Lambda Functions in Python

Kelly Chang

＠rasca0027

kelly.chang@nyu.edu

Where did lambda come from?

Lambda Calculus, Alonzo Church, 1936

(\lambda x. x + x) 3 = 3 + 3 = 6

(\lambda x. x + x) 3 = 3 + 3 = 6

(\lambda x. x + 1) y = [y/x] x + 1 = y + 1

(\lambda x. x + 1) y = [y/x] x + 1 = y + 1

Turing Complete:

it is a universal model of computation that can be used to simulate any Turing machine

(\lambda x. x y)(\lambda z.z)

(\lambda x. x y)(\lambda z.z)

= ([(\lambda z.z)/x]. (x y))

= ([(\lambda z.z)/x]. (x y))

= (\lambda z.z) y

= (\lambda z.z) y

= [y/z] z

= [y/z] z

= y

= y

Lambda Functions

Also called: Anonymous function

Functions as first-class citizens
Often used as arguments in
higher-order functions

def addition(a, b):
    return a + b

>>> addition(1, 3)
>>> 4

add = lambda a, b: a + b

>>> add(1, 2)
>>> 3

MAP

map(function, sequence)

def plus(x): 
    return x + 1
map(plus, range(3))
>>> [1, 2, 3]

map(lambda x: x + 1, range(3))
>>> [1, 2, 3]

FILTER

def f(x):
    return x % 2 == 0
filter(f, range(10))
>>> [0, 2, 4, 6, 8]

filter(lambda x: x % 2 == 0, range(10))
>>> [0, 2, 4, 6, 8]

price = '3,450 元'
filter(lambda x: x.isdigit(), price)
>>> 3450

filter(function, sequence)

Higher-Order Functions

Currying Functions

Currying

"The technique of transforming a function that takes multiple arguments in such a way that it can be called as a chain of functions each with a single argument"

h(x) = g(f(x)) = (g.f)(x)

h(x) = g(f(x)) = (g.f)(x)

def comp(threshold):
    return lambda x: x < threshold

>>> comp
<function comp at 0x10703e048>
>>> comp(10)
<function comp.<locals>.<lambda> at 0x10703e1e0>
>>> f = comp(10)
>>> f(1)
True

>>> func_a = comp(10)
>>> func_b = comp(20)

>>> print(func_a(5), func_a(8), func_a(13), func_a(21))
True True False False

Turn a function into curried function

with functools and lambda

def add(x, y):
    return x + y

add(5)
>>> Traceback (most recent call last):
    File "<stdin>", line 1, in <module>
    TypeError: add() takes exactly 2 arguments (1 given)

# try using functool
from functools import partial
f = partial(add, y=3)
f(2)
>>> 5

# using lambda
def example(a, b, c):
  return (a, b, c)
  
curried1 = lambda b, c: example(1, b, c)
curried1(2, 3)
>>> (1, 2, 3)

Reference

http://kachayev.github.io/talks/uapycon2012/
Haskell趣學指南
FLOLAC 2015
http://www.jianshu.com/p/81b12f4eae3a
https://www.python-course.eu/currying_in_python.php
https://mtomassoli.wordpress.com/2012/03/18/currying-in-python/
https://www.inf.fu-berlin.de/lehre/WS03/alpi/lambda.pdf
https://safalra.com/lambda-calculus/