SE4Sci

Prelude

To keep the slides simple, I will assume the following imports:

import dataclasses
import functools

Python is a multi-paradigm language

But it favors OO programming pretty heavily. We may reach out to other languages to learn lessons about different paradigms.

Mutability and state

First we need to talk about mutability and state. Functional programming is all about avoiding them.

Mutability in Python

• Some built-in objects are truly immutable (like int). You can't mutate them.
• Immutable objects have a hash (__hash__ is present and not None)

Immutability by convention more than language.

Why do we introduce mutability?

• Easy to change
• Saves memory
• Easy API (but maybe not a good one!)

Easy to change

@dataclasses.dataclass
class Mutable:
    x: int
    y: int


mutable = Mutable(1, 2)
mutable.x = 2
print(mutable)

Mutable(x=2, y=2)

Easy to change (2)

@dataclasses.dataclass(frozen=True)
class Immutable:
    x: int
    y: int


immutable_1 = Immutable(1, 2)
immutable_2 = Immutable(2, immutable_1.y)
print(immutable_2)

Immutable(x=2, y=2)

Easy to change (3)

@dataclasses.dataclass(frozen=True)
class Immutable:
    x: int
    y: int


immutable_1 = Immutable(1, 2)
immutable_2 = dataclasses.replace(immutable_1, x=2)
print(immutable_2)

Immutable(x=2, y=2)

Easy to build API

data = Data()
data.load_data()
data.prepare()
data.do_calculations()
data.plot()

What happens if you forget a step?

Immutable API + classes

We could replace a mutating state with (immutable) classes:

empty_data = EmptyData()
loaded_data = empty_data.load_data()
prepared_data = loaded_data.prepare()
computed_data = prepared_data.do_calculations()
computed_data.plot()

Now mistakes can be detected statically! Tab completion will tell you what you can do. Etc.

Chained style

We could also use a chained style:

computed_data = EmptyData().load_data().prepare().do_calculations()
computed_data.plot()

This style is common in functional programming (which is where we are headed).

Copy vs. reference

def evil(x):
    x.append("Muhahaha")


mutable = []
evil(mutable)
print(mutable)

What will this output?

Design suggestion

A function should be of the form

name(input, ...) -> output

We tend to allow:

x.do_something()

Though that also mutates an argument (self).

What does immutability give us?

• Optimization by the compiler (if you have one)
• Chaining of methods
• No issues with copying vs. references
• Avoid one mutable reference breaking another

These don't require immutability, they require we don't mutate.

Functional programming

Defining pure function:

• Does not mutate arguments
• Does not contain internal state
• No side effects (like printing to screen!)

Think about some functions and see which ones are pure.

map, filter, reduce

Functional programming often involves passing functions to functions.

Here's Pythonic code running on items = [1, 2, 3, 4, 5]:

sum_sq_odds = sum(x**2 for x in items if x % 2 == 1)

Written in a functional style:

sum_sq_odds = functools.reduce(
    lambda x, y: x + y, filter(lambda x: x % 2 == 1, map(lambda x: x**2, items))
)

Improving the syntax

class FunctionalIterable:
    def __init__(self, this, /):
        self._this = this

    def __repr__(self):
        return repr(self._this)

    def map(self, func):
        return self.__class__(map(func, self._this))

    def filter(self, func):
        return self.__class__(filter(func, self._this))

    def reduce(self, func):
        return functools.reduce(func, self._this)

Improving the syntax (2)

items = FunctionalIterable([1, 2, 3, 4, 5])
sum_sq_odds = (
    items.map(lambda x: x**2).filter(lambda x: x % 2).reduce(lambda x, y: x + y)
)

Other languages: Ruby

items = [1,2,3,4,5]
sum_sq_odds = items.map{_1**2}.filter{_1 % 2 == 1}.reduce{_1 + _2}
puts items

Other languages: Rust

fn main() {
    let items = [1,2,3,4,5];
    let sum_sq_odds = items.iter()
                      .map(|x| x*x)
                      .filter(|&x| x%2==1)
                      .fold(0, |acc, x| acc + x);
    println!("{}", sum_sq_odds);
}

Other languages: C++23 (modules not supported yet)

import std;

int main() {
    std::vector items {1, 2, 3, 4, 5};
    auto odd_sq = items | std::views::transform([](int i){return i*i;})
                        | std::views::filter([](int i){return i%2==1;});
    auto sum_sq_odds = std::fold_left(odd_sq, 0, [](int a, int b){return a + b;});
    std::println("{}", sum_sq_odds);
    return 0;
}

Currying

def power(y, x):
    return x**y


pow2 = functools.partial(power, 2)
pow3 = functools.partial(power, 3)

print(f"{pow2(10) = }")
print(f"{pow3(10) = }")

pow2(10) = 100
pow3(10) = 1000

Subset of functors!

So what can you get?

Lazy evaluation

def not_pure(x):
    print("computing x")
    return x


values = [1, 2, 3]
results = map(not_pure, values)
filtered_results = filter(lambda x: x % 2 == 0, results)
print(sum(filtered_results))

Where does the print statement run?

So what can you get?

Parallelization

(Not Python) Can run in parallel, since when you run doesn't matter.

Easy to optimize

(Not Python) Easy to reason about.

Not Python only means not the language, libraries can implement!

JAX

A library that makes use of this is JAX. Let's look at it:

import jax
import jax.numpy as jnp

arr = jnp.array([1, 2, 3])

Looks like NumPy right? Try to modify the array. ;)

JAX (2)

Here's how you write arr[0] = 4:

arr = arr.at[0].set(4)

What you get:

• You can fuse functions together with jax.jit & they get compiled into machine code
• You can target CPU, GPU, and TPU (Google’s tensor processing units)
• You can compute gradients of functions

JAX (3)

@jax.jit
def f(x):
    return x**3 + x**2 + x


dfdx = jax.grad(f)
print(f"{dfdx(1.0) = }")

dfdx(1.0) = DeviceArray(6., dtype=float32, weak_type=True)