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
• Modularity
• Composability
• 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 <http://kachayev.github.com/talks/uapycon2012/index.html>_.

Scala-style lambdas definition

.. code-block:: python

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])) == [9]
assert list(zipwith(_ + _)([0,1,2], repeat(10))) == [10,11,12]

More examples of using _ you can find in test cases <https://github.com/kachayev/fn.py/blob/master/tests.py>_ 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:

.. code-block:: python

from fn import _

print (_ + 2) # "(x1) => (x1 + 2)"
print (_ + _ * _) # "(x1, x2, x3) => (x1 + (x2 * x3))"

_ will fail with ArityError (TypeError subclass) on inaccurate number of passed arguments. This is one more restrictions to ensure that you did everything right:

.. code-block:: python

>>> 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 <http://goo.gl/8VveOH>_). 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:

.. code-block:: python

>>> 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 <http://en.wikipedia.org/wiki/Persistent_data_structure#Examples_of_persistent_data_structures>_ and path copying <http://en.wikipedia.org/wiki/Persistent_data_structure#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" <http://goo.gl/Cp1Qsq>_.

And, if you are brave enough, go and read:

• Chris Okasaki, "Purely Functional Data Structures" (Amazon <http://goo.gl/c7ptkk>_)
• Fethi Rabhi and Guy Lapalme, "Algorithms: A Functional Programming Approach" (Amazon <http://goo.gl/00BxTO>_)

Available immutable data structures in fn.immutable module:

• 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" <http://goo.gl/vVTzx3>_
• Deque based on FingerTree data 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 list
• SkewHeap: self-adjusting heap implemented as a binary tree with specific branching model, uses heap merge as basic operation, more information - "Self-adjusting heaps" <http://goo.gl/R1PZME>_
• PairingHeap: "The Pairing-Heap: A New Form of Self-Adjusting Heap" <http://goo.gl/aiVtPH>_
• Dict (in progress): persistent hash map implementation based on BitmappedTrie
• FingerTree (in progress): "Finger Trees: A Simple General-purpose Data Structure" <http://goo.gl/Bzo0df>_

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 (SkewHeap and PairingHeap), you can look at slides from my talk "Union-based heaps" <http://goo.gl/VMgdG2>_ (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?":

• "The Value of Values" <http://goo.gl/137UG5>_
• "Persistent Data Structures and Managed References" <http://goo.gl/M3vZ7E>_

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.

Simplest cases:

.. code-block:: python

from fn import Stream

s = Stream() << [1,2,3,4,5]
assert list(s) == [1,2,3,4,5]
assert s[1] == 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:

.. code-block:: python

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[20] == 6765
assert list(fib[30:35]) == [832040,1346269,2178309,3524578,5702887]

Trampolines decorator

fn.recur.tco is a workaround for dealing with TCO without heavy stack utilization. Let's start from simple example of recursive factorial calculation:

.. code-block:: python

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

.. code-block:: python

>>> 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:

.. code-block:: python

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 <http://en.wikipedia.org/wiki/Tail_call>_ 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):

.. code-block:: python

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:

.. code-block:: python

>>> 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.

Itertools recipes

fn.uniform provides you with "unification" of lazy functionality for few functions to work the same way