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 + 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 z.z)/x]. (x y))
= (\lambda z.z) y
= [y/z] z
= 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)
>>> 3450filter(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)
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 FalseTurn 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/
Lambda in Python
By Kelly Chang
Lambda in Python
Explaining Lambda Functions in Python
