Fn.py: enjoy FP in Python
Despite the fact that Python is not pure-functional programming language, it’s multi-paradigm PL and it gives you enough freedom to take credits from functional programming approach. There are theoretical and practical advantages to the functional style:
- Formal provability
- Ease of debugging and testing
Fn.py library provides you with missing “batteries” to get maximum from functional approach even in mostly-imperative program.
More about functional approach from my Pycon UA 2012 talks: Functional Programming with Python.
Scala-style lambdas definition
from fn import _ from fn.op import zipwith from itertools import repeat assert list(map(_ * 2, range(5))) == [0,2,4,6,8] assert list(filter(_ < 10, [9,10,11])) ==  assert list(zipwith(_ + _)([0,1,2], repeat(10))) == [10,11,12]
More examples of using
_ you can find in test cases declaration (attributes resolving, method calling, slicing).
Attention! If you work in interactive python shell, your should remember that
_ means “latest output” and you’ll get unpredictable results. In this case, you can do something like
from fn import _ as X (and then write functions like
X * 2).
If you are not sure, what your function is going to do, you can print it:
from fn import _ print (_ + 2) # "(x1) => (x1 + 2)" print (_ + _ * _) # "(x1, x2, x3) => (x1 + (x2 * x3))"
_ will fail with
TypeError subclass) on inaccurate number of passed arguments. This is one more restrictions to ensure that you did everything right:
>>> from fn import _ >>> (_ + _)(1) Traceback (most recent call last): File "<stdin>", line 1, in <module> File "fn/underscore.py", line 82, in __call__ raise ArityError(self, self._arity, len(args)) fn.underscore.ArityError: (_ + _) expected 2 arguments, got 1
Persistent data structures
Attention: Persistent data structures are under active development.
Persistent data structure is a data structure that always preserves the previous version of itself when it is modified (more formal information on Wikipedia). Each operation with such data structure yields a new updated structure instead of in-place modification (all previous versions are potentially available or GC-ed when possible).
Lets take a quick look:
>>> from fn.immutable import SkewHeap >>> s1 = SkewHeap(10) >>> s2 = s1.insert(20) >>> s2 <fn.immutable.heap.SkewHeap object at 0x10b14c050> >>> s3 = s2.insert(30) >>> s3 <fn.immutable.heap.SkewHeap object at 0x10b14c158> # <-- other object >>> s3.extract() (10, <fn.immutable.heap.SkewHeap object at 0x10b14c050>) >>> s3.extract() # <-- s3 isn't changed (10, <fn.immutable.heap.SkewHeap object at 0x10b11c052>)
If you think I’m totally crazy and it will work despairingly slow, just give it 5 minutes. Relax, take a deep breath and read about few techniques that make persistent data structures fast and efficient: structural sharing and path copying.
To see how it works in “pictures”, you can check great slides from Zach Allaun’s talk (StrangeLoop 2013): “Functional Vectors, Maps And Sets In Julia”.
And, if you are brave enough, go and read:
- Chris Okasaki, “Purely Functional Data Structures” (Amazon)
- Fethi Rabhi and Guy Lapalme, “Algorithms: A Functional Programming Approach” (Amazon)
Available immutable data structures in
LinkedList: most “obvious” persistent data structure, used as building block for other list-based structures (stack, queue)
Stack: wraps linked list implementation with well-known pop/push API
Queue: uses two linked lists and lazy copy to provide O(1) enqueue and dequeue operations
Deque(in progress): “Confluently Persistent Deques via Data Structural Bootstrapping”
FingerTreedata structure (see more information below)
Vector: O(log32(n)) access to elements by index (which is near-O(1) for reasonable vector size), implementation is based on
BitmappedTrie, almost drop-in replacement for built-in Python
SkewHeap: self-adjusting heap implemented as a binary tree with specific branching model, uses heap merge as basic operation, more information – “Self-adjusting heaps”
PairingHeap: “The Pairing-Heap: A New Form of Self-Adjusting Heap”
Dict(in progress): persistent hash map implementation based on
FingerTree(in progress): “Finger Trees: A Simple General-purpose Data Structure”
Use appropriate doc strings to get more information about each data structure as well as sample code.
To get more clear vision of how persistent heaps work (
PairingHeap), you can look at slides from my talk “Union-based heaps” (with analyzed data structures definitions in Python and Haskell).
Note. Most functional languages use persistent data structures as basic building blocks, well-known examples are Clojure, Haskell and Scala. Clojure community puts much effort to popularize programming based on the idea of data immutability. There are few amazing talk given by Rich Hickey (creator of Clojure), you can check them to find answers on both questions “How?” and “Why?”:
Streams and infinite sequences declaration
Lazy-evaluated Scala-style streams. Basic idea: evaluate each new element “on demand” and share calculated elements between all created iterators.
Stream object supports
<< operator that means pushing new elements when it’s necessary.
from fn import Stream s = Stream() << [1,2,3,4,5] assert list(s) == [1,2,3,4,5] assert s == 2 assert list(s[0:2]) == [1,2] s = Stream() << range(6) << [6,7] assert list(s) == [0,1,2,3,4,5,6,7] def gen(): yield 1 yield 2 yield 3 s = Stream() << gen << (4,5) assert list(s) == [1,2,3,4,5]
Lazy-evaluated stream is useful for infinite sequences, i.e. fibonacci sequence can be calculated as:
from fn import Stream from fn.iters import take, drop, map from operator import add f = Stream() fib = f << [0, 1] << map(add, f, drop(1, f)) assert list(take(10, fib)) == [0,1,1,2,3,5,8,13,21,34] assert fib == 6765 assert list(fib[30:35]) == [832040,1346269,2178309,3524578,5702887]
fn.recur.tco is a workaround for dealing with TCO without heavy stack utilization. Let’s start from simple example of recursive factorial calculation:
def fact(n): if n == 0: return 1 return n * fact(n-1)
This variant works, but it’s really ugly. Why? It will utilize memory too heavy cause of recursive storing all previous values to calculate final result. If you will execute this function with big
n (more than
sys.getrecursionlimit()) CPython will fail with
>>> import sys >>> fact(sys.getrecursionlimit() * 2) ... many many lines of stacktrace ... RuntimeError: maximum recursion depth exceeded
Which is good, cause it prevents you from terrible mistakes in your code.
How can we optimize this solution? Answer is simple, lets transform function to use tail call:
def fact(n, acc=1): if n == 0: return acc return fact(n-1, acc*n)
Why this variant is better? Cause you don’t need to remember previous values to calculate final result. More about tail call optimization on Wikipedia. But… Python interpreter will execute this function the same way as previous one, so you won’t win anything.
fn.recur.tco gives you mechanism to write “optimized a bit” tail call recursion (using “trampoline” approach):
from fn import recur @recur.tco def fact(n, acc=1): if n == 0: return False, acc return True, (n-1, acc*n)
@recur.tco is a decorator that execute your function in
while loop and check output:
(False, result)means that we finished
(True, args, kwargs)means that we need to call function again with other arguments
(func, args, kwargs)to switch function to be executed inside while loop
The last variant is really useful, when you need to switch callable inside evaluation loop. Good example for such situation is recursive detection if given number is odd or even:
>>> from fn import recur >>> @recur.tco ... def even(x): ... if x == 0: return False, True ... return odd, (x-1,) ... >>> @recur.tco ... def odd(x): ... if x == 0: return False, False ... return even, (x-1,) ... >>> print even(100000) True
Attention: be careful with mutable/immutable data structures processing.
fn.uniform provides you with “unification” of lazy functionality for few functions to work the same way in Python 2+/3+:
itertools.imapin Python 2+)
itertools.ifilterin Python 2+)
functools.reducein Python 3+)
itertools.izipin Python 2+)
xrangein Python 2+)
itertools.ifilterfalsein Python 2+)
itertools.izip_longestin Python 2+)
accumulate(backported to Python < 3.3)
fn.iters is high-level recipes to work with iterators. Most of them taken from Python docs and adopted to work both with Python 2+/3+. Such recipes as
splitby I have already submitted as docs patch which is review status just now.
High-level operations with functions
fn.F is a useful function wrapper to provide easy-to-use partial application and functions composition.
from fn import F, _ from operator import add, mul # F(f, *args) means partial application # same as functools.partial but returns fn.F instance assert F(add, 1)(10) == 11 # F << F means functions composition, # so (F(f) << g)(x) == f(g(x)) f = F(add, 1) << F(mul, 100) assert list(map(f, [0, 1, 2])) == [1, 101, 201] assert list(map(F() << str << (_ ** 2) << (_ + 1), range(3))) == ["1", "4", "9"]
It also give you move readable in many cases “pipe” notation to deal with functions composition:
from fn import F, _ from fn.iters import filter, range func = F() >> (filter, _ < 6) >> sum assert func(range(10)) == 15
You can find more examples for compositions usage in
fn._ implementation source code.
fn.op.apply executes given function with given positional arguments in list (or any other iterable).
fn.op.flip returns you function that will reverse arguments order before apply.
from fn.op import apply, flip from operator import add, sub assert apply(add, [1, 2]) == 3 assert flip(sub)(20,10) == -10 assert list(map(apply, [add, mul], [(1,2), (10,20)])) == [3, 200]
fn.op.foldr are folding operators. Each accepts function with arity 2 and returns function that can be used to reduce iterable to scalar: from left-to-right and from right-to-left in case of
from fn import op, _ folder = op.foldr(_ * _, 1) assert 6 == op.foldl(_ + _)([1,2,3]) assert 6 == folder([1,2,3])
Use case specific for right-side folding is:
from fn.op import foldr, call assert 100 == foldr(call, 0 )([lambda s: s**2, lambda k: k+10]) assert 400 == foldr(call, 10)([lambda s: s**2, lambda k: k+10])
fn.func.curried is a decorator for building curried functions, for example:
>>> from fn.func import curried >>> @curried ... def sum5(a, b, c, d, e): ... return a + b + c + d + e ... >>> sum5(1)(2)(3)(4)(5) 15 >>> sum5(1, 2, 3)(4, 5) 15
Functional style for error-handling
fn.monad.Option represents optional values, each instance of
Option can be either instance of
Empty. It provides you with simple way to write long computation sequences and get rid of many
if/else blocks. See usage examples below.
Assume that you have
Request class that gives you parameter value by its name. To get uppercase notation for non-empty striped value:
class Request(dict): def parameter(self, name): return self.get(name, None) r = Request(testing="Fixed", empty=" ") param = r.parameter("testing") if param is None: fixed = "" else: param = param.strip() if len(param) == 0: fixed = "" else: fixed = param.upper()
Hmm, looks ugly.. Update code with
from operator import methodcaller from fn.monad import optionable class Request(dict): @optionable def parameter(self, name): return self.get(name, None) r = Request(testing="Fixed", empty=" ") fixed = r.parameter("testing") .map(methodcaller("strip")) .filter(len) .map(methodcaller("upper")) .get_or("")
fn.monad.Option.or_call is good method for trying several variant to end computation. I.e. use have
Request class with optional attributes
url. You need to evaluate “request type” using at least one attribute:
from fn.monad import Option request = dict(url="face.png", mimetype="PNG") tp = Option \ .from_value(request.get("type", None)) \ # check "type" key first .or_call(from_mimetype, request) \ # or.. check "mimetype" key .or_call(from_extension, request) \ # or... get "url" and check extension .get_or("application/undefined")
$ pip install fn
Or, if you absolutely must:
$ easy_install fn
You can also build library from source
$ git clone https://github.com/kachayev/fn.py.git $ cd fn.py $ python setup.py install
Work in progress
fn.monad.Eitherto deal with error logging
- C-accelerator for most modules
Ideas to think about:
- Scala-style for-yield loop to simplify long map/filter blocks
- Check for open issues or open a fresh issue to start a discussion around a feature idea or a bug.
- Fork the repository on Github to start making your changes to the master branch (or branch off of it).
- Write a test which shows that the bug was fixed or that the feature works as expected.
How to find me
- Twitter: @kachayev
- Email: kachayev <at> gmail.com