engineer comes in to play.

### Recursive Types and Pattern Matching

When learning Haskell, the classic algebraic data type example is a cons-list: a homogeneous, singly-linked list made up of cons cells. This can be expressed as:

data List a = Cons a (List a) | Nil

Following the protocol I’ve outlined above, this can be translated mechanically into Python:

from typing import Generic, TypeVar, final
from dataclasses import dataclass

T = TypeVar("T")

class List(Generic[T]): ...

@final
@dataclass(frozen=True)
class Cons(List[T]):
car: T
cdr: List[T]

@final
class Nil(List): ...

Granted, it’s not one line of code any more and it may look a bit alien, as far as Python code goes, but it is readable. It’s also worth emphasising that this is again more illustrative than useful: Don’t implement your Python lists like this! So let’s get on and illustrate by defining some linked lists and showing how the type checker reacts:

# The type checker approves of this
correct: List[int] = Cons(1, Cons(2, Cons(3, Nil())))

# The type checker doesn't like these
# mypy: Argument 1 to "Cons" has incompatible type "str"; expected "int"
mistyped: List[int] = Cons("foo", Nil())
hetero: List[int] = Cons(1, Cons("2", Nil()))

“This seems like a lot of effort to go to,” I hear you cry. “Can we do anything cool with this?”

The great thing about structures that follow a predictable pattern is that they can be deconstructed in a predictable way. You see this all the time in idiomatic Python code, with destructuring of tuples and dictionaries to get at their parts. With our sum and product types, let me give an example which allows you to go one step further:

from typing import Callable, TypeVar

S = TypeVar("S")
T = TypeVar("T")

def foldr(fn: Callable[[S, T], T], acc: T, lst: List[S]) -> T:
match lst:
case Nil():
return acc

case Cons(x, xs):
return fn(x, foldr(fn, acc, xs))

Structural pattern matching landed in Python 3.10 and this is where algebraic data types really shine. It allows us to leverage the structural patterns that are naturally embedded within them without having to write a lot of tiresome boilerplate. The above is a recursive (strictly evaluated) implementation of a right fold,6 which is about as close to a perfect translation of the Haskell equivalent as you can get:

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr _  acc []     = acc
foldr fn acc (x:xs) = fn x (foldr fn acc xs)

Let’s give it a spin:

>>> foldr(lambda x, y: x + y, 0, Cons(1, Cons(2, Cons(3, Nil()))))
6

>>> foldr(lambda x, y: f"{x}{y}", "", Cons("Hello", Cons("World", Nil())))
'HelloWorld'

In functional programming languages, many such abstractions exist — so-called “higher-order functions” — and are used as component building blocks to compose useful software. As we can reason about each component, we can reason about their composition. Functional programming is all about composition and now we can do the same in our Python code.

Of course, not all is sunshine and rainbows. There are some caveats:

• As mentioned previously, the root class (List, here) is a genuine type. The type checker realises that the match clause is therefore inexhaustive and so it (correctly) concludes that there’s a non-return path through the function; which is a type error. It’s not as pretty, but we can fix this easily by adding a dummy match branch that is never taken.

• Pythonistas may baulk at the recursion… and for good reason: Python does not do tail-call optimisation — again, by decree — and so deep recursion can blow the stack. In the next episode, I’ll show how we can resolve this.

## Conclusion

Functional programming takes many of its cues from mathematics, where larger, more-specific structures (programs) are built from smaller, more-general ones. You start from the bottom and work your way up. This ensures the correctness at each level of abstraction and is a robust philosophy for writing well-behaved software.

I have shown that the axiomatic level — types — can now be imitated in the Python ecosystem to achieve the same end. In the next episode, I’ll generalise this further and implement some nifty computer science concepts to assuage Python’s “mechanical sympathies”.

Thanks to Gala Camacho, Simeon Carstens, Guillaume Desforges, Clément Hurlin, Steve Purcell and Noon van der Silk for their reviews of this article.

1. We are not limited to Python; these techniques can be applied in any language with suitable support, libraries and tooling.
2. Why they’re “algebraic” is because algebraic data types form a semiring; a structure from abstract algebra. Bartosz Milewski goes into depth on this, with a slight Haskell bent.
3. Since Python 3.9, standard collections can be used as their own type annotations. Prior to this, collection types could be found in the typing standard library module.
4. The attrs library is a common dependency that achieves a similar goal, while dataclasses fulfils the “Pareto principle” from within the Python standard library.
5. It would be more useful here to split the TypingDiscipline enumeration into two Enums: one for strong/weak and the other for static/dynamic. As I say, it’s just an example!
6. You may be familiar with Python’s functools.reduce, which is a left fold.
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