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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>FP & Python</title>
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<textarea id="source">
class: center, middle, main-title
# FP & Python
[GothPy](https://www.meetup.com/GothPy/) - Gothenburg's Python Meetup group
Johan Lodin, 2019-11-21
github.com/jolod
---
## Outline
- Motivating examples
- Challenges applying FP
- What *is* FP?
- State in functional programs
- Principles
- Abstraction
- Interpretation
- Composition
- Tools for FP in Python
- Summary
--
- Slides are written in Markdown.
- Slides are wordy and simple, so that they can be read directly on GitHub.
`github.com/jolod/presentation-fp-python`
---
class: center, middle, main-title
# Motivating examples
---
## Reasoning
```python
x = 3
y = f(x)
z = g(y)
print(x) # 3
```
--
```perl
my $x = 3;
my $y = f($x);
my $z = g($y);
say $x; # ???
```
--
```python
x = [3]
y = f(x)
z = g(y)
print(x[0]) # 3 ???
```
--
```python
x = [3]
y = f(x)
y = g(y)
y = h(y)
y = i(y)
y = j(y)
y = k(y)
y = l(y)
y = m(y)
y = n(y)
y = o(y)
y = p(y)
y = q(y)
print(x[0]) # 3 ???
```
---
## Compositional APIs
```python
import matplotlib.pyplot as plt
x = [1, 2, 3]
y = [2, 4, 8]
plt.plot(x, y, '-')
plt.show()
plt.plot(x, y, '.-')
plt.show()
plt.subplot(1,2,1)
plt.plot(x, y, '-')
plt.subplot(1,2,2)
plt.plot(x, y, '.-')
plt.show()
```
---
## Compositional APIs
```R
library("ggplot2")
x <- c(1, 2, 3)
y <- c(2, 4, 8)
p <- ggplot() + aes(x, y)
p
p1 <- p + geom_line()
p1
p2 <- p1 + geom_point()
p2
require(gridExtra)
grid.arrange(p1, p2, ncol=2)
```
---
## Honorable mention: generators
```python
def fibonacci(n):
"""Compute the nth Fibonacci number."""
(a, b) = (0, 1)
for k in range(n):
(a, b) = (b, a + b)
return a
```
Consider updating to take the `n`th number divisible by `k` (or some other criterion).
- Write a new function?
- Pass in filter criterion?
--
```python
def fibonacci(n, pred):
"""Compute the nth Fibonacci number that fulfills the criterion pred."""
if n <= 0:
return
(a, b) = (0, 1)
k = 1 if pred(a) else 0
while k < n:
(a, b) = (b, a + b)
if pred(a):
k += 1
return a
```
---
## Honorable mention: generators
Generators are mutating objects, so not very functional, but serve to *invert the control*.
```python
def fibonacci_gen():
"""Generate the Fibonacci sequence."""
(a, b) = (0, 1)
while True:
yield a
(a, b) = (b, a + b)
```
```python
def fibonacci(n):
g = fibonacci_gen()
skip(n, g)
return next(g)
```
```python
n = 3
k = 7
g = (a for a in fibonacci_gen() if a % k == 0)
skip(n - 1, g)
print(next(g))
```
---
## Common selling points
- Easy to reason about / Reduces complexity
- Inherently testable
- Easy to parallelize
--
All this is true for Matlab too!
- Matlab is imperative but with pure functions.
- Matlab has (clever) copy-on-write semantics.
---
class: center, middle, main-title
# Challenges applying FP
---
## Abstraction inversion
https://softwareengineering.stackexchange.com/questions/9006/whats-your-strongest-opinion-against-functional-programming
--
Answer by Mason Wheeler, 2010-10-02: (bold emphasis added by me)
> I think that the reason functional programming isn't used very widely is because it gets in your way too much. It's hard to take a serious look at, for example, Lisp or Haskell, without saying "this whole language is **one big abstraction inversion**."
--
> When you establish baseline abstractions that the coder can't get beneath when necessary, you establish things that **the language simply can't do**, and the more functional the language is, the more of these it tends to have.
--
> Take Haskell, for example. In the name of functional purity, you're required to use **brain-breaking abstraction inversions that nobody understands** in order to manage state and I/O, *the two most fundamental parts of any and every computer program that interacts with anything!* That gets old fast.
---
## "Brain breaking"?
- Often brain breaking because you've *learned a different way already*.
- 20 years ago some companies did not allow `map` in the code base because "the next programmer wouldn't understand it".
What's brain breaking today, might very well be obvious tomorrow.
---
## The learning resources gap
A large portion of articles write about functional programming in the small.
- Map, filter, reduce.
- Partial functions and currying.
--
A small portion of articles write about functional programming in the large.
- IO
- Modularity
- Extensibility
- Testing
--
---
## The learning resources gap
A large portion of articles write about functional programming in the small.
- Map, filter, reduce.
- Partial functions and currying.
A small portion of articles write about functional programming in the large.
- IO
- Modularity
- Extensibility
- Testing
---
class: center, middle, main-title
# What do I mean by FP?
Not just immutable data and higher-order functions
Structure vs techniques
---
## The IP-FP spectrum
Extreme imperative programming (IP):
> A *Turing machine* is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, given any computer algorithm, a Turing machine capable of simulating that algorithm's logic can be constructed. (1936)
Easy to imagine how a physical Turing machine affects the world.
http://turingmachine.io/
--
You don't program Turing machines:
- Register machines (assembly; gotos)
- Structured programming (statements, while, if)
- Procedural programming (blocks, scopes, return)
---
## The IP-FP spectrum
Extreme functional programming (FP):
> *Lambda calculus* is a formal system in mathematical logic for expressing computation based on **function abstraction** and **application** using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. (1930s)
--
[Visualization](https://www.cl.cam.ac.uk/~rmk35/lambda_calculus/lambda_calculus.html) of 2 + 3.
```text
((fn n m => fn f x => n f (m f x)) (fn f => fn x => f (f x)) (fn f => fn x => f (f (f x))))
```
--
Not realized to be a "programming language" until around 1960.
---
## Church encoding examples
```python
TRUE = lambda then: lambda _: then
FALSE = lambda _: lambda otherwise: otherwise
IF = lambda cond: lambda then: lambda otherwise: cond(then)(otherwise) # Redundant
AND = lambda p: lambda q: p(q)(p)
TWO = lambda f: lambda x: f(f(x))
FIVE = lambda f: lambda x: f(f(f(f(f(x)))))
INC = lambda n: lambda f: lambda x: f(n(f)(x))
THREE = INC(TWO)
PLUS = lambda n: n(INC)
DEC = lambda n: lambda f: lambda x: n(lambda g: lambda h: h(g(f)))(lambda _: x)(lambda y: y)
MINUS = lambda m: lambda n: n(DEC)(m)
ISZERO = lambda n: n(lambda x: FALSE)(TRUE)
EQ = lambda m: lambda n: AND(ISZERO(MINUS(m)(n)))(ISZERO(MINUS(n)(m)))
PAIR = lambda a: lambda b: lambda selector: selector(a)(b)
FIRST = lambda pair: pair(lambda a: lambda _: a)
SECOND = lambda pair: pair(lambda _: lambda b: b)
RESULT = EQ(PLUS(TWO)(THREE))(FIVE)
```
```python
outputs = PAIR("It's true!")("I think there is a bug somewhere.")
print(
IF(RESULT) \
(FIRST(outputs)) \
(SECOND(outputs))
)
```
```text
It's true!
```
---
## The point: functions are "all you need"
Data:
- Numerals => chars
- Variants (pairs) => lists
- Chars and lists => strings
- Lists and pairs => dictionaries
- Dictionaries and lambdas => prototypal OO
- **Etc!**
Logic:
- Variants for branching
- Recursion for looping
- **Etc!**
Pure λ-calculus isn't exactly "ergonomic" though.
---
## Characteristics of λ-calculus
`Data == functions (because only functions)`
--
`Control flow == data (because only functions)`
--
`Higher order functions (because only functions)`
--
`Only one-argument functions (reductionist, but practical!)`
--
`Non-strict evaluation (for technical reasons)`
(You don't actually *evaluate* λ-calculus, you *reduce* terms.)
--
`No mutable data (makes no sense)`
--
`No statements, only expressions (makes no sense)`
--
`No side effects of any kind (makes no sense)`
--
Not here:
- Pattern matching
- Variants very important though!
- Types
- Can carry information!
---
class: center, middle, main-title
# State
"There is no *shared mutable* state in FP"
---
## "Imperative" vs functional state
--
Raise your hand when you are *certain* of what this does:
--
```python
def foo(n, k=0):
result = 0
while True:
if k >= n:
break
result += k
k += 1
return result
```
--
What is `foo(5, 3)`?
--
```python
def foo(n, k=0):
result = 0
for m in range(k, n):
result += m
return result
```
- Which is easier to understand?
- Why?
---
## "Imperative" vs functional state
```python
def range_sum(n, k=0):
result = 0
while True:
if k >= n:
break
result += k
k += 1
return result
```
- What happens if we do `k += 1` before `result += k`?
--
```python
def range_sum(n, k=0, result=0):
if k >= n:
return result
else:
return range_sum(n, k + 1, result + k)
```
State moved from loop variables to function arguments.
--
- `k + 1` and `result + k` are unordered.
- Still a "manual" loop though.
- Doesn't sell FP on anyone.
---
## "Imperative" vs functional state
```python
def range_sum(n, k=0):
result = 0
for m in range(k, n):
result = result + m
return result
```
--
Another "abstraction inversion":
```python
def range_sum(n, k=0):
return reduce(
lambda result, m: result + m,
range(k, n),
0
)
```
- 1-to-1 with the imperative version.
- But even more structure.
---
## "Imperative" vs functional state
FP has "local" state just as IP does:
- General recursion is the "least structured" way.
- Often the most structured way is favored.
- Just like `for` is favored over `while`.
Key difference: *all* state at *every level* is local state. (Except the top level, where IO is allowed.)
--
Yet, at this scale, almost no benefit regarding
- reasonability,
- testability, or
- parallelism.
---
class: center, middle, main-title
# Some core FP principles
Abstraction, interpretation & composition
---
class: center, middle, main-title
# Abstraction
---
## Higher-order functions
- `reduce` abstracts over *structure*.
--
- `reduce` is a function and can be *abstracted over*.
- Cannot abstract over `for` directly.
--
```python
def range_sum(reducer, n, k=0):
return reducer(operator.add, range(k, n), 0)
```
- `range_sum` is now a *third*-order function (takes a second-order function).
---
## Inversion of Control (IoC)
- Higher-order functions (HOF) are a form of dependency inversion (DI).
- Too high order might hint at mixing high and low level abstractions.
```python
def range_sum(summer, n, k=0):
return summer(range(k, n))
```
- Reduced to second-order again.
---
## Building computations
Functions as values.
```python
def range_sum(n, k=0):
return lambda summer: summer(range(k, n))
```
--
Can talk about range sums without talking about how to sum it (yet).
```python
def plus(a, b):
return lambda summer: summer(n(summer) for n in [a, b])
```
Very light-weight "pattern".
(This is why it is practical to have one-argument functions only (or "curried" functions); you don't have to be explicit about whether `summer` is the third argument of `plus`, or an argument of the return value.)
--
```python
total = plus(range_sum(5, 1), range_sum(3, 1))
mysum = lambda xs: reduce(operator.add, xs, 0)
print(total(mysum)) # 1+2+3+4 + 1+2 = 13
myprod = lambda xs: reduce(operator.mul, xs, 1)
print(total(myprod)) # 1*2*3*4 * 1*2 = 48
print(total(lambda xs: xs)) # [range(1, 5), range(1, 3)]
```
The lack of (visible) argument names for the closures can make this style harder to read.
---
class: center, middle, main-title
# Interpretation
Inversion of control *flow*
---
## Interpretation vs dependency injection
- No side effects.
- Turn a value into another value.
- Turn a structure into another structure.
--
Point of view: all values are structures.
- Lists (etc) are structures (interpreted using `for`/`reduce`).
- Records/objects are structures (interpreted using attribute lookup).
- Functions are structures (interpreted by calling them).
- Booleans are structures (interpreted using `if`).
Booleans are the simplest example of a *variant data type*.
---
## Variant data types
Cannot rely on only passing in behavior.
- Want side effects close to the top level.
- Must communicate actions through return values.
--
- Variants model branching, in contrast to aggregations.
- Python (and most OO languages) do not support branching on variants syntactically (except booleans).
- Variants ~~ visitor pattern.
- Visitor implementations is rare in OOP, but variants are *everywhere* in FP.
Remember: booleans are variants.
---
## Booleans and beyond
```haskell
-- Haskell, sorry. :-(
data Boolean = True | False
case result of
True -> ...
False -> ...
```
--
```haskell
-- Explicitly encoding possibility of None.
data Maybe a = Just a | Nothing
case result of
Just x -> ... -- Make good use of x.
Nothing -> ... -- Do thing else.
```
- `Just` is like `True` but carries a value.
- `Nothing` is like `False`. (Or vice versa.)
--
```haskell
-- Handle exceptions etc.
data Result error value = Failure error | Success value
```
Variants can have any number of cases, and store any number of values.
---
## Variants in Python
```python
def f(result):
if result.tag == "success":
value = result.value
return ...
elif result.tag == "failure":
error = result.error
return ...
else:
raise Exception("Unknown tag: %s" % (result.tag,))
```
This might look upsetting to some.
Remember: booleans are variants!
---
## How to *not* use variants
```haskell
data Shape a = Circle a
| Ellipse a a
| Square a
```
This will lead to pain down the line.
--
Use variants when
- The cases aren't meaningful *by themselves*.
- **And** the cases are fundamental/primitives.
- Fundamental means that you don't want to add new cases.
- If you *do* add cases you *want* to update all the code using them.
--
Booleans are good:
- True is only meaningful as a contrast to false (and vice versa).
--
`Maybe` is good:
- `Just` is only meaningful in the presence of `Nothing`.
--
`Shape` above is bad:
- Circles are useful by themselves.
- Might want to add more shapes (e.g. `Rectangle`)
---
## Variants in Python redux
Booleans:
```python
TRUE = lambda then, otherwise: then()
FALSE = lambda then, otherwise: otherwise()
print(TRUE(lambda: 42, lambda: "Dunno")) # 42
print(FALSE(lambda: 42, lambda: "Dunno")) # Dunno
```
Very light-weight compared to the visitor pattern.
See one of the exercises.
---
class: center, middle, main-title
# Composition
---
## Abstraction + interpretation
Abstraction and interpretation work in tandem to
- focus libraries on the core problem, and
- push side effects to the edge.
Libraries > frameworks w.r.t. composability
Libraries are built using other libraries.
Frameworks are built using ...?
---
## Acting on results
"Naïve" variants only take you so far.
What if you want to act on the result of an action that requires interpretation?
For instance:
```python
# Ignore exceptions for now.
import os
def count_chars_of_file(filename):
f = os.open(filename)
text = os.read(f)
n = len(text)
os.close(f)
return n
```
--
(The answer is *not* monads in Python.)
---
## Acting on results
Made-up node.js library:
```javascript
function countCharsOfFile(filename) {
return action("open", filename).then((f) => {
return action("read", f).then((text) => {
let n = text.length();
return action("close", f).then(() => {
return result(n);
})
})
})
}
```
Builds computations stored in variants (`action` and `result`).
---
## Acting on results
In Python:
```javascript
def count_chars_of_file(filename):
def after_open(f):
def after_read(text):
n = len(text)
def after_close():
return Result(n)
return Action("close", f).then(after_close)
return Action("read", f).then(after_read)
return Action("open", filename).then(after_open)
```
Not pretty. :-(
But see one of the exercises nonetheless.
---
## Coroutines
(Credit: Magnus Therning, https://magnus.therning.org/posts/2017-01-31-000-on-mocks-and-stubs-in-python--free-monad-or-interpreter-pattern-.html)
```python
os = Actions('os')
def count_chars_of_file(filename):
f = yield os.open(filename)
text = yield os.read(f)
n = len(text)
yield os.close(fd)
return n
```
- `os` uses dynamic lookup to return the method name and arguments as data instead of performing the action.
- The consumer of `count_chars_of_file` uses the `send` method to communicate the results back.
- `... = yield from ...` allows refactoring.
--
- The caller makes the interpretation, or passes on the description.
- Depend on globally available *descriptions* (i.e. data).
See one of the exercises.
---
class: center, middle, main-title
# Tools for FP in Python
---
## Libraries
- [functools](https://docs.python.org/3.8/library/functools.html)
- [operator](https://docs.python.org/3.8/library/operator.html)
- [pyrsistent](https://pypi.org/project/pyrsistent/)
Honorable mention: