| ******************************** |
| Functional Programming HOWTO |
| ******************************** |
| |
| :Author: A. M. Kuchling |
| :Release: 0.32 |
| |
| In this document, we'll take a tour of Python's features suitable for |
| implementing programs in a functional style. After an introduction to the |
| concepts of functional programming, we'll look at language features such as |
| :term:`iterator`\s and :term:`generator`\s and relevant library modules such as |
| :mod:`itertools` and :mod:`functools`. |
| |
| |
| Introduction |
| ============ |
| |
| This section explains the basic concept of functional programming; if |
| you're just interested in learning about Python language features, |
| skip to the next section on :ref:`functional-howto-iterators`. |
| |
| Programming languages support decomposing problems in several different ways: |
| |
| * Most programming languages are **procedural**: programs are lists of |
| instructions that tell the computer what to do with the program's input. C, |
| Pascal, and even Unix shells are procedural languages. |
| |
| * In **declarative** languages, you write a specification that describes the |
| problem to be solved, and the language implementation figures out how to |
| perform the computation efficiently. SQL is the declarative language you're |
| most likely to be familiar with; a SQL query describes the data set you want |
| to retrieve, and the SQL engine decides whether to scan tables or use indexes, |
| which subclauses should be performed first, etc. |
| |
| * **Object-oriented** programs manipulate collections of objects. Objects have |
| internal state and support methods that query or modify this internal state in |
| some way. Smalltalk and Java are object-oriented languages. C++ and Python |
| are languages that support object-oriented programming, but don't force the |
| use of object-oriented features. |
| |
| * **Functional** programming decomposes a problem into a set of functions. |
| Ideally, functions only take inputs and produce outputs, and don't have any |
| internal state that affects the output produced for a given input. Well-known |
| functional languages include the ML family (Standard ML, OCaml, and other |
| variants) and Haskell. |
| |
| The designers of some computer languages choose to emphasize one |
| particular approach to programming. This often makes it difficult to |
| write programs that use a different approach. Other languages are |
| multi-paradigm languages that support several different approaches. |
| Lisp, C++, and Python are multi-paradigm; you can write programs or |
| libraries that are largely procedural, object-oriented, or functional |
| in all of these languages. In a large program, different sections |
| might be written using different approaches; the GUI might be |
| object-oriented while the processing logic is procedural or |
| functional, for example. |
| |
| In a functional program, input flows through a set of functions. Each function |
| operates on its input and produces some output. Functional style discourages |
| functions with side effects that modify internal state or make other changes |
| that aren't visible in the function's return value. Functions that have no side |
| effects at all are called **purely functional**. Avoiding side effects means |
| not using data structures that get updated as a program runs; every function's |
| output must only depend on its input. |
| |
| Some languages are very strict about purity and don't even have assignment |
| statements such as ``a=3`` or ``c = a + b``, but it's difficult to avoid all |
| side effects. Printing to the screen or writing to a disk file are side |
| effects, for example. For example, in Python a call to the :func:`print` or |
| :func:`time.sleep` function both return no useful value; they're only called for |
| their side effects of sending some text to the screen or pausing execution for a |
| second. |
| |
| Python programs written in functional style usually won't go to the extreme of |
| avoiding all I/O or all assignments; instead, they'll provide a |
| functional-appearing interface but will use non-functional features internally. |
| For example, the implementation of a function will still use assignments to |
| local variables, but won't modify global variables or have other side effects. |
| |
| Functional programming can be considered the opposite of object-oriented |
| programming. Objects are little capsules containing some internal state along |
| with a collection of method calls that let you modify this state, and programs |
| consist of making the right set of state changes. Functional programming wants |
| to avoid state changes as much as possible and works with data flowing between |
| functions. In Python you might combine the two approaches by writing functions |
| that take and return instances representing objects in your application (e-mail |
| messages, transactions, etc.). |
| |
| Functional design may seem like an odd constraint to work under. Why should you |
| avoid objects and side effects? There are theoretical and practical advantages |
| to the functional style: |
| |
| * Formal provability. |
| * Modularity. |
| * Composability. |
| * Ease of debugging and testing. |
| |
| |
| Formal provability |
| ------------------ |
| |
| A theoretical benefit is that it's easier to construct a mathematical proof that |
| a functional program is correct. |
| |
| For a long time researchers have been interested in finding ways to |
| mathematically prove programs correct. This is different from testing a program |
| on numerous inputs and concluding that its output is usually correct, or reading |
| a program's source code and concluding that the code looks right; the goal is |
| instead a rigorous proof that a program produces the right result for all |
| possible inputs. |
| |
| The technique used to prove programs correct is to write down **invariants**, |
| properties of the input data and of the program's variables that are always |
| true. For each line of code, you then show that if invariants X and Y are true |
| **before** the line is executed, the slightly different invariants X' and Y' are |
| true **after** the line is executed. This continues until you reach the end of |
| the program, at which point the invariants should match the desired conditions |
| on the program's output. |
| |
| Functional programming's avoidance of assignments arose because assignments are |
| difficult to handle with this technique; assignments can break invariants that |
| were true before the assignment without producing any new invariants that can be |
| propagated onward. |
| |
| Unfortunately, proving programs correct is largely impractical and not relevant |
| to Python software. Even trivial programs require proofs that are several pages |
| long; the proof of correctness for a moderately complicated program would be |
| enormous, and few or none of the programs you use daily (the Python interpreter, |
| your XML parser, your web browser) could be proven correct. Even if you wrote |
| down or generated a proof, there would then be the question of verifying the |
| proof; maybe there's an error in it, and you wrongly believe you've proved the |
| program correct. |
| |
| |
| Modularity |
| ---------- |
| |
| A more practical benefit of functional programming is that it forces you to |
| break apart your problem into small pieces. Programs are more modular as a |
| result. It's easier to specify and write a small function that does one thing |
| than a large function that performs a complicated transformation. Small |
| functions are also easier to read and to check for errors. |
| |
| |
| Ease of debugging and testing |
| ----------------------------- |
| |
| Testing and debugging a functional-style program is easier. |
| |
| Debugging is simplified because functions are generally small and clearly |
| specified. When a program doesn't work, each function is an interface point |
| where you can check that the data are correct. You can look at the intermediate |
| inputs and outputs to quickly isolate the function that's responsible for a bug. |
| |
| Testing is easier because each function is a potential subject for a unit test. |
| Functions don't depend on system state that needs to be replicated before |
| running a test; instead you only have to synthesize the right input and then |
| check that the output matches expectations. |
| |
| |
| Composability |
| ------------- |
| |
| As you work on a functional-style program, you'll write a number of functions |
| with varying inputs and outputs. Some of these functions will be unavoidably |
| specialized to a particular application, but others will be useful in a wide |
| variety of programs. For example, a function that takes a directory path and |
| returns all the XML files in the directory, or a function that takes a filename |
| and returns its contents, can be applied to many different situations. |
| |
| Over time you'll form a personal library of utilities. Often you'll assemble |
| new programs by arranging existing functions in a new configuration and writing |
| a few functions specialized for the current task. |
| |
| |
| .. _functional-howto-iterators: |
| |
| Iterators |
| ========= |
| |
| I'll start by looking at a Python language feature that's an important |
| foundation for writing functional-style programs: iterators. |
| |
| An iterator is an object representing a stream of data; this object returns the |
| data one element at a time. A Python iterator must support a method called |
| :meth:`~iterator.__next__` that takes no arguments and always returns the next |
| element of the stream. If there are no more elements in the stream, |
| :meth:`~iterator.__next__` must raise the :exc:`StopIteration` exception. |
| Iterators don't have to be finite, though; it's perfectly reasonable to write |
| an iterator that produces an infinite stream of data. |
| |
| The built-in :func:`iter` function takes an arbitrary object and tries to return |
| an iterator that will return the object's contents or elements, raising |
| :exc:`TypeError` if the object doesn't support iteration. Several of Python's |
| built-in data types support iteration, the most common being lists and |
| dictionaries. An object is called :term:`iterable` if you can get an iterator |
| for it. |
| |
| You can experiment with the iteration interface manually: |
| |
| >>> L = [1, 2, 3] |
| >>> it = iter(L) |
| >>> it #doctest: +ELLIPSIS |
| <...iterator object at ...> |
| >>> it.__next__() # same as next(it) |
| 1 |
| >>> next(it) |
| 2 |
| >>> next(it) |
| 3 |
| >>> next(it) |
| Traceback (most recent call last): |
| File "<stdin>", line 1, in <module> |
| StopIteration |
| >>> |
| |
| Python expects iterable objects in several different contexts, the most |
| important being the :keyword:`for` statement. In the statement ``for X in Y``, |
| Y must be an iterator or some object for which :func:`iter` can create an |
| iterator. These two statements are equivalent:: |
| |
| |
| for i in iter(obj): |
| print(i) |
| |
| for i in obj: |
| print(i) |
| |
| Iterators can be materialized as lists or tuples by using the :func:`list` or |
| :func:`tuple` constructor functions: |
| |
| >>> L = [1, 2, 3] |
| >>> iterator = iter(L) |
| >>> t = tuple(iterator) |
| >>> t |
| (1, 2, 3) |
| |
| Sequence unpacking also supports iterators: if you know an iterator will return |
| N elements, you can unpack them into an N-tuple: |
| |
| >>> L = [1, 2, 3] |
| >>> iterator = iter(L) |
| >>> a, b, c = iterator |
| >>> a, b, c |
| (1, 2, 3) |
| |
| Built-in functions such as :func:`max` and :func:`min` can take a single |
| iterator argument and will return the largest or smallest element. The ``"in"`` |
| and ``"not in"`` operators also support iterators: ``X in iterator`` is true if |
| X is found in the stream returned by the iterator. You'll run into obvious |
| problems if the iterator is infinite; :func:`max`, :func:`min` |
| will never return, and if the element X never appears in the stream, the |
| ``"in"`` and ``"not in"`` operators won't return either. |
| |
| Note that you can only go forward in an iterator; there's no way to get the |
| previous element, reset the iterator, or make a copy of it. Iterator objects |
| can optionally provide these additional capabilities, but the iterator protocol |
| only specifies the :meth:`~iterator.__next__` method. Functions may therefore |
| consume all of the iterator's output, and if you need to do something different |
| with the same stream, you'll have to create a new iterator. |
| |
| |
| |
| Data Types That Support Iterators |
| --------------------------------- |
| |
| We've already seen how lists and tuples support iterators. In fact, any Python |
| sequence type, such as strings, will automatically support creation of an |
| iterator. |
| |
| Calling :func:`iter` on a dictionary returns an iterator that will loop over the |
| dictionary's keys:: |
| |
| >>> m = {'Jan': 1, 'Feb': 2, 'Mar': 3, 'Apr': 4, 'May': 5, 'Jun': 6, |
| ... 'Jul': 7, 'Aug': 8, 'Sep': 9, 'Oct': 10, 'Nov': 11, 'Dec': 12} |
| >>> for key in m: |
| ... print(key, m[key]) |
| Jan 1 |
| Feb 2 |
| Mar 3 |
| Apr 4 |
| May 5 |
| Jun 6 |
| Jul 7 |
| Aug 8 |
| Sep 9 |
| Oct 10 |
| Nov 11 |
| Dec 12 |
| |
| Note that starting with Python 3.7, dictionary iteration order is guaranteed |
| to be the same as the insertion order. In earlier versions, the behaviour was |
| unspecified and could vary between implementations. |
| |
| Applying :func:`iter` to a dictionary always loops over the keys, but |
| dictionaries have methods that return other iterators. If you want to iterate |
| over values or key/value pairs, you can explicitly call the |
| :meth:`~dict.values` or :meth:`~dict.items` methods to get an appropriate |
| iterator. |
| |
| The :func:`dict` constructor can accept an iterator that returns a finite stream |
| of ``(key, value)`` tuples: |
| |
| >>> L = [('Italy', 'Rome'), ('France', 'Paris'), ('US', 'Washington DC')] |
| >>> dict(iter(L)) |
| {'Italy': 'Rome', 'France': 'Paris', 'US': 'Washington DC'} |
| |
| Files also support iteration by calling the :meth:`~io.TextIOBase.readline` |
| method until there are no more lines in the file. This means you can read each |
| line of a file like this:: |
| |
| for line in file: |
| # do something for each line |
| ... |
| |
| Sets can take their contents from an iterable and let you iterate over the set's |
| elements:: |
| |
| S = {2, 3, 5, 7, 11, 13} |
| for i in S: |
| print(i) |
| |
| |
| |
| Generator expressions and list comprehensions |
| ============================================= |
| |
| Two common operations on an iterator's output are 1) performing some operation |
| for every element, 2) selecting a subset of elements that meet some condition. |
| For example, given a list of strings, you might want to strip off trailing |
| whitespace from each line or extract all the strings containing a given |
| substring. |
| |
| List comprehensions and generator expressions (short form: "listcomps" and |
| "genexps") are a concise notation for such operations, borrowed from the |
| functional programming language Haskell (https://www.haskell.org/). You can strip |
| all the whitespace from a stream of strings with the following code:: |
| |
| line_list = [' line 1\n', 'line 2 \n', ...] |
| |
| # Generator expression -- returns iterator |
| stripped_iter = (line.strip() for line in line_list) |
| |
| # List comprehension -- returns list |
| stripped_list = [line.strip() for line in line_list] |
| |
| You can select only certain elements by adding an ``"if"`` condition:: |
| |
| stripped_list = [line.strip() for line in line_list |
| if line != ""] |
| |
| With a list comprehension, you get back a Python list; ``stripped_list`` is a |
| list containing the resulting lines, not an iterator. Generator expressions |
| return an iterator that computes the values as necessary, not needing to |
| materialize all the values at once. This means that list comprehensions aren't |
| useful if you're working with iterators that return an infinite stream or a very |
| large amount of data. Generator expressions are preferable in these situations. |
| |
| Generator expressions are surrounded by parentheses ("()") and list |
| comprehensions are surrounded by square brackets ("[]"). Generator expressions |
| have the form:: |
| |
| ( expression for expr in sequence1 |
| if condition1 |
| for expr2 in sequence2 |
| if condition2 |
| for expr3 in sequence3 ... |
| if condition3 |
| for exprN in sequenceN |
| if conditionN ) |
| |
| Again, for a list comprehension only the outside brackets are different (square |
| brackets instead of parentheses). |
| |
| The elements of the generated output will be the successive values of |
| ``expression``. The ``if`` clauses are all optional; if present, ``expression`` |
| is only evaluated and added to the result when ``condition`` is true. |
| |
| Generator expressions always have to be written inside parentheses, but the |
| parentheses signalling a function call also count. If you want to create an |
| iterator that will be immediately passed to a function you can write:: |
| |
| obj_total = sum(obj.count for obj in list_all_objects()) |
| |
| The ``for...in`` clauses contain the sequences to be iterated over. The |
| sequences do not have to be the same length, because they are iterated over from |
| left to right, **not** in parallel. For each element in ``sequence1``, |
| ``sequence2`` is looped over from the beginning. ``sequence3`` is then looped |
| over for each resulting pair of elements from ``sequence1`` and ``sequence2``. |
| |
| To put it another way, a list comprehension or generator expression is |
| equivalent to the following Python code:: |
| |
| for expr1 in sequence1: |
| if not (condition1): |
| continue # Skip this element |
| for expr2 in sequence2: |
| if not (condition2): |
| continue # Skip this element |
| ... |
| for exprN in sequenceN: |
| if not (conditionN): |
| continue # Skip this element |
| |
| # Output the value of |
| # the expression. |
| |
| This means that when there are multiple ``for...in`` clauses but no ``if`` |
| clauses, the length of the resulting output will be equal to the product of the |
| lengths of all the sequences. If you have two lists of length 3, the output |
| list is 9 elements long: |
| |
| >>> seq1 = 'abc' |
| >>> seq2 = (1, 2, 3) |
| >>> [(x, y) for x in seq1 for y in seq2] #doctest: +NORMALIZE_WHITESPACE |
| [('a', 1), ('a', 2), ('a', 3), |
| ('b', 1), ('b', 2), ('b', 3), |
| ('c', 1), ('c', 2), ('c', 3)] |
| |
| To avoid introducing an ambiguity into Python's grammar, if ``expression`` is |
| creating a tuple, it must be surrounded with parentheses. The first list |
| comprehension below is a syntax error, while the second one is correct:: |
| |
| # Syntax error |
| [x, y for x in seq1 for y in seq2] |
| # Correct |
| [(x, y) for x in seq1 for y in seq2] |
| |
| |
| Generators |
| ========== |
| |
| Generators are a special class of functions that simplify the task of writing |
| iterators. Regular functions compute a value and return it, but generators |
| return an iterator that returns a stream of values. |
| |
| You're doubtless familiar with how regular function calls work in Python or C. |
| When you call a function, it gets a private namespace where its local variables |
| are created. When the function reaches a ``return`` statement, the local |
| variables are destroyed and the value is returned to the caller. A later call |
| to the same function creates a new private namespace and a fresh set of local |
| variables. But, what if the local variables weren't thrown away on exiting a |
| function? What if you could later resume the function where it left off? This |
| is what generators provide; they can be thought of as resumable functions. |
| |
| Here's the simplest example of a generator function: |
| |
| >>> def generate_ints(N): |
| ... for i in range(N): |
| ... yield i |
| |
| Any function containing a :keyword:`yield` keyword is a generator function; |
| this is detected by Python's :term:`bytecode` compiler which compiles the |
| function specially as a result. |
| |
| When you call a generator function, it doesn't return a single value; instead it |
| returns a generator object that supports the iterator protocol. On executing |
| the ``yield`` expression, the generator outputs the value of ``i``, similar to a |
| ``return`` statement. The big difference between ``yield`` and a ``return`` |
| statement is that on reaching a ``yield`` the generator's state of execution is |
| suspended and local variables are preserved. On the next call to the |
| generator's :meth:`~generator.__next__` method, the function will resume |
| executing. |
| |
| Here's a sample usage of the ``generate_ints()`` generator: |
| |
| >>> gen = generate_ints(3) |
| >>> gen #doctest: +ELLIPSIS |
| <generator object generate_ints at ...> |
| >>> next(gen) |
| 0 |
| >>> next(gen) |
| 1 |
| >>> next(gen) |
| 2 |
| >>> next(gen) |
| Traceback (most recent call last): |
| File "stdin", line 1, in <module> |
| File "stdin", line 2, in generate_ints |
| StopIteration |
| |
| You could equally write ``for i in generate_ints(5)``, or ``a, b, c = |
| generate_ints(3)``. |
| |
| Inside a generator function, ``return value`` causes ``StopIteration(value)`` |
| to be raised from the :meth:`~generator.__next__` method. Once this happens, or |
| the bottom of the function is reached, the procession of values ends and the |
| generator cannot yield any further values. |
| |
| You could achieve the effect of generators manually by writing your own class |
| and storing all the local variables of the generator as instance variables. For |
| example, returning a list of integers could be done by setting ``self.count`` to |
| 0, and having the :meth:`~iterator.__next__` method increment ``self.count`` and |
| return it. |
| However, for a moderately complicated generator, writing a corresponding class |
| can be much messier. |
| |
| The test suite included with Python's library, |
| :source:`Lib/test/test_generators.py`, contains |
| a number of more interesting examples. Here's one generator that implements an |
| in-order traversal of a tree using generators recursively. :: |
| |
| # A recursive generator that generates Tree leaves in in-order. |
| def inorder(t): |
| if t: |
| for x in inorder(t.left): |
| yield x |
| |
| yield t.label |
| |
| for x in inorder(t.right): |
| yield x |
| |
| Two other examples in ``test_generators.py`` produce solutions for the N-Queens |
| problem (placing N queens on an NxN chess board so that no queen threatens |
| another) and the Knight's Tour (finding a route that takes a knight to every |
| square of an NxN chessboard without visiting any square twice). |
| |
| |
| |
| Passing values into a generator |
| ------------------------------- |
| |
| In Python 2.4 and earlier, generators only produced output. Once a generator's |
| code was invoked to create an iterator, there was no way to pass any new |
| information into the function when its execution is resumed. You could hack |
| together this ability by making the generator look at a global variable or by |
| passing in some mutable object that callers then modify, but these approaches |
| are messy. |
| |
| In Python 2.5 there's a simple way to pass values into a generator. |
| :keyword:`yield` became an expression, returning a value that can be assigned to |
| a variable or otherwise operated on:: |
| |
| val = (yield i) |
| |
| I recommend that you **always** put parentheses around a ``yield`` expression |
| when you're doing something with the returned value, as in the above example. |
| The parentheses aren't always necessary, but it's easier to always add them |
| instead of having to remember when they're needed. |
| |
| (:pep:`342` explains the exact rules, which are that a ``yield``-expression must |
| always be parenthesized except when it occurs at the top-level expression on the |
| right-hand side of an assignment. This means you can write ``val = yield i`` |
| but have to use parentheses when there's an operation, as in ``val = (yield i) |
| + 12``.) |
| |
| Values are sent into a generator by calling its :meth:`send(value) |
| <generator.send>` method. This method resumes the generator's code and the |
| ``yield`` expression returns the specified value. If the regular |
| :meth:`~generator.__next__` method is called, the ``yield`` returns ``None``. |
| |
| Here's a simple counter that increments by 1 and allows changing the value of |
| the internal counter. |
| |
| .. testcode:: |
| |
| def counter(maximum): |
| i = 0 |
| while i < maximum: |
| val = (yield i) |
| # If value provided, change counter |
| if val is not None: |
| i = val |
| else: |
| i += 1 |
| |
| And here's an example of changing the counter: |
| |
| >>> it = counter(10) #doctest: +SKIP |
| >>> next(it) #doctest: +SKIP |
| 0 |
| >>> next(it) #doctest: +SKIP |
| 1 |
| >>> it.send(8) #doctest: +SKIP |
| 8 |
| >>> next(it) #doctest: +SKIP |
| 9 |
| >>> next(it) #doctest: +SKIP |
| Traceback (most recent call last): |
| File "t.py", line 15, in <module> |
| it.next() |
| StopIteration |
| |
| Because ``yield`` will often be returning ``None``, you should always check for |
| this case. Don't just use its value in expressions unless you're sure that the |
| :meth:`~generator.send` method will be the only method used to resume your |
| generator function. |
| |
| In addition to :meth:`~generator.send`, there are two other methods on |
| generators: |
| |
| * :meth:`throw(type, value=None, traceback=None) <generator.throw>` is used to |
| raise an exception inside the generator; the exception is raised by the |
| ``yield`` expression where the generator's execution is paused. |
| |
| * :meth:`~generator.close` raises a :exc:`GeneratorExit` exception inside the |
| generator to terminate the iteration. On receiving this exception, the |
| generator's code must either raise :exc:`GeneratorExit` or |
| :exc:`StopIteration`; catching the exception and doing anything else is |
| illegal and will trigger a :exc:`RuntimeError`. :meth:`~generator.close` |
| will also be called by Python's garbage collector when the generator is |
| garbage-collected. |
| |
| If you need to run cleanup code when a :exc:`GeneratorExit` occurs, I suggest |
| using a ``try: ... finally:`` suite instead of catching :exc:`GeneratorExit`. |
| |
| The cumulative effect of these changes is to turn generators from one-way |
| producers of information into both producers and consumers. |
| |
| Generators also become **coroutines**, a more generalized form of subroutines. |
| Subroutines are entered at one point and exited at another point (the top of the |
| function, and a ``return`` statement), but coroutines can be entered, exited, |
| and resumed at many different points (the ``yield`` statements). |
| |
| |
| Built-in functions |
| ================== |
| |
| Let's look in more detail at built-in functions often used with iterators. |
| |
| Two of Python's built-in functions, :func:`map` and :func:`filter` duplicate the |
| features of generator expressions: |
| |
| :func:`map(f, iterA, iterB, ...) <map>` returns an iterator over the sequence |
| ``f(iterA[0], iterB[0]), f(iterA[1], iterB[1]), f(iterA[2], iterB[2]), ...``. |
| |
| >>> def upper(s): |
| ... return s.upper() |
| |
| >>> list(map(upper, ['sentence', 'fragment'])) |
| ['SENTENCE', 'FRAGMENT'] |
| >>> [upper(s) for s in ['sentence', 'fragment']] |
| ['SENTENCE', 'FRAGMENT'] |
| |
| You can of course achieve the same effect with a list comprehension. |
| |
| :func:`filter(predicate, iter) <filter>` returns an iterator over all the |
| sequence elements that meet a certain condition, and is similarly duplicated by |
| list comprehensions. A **predicate** is a function that returns the truth |
| value of some condition; for use with :func:`filter`, the predicate must take a |
| single value. |
| |
| >>> def is_even(x): |
| ... return (x % 2) == 0 |
| |
| >>> list(filter(is_even, range(10))) |
| [0, 2, 4, 6, 8] |
| |
| |
| This can also be written as a list comprehension: |
| |
| >>> list(x for x in range(10) if is_even(x)) |
| [0, 2, 4, 6, 8] |
| |
| |
| :func:`enumerate(iter, start=0) <enumerate>` counts off the elements in the |
| iterable returning 2-tuples containing the count (from *start*) and |
| each element. :: |
| |
| >>> for item in enumerate(['subject', 'verb', 'object']): |
| ... print(item) |
| (0, 'subject') |
| (1, 'verb') |
| (2, 'object') |
| |
| :func:`enumerate` is often used when looping through a list and recording the |
| indexes at which certain conditions are met:: |
| |
| f = open('data.txt', 'r') |
| for i, line in enumerate(f): |
| if line.strip() == '': |
| print('Blank line at line #%i' % i) |
| |
| :func:`sorted(iterable, key=None, reverse=False) <sorted>` collects all the |
| elements of the iterable into a list, sorts the list, and returns the sorted |
| result. The *key* and *reverse* arguments are passed through to the |
| constructed list's :meth:`~list.sort` method. :: |
| |
| >>> import random |
| >>> # Generate 8 random numbers between [0, 10000) |
| >>> rand_list = random.sample(range(10000), 8) |
| >>> rand_list #doctest: +SKIP |
| [769, 7953, 9828, 6431, 8442, 9878, 6213, 2207] |
| >>> sorted(rand_list) #doctest: +SKIP |
| [769, 2207, 6213, 6431, 7953, 8442, 9828, 9878] |
| >>> sorted(rand_list, reverse=True) #doctest: +SKIP |
| [9878, 9828, 8442, 7953, 6431, 6213, 2207, 769] |
| |
| (For a more detailed discussion of sorting, see the :ref:`sortinghowto`.) |
| |
| |
| The :func:`any(iter) <any>` and :func:`all(iter) <all>` built-ins look at the |
| truth values of an iterable's contents. :func:`any` returns ``True`` if any element |
| in the iterable is a true value, and :func:`all` returns ``True`` if all of the |
| elements are true values: |
| |
| >>> any([0, 1, 0]) |
| True |
| >>> any([0, 0, 0]) |
| False |
| >>> any([1, 1, 1]) |
| True |
| >>> all([0, 1, 0]) |
| False |
| >>> all([0, 0, 0]) |
| False |
| >>> all([1, 1, 1]) |
| True |
| |
| |
| :func:`zip(iterA, iterB, ...) <zip>` takes one element from each iterable and |
| returns them in a tuple:: |
| |
| zip(['a', 'b', 'c'], (1, 2, 3)) => |
| ('a', 1), ('b', 2), ('c', 3) |
| |
| It doesn't construct an in-memory list and exhaust all the input iterators |
| before returning; instead tuples are constructed and returned only if they're |
| requested. (The technical term for this behaviour is `lazy evaluation |
| <https://en.wikipedia.org/wiki/Lazy_evaluation>`__.) |
| |
| This iterator is intended to be used with iterables that are all of the same |
| length. If the iterables are of different lengths, the resulting stream will be |
| the same length as the shortest iterable. :: |
| |
| zip(['a', 'b'], (1, 2, 3)) => |
| ('a', 1), ('b', 2) |
| |
| You should avoid doing this, though, because an element may be taken from the |
| longer iterators and discarded. This means you can't go on to use the iterators |
| further because you risk skipping a discarded element. |
| |
| |
| The itertools module |
| ==================== |
| |
| The :mod:`itertools` module contains a number of commonly-used iterators as well |
| as functions for combining several iterators. This section will introduce the |
| module's contents by showing small examples. |
| |
| The module's functions fall into a few broad classes: |
| |
| * Functions that create a new iterator based on an existing iterator. |
| * Functions for treating an iterator's elements as function arguments. |
| * Functions for selecting portions of an iterator's output. |
| * A function for grouping an iterator's output. |
| |
| Creating new iterators |
| ---------------------- |
| |
| :func:`itertools.count(start, step) <itertools.count>` returns an infinite |
| stream of evenly spaced values. You can optionally supply the starting number, |
| which defaults to 0, and the interval between numbers, which defaults to 1:: |
| |
| itertools.count() => |
| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... |
| itertools.count(10) => |
| 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ... |
| itertools.count(10, 5) => |
| 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, ... |
| |
| :func:`itertools.cycle(iter) <itertools.cycle>` saves a copy of the contents of |
| a provided iterable and returns a new iterator that returns its elements from |
| first to last. The new iterator will repeat these elements infinitely. :: |
| |
| itertools.cycle([1, 2, 3, 4, 5]) => |
| 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, ... |
| |
| :func:`itertools.repeat(elem, [n]) <itertools.repeat>` returns the provided |
| element *n* times, or returns the element endlessly if *n* is not provided. :: |
| |
| itertools.repeat('abc') => |
| abc, abc, abc, abc, abc, abc, abc, abc, abc, abc, ... |
| itertools.repeat('abc', 5) => |
| abc, abc, abc, abc, abc |
| |
| :func:`itertools.chain(iterA, iterB, ...) <itertools.chain>` takes an arbitrary |
| number of iterables as input, and returns all the elements of the first |
| iterator, then all the elements of the second, and so on, until all of the |
| iterables have been exhausted. :: |
| |
| itertools.chain(['a', 'b', 'c'], (1, 2, 3)) => |
| a, b, c, 1, 2, 3 |
| |
| :func:`itertools.islice(iter, [start], stop, [step]) <itertools.islice>` returns |
| a stream that's a slice of the iterator. With a single *stop* argument, it |
| will return the first *stop* elements. If you supply a starting index, you'll |
| get *stop-start* elements, and if you supply a value for *step*, elements |
| will be skipped accordingly. Unlike Python's string and list slicing, you can't |
| use negative values for *start*, *stop*, or *step*. :: |
| |
| itertools.islice(range(10), 8) => |
| 0, 1, 2, 3, 4, 5, 6, 7 |
| itertools.islice(range(10), 2, 8) => |
| 2, 3, 4, 5, 6, 7 |
| itertools.islice(range(10), 2, 8, 2) => |
| 2, 4, 6 |
| |
| :func:`itertools.tee(iter, [n]) <itertools.tee>` replicates an iterator; it |
| returns *n* independent iterators that will all return the contents of the |
| source iterator. |
| If you don't supply a value for *n*, the default is 2. Replicating iterators |
| requires saving some of the contents of the source iterator, so this can consume |
| significant memory if the iterator is large and one of the new iterators is |
| consumed more than the others. :: |
| |
| itertools.tee( itertools.count() ) => |
| iterA, iterB |
| |
| where iterA -> |
| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... |
| |
| and iterB -> |
| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... |
| |
| |
| Calling functions on elements |
| ----------------------------- |
| |
| The :mod:`operator` module contains a set of functions corresponding to Python's |
| operators. Some examples are :func:`operator.add(a, b) <operator.add>` (adds |
| two values), :func:`operator.ne(a, b) <operator.ne>` (same as ``a != b``), and |
| :func:`operator.attrgetter('id') <operator.attrgetter>` |
| (returns a callable that fetches the ``.id`` attribute). |
| |
| :func:`itertools.starmap(func, iter) <itertools.starmap>` assumes that the |
| iterable will return a stream of tuples, and calls *func* using these tuples as |
| the arguments:: |
| |
| itertools.starmap(os.path.join, |
| [('/bin', 'python'), ('/usr', 'bin', 'java'), |
| ('/usr', 'bin', 'perl'), ('/usr', 'bin', 'ruby')]) |
| => |
| /bin/python, /usr/bin/java, /usr/bin/perl, /usr/bin/ruby |
| |
| |
| Selecting elements |
| ------------------ |
| |
| Another group of functions chooses a subset of an iterator's elements based on a |
| predicate. |
| |
| :func:`itertools.filterfalse(predicate, iter) <itertools.filterfalse>` is the |
| opposite of :func:`filter`, returning all elements for which the predicate |
| returns false:: |
| |
| itertools.filterfalse(is_even, itertools.count()) => |
| 1, 3, 5, 7, 9, 11, 13, 15, ... |
| |
| :func:`itertools.takewhile(predicate, iter) <itertools.takewhile>` returns |
| elements for as long as the predicate returns true. Once the predicate returns |
| false, the iterator will signal the end of its results. :: |
| |
| def less_than_10(x): |
| return x < 10 |
| |
| itertools.takewhile(less_than_10, itertools.count()) => |
| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| |
| itertools.takewhile(is_even, itertools.count()) => |
| 0 |
| |
| :func:`itertools.dropwhile(predicate, iter) <itertools.dropwhile>` discards |
| elements while the predicate returns true, and then returns the rest of the |
| iterable's results. :: |
| |
| itertools.dropwhile(less_than_10, itertools.count()) => |
| 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, ... |
| |
| itertools.dropwhile(is_even, itertools.count()) => |
| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... |
| |
| :func:`itertools.compress(data, selectors) <itertools.compress>` takes two |
| iterators and returns only those elements of *data* for which the corresponding |
| element of *selectors* is true, stopping whenever either one is exhausted:: |
| |
| itertools.compress([1, 2, 3, 4, 5], [True, True, False, False, True]) => |
| 1, 2, 5 |
| |
| |
| Combinatoric functions |
| ---------------------- |
| |
| The :func:`itertools.combinations(iterable, r) <itertools.combinations>` |
| returns an iterator giving all possible *r*-tuple combinations of the |
| elements contained in *iterable*. :: |
| |
| itertools.combinations([1, 2, 3, 4, 5], 2) => |
| (1, 2), (1, 3), (1, 4), (1, 5), |
| (2, 3), (2, 4), (2, 5), |
| (3, 4), (3, 5), |
| (4, 5) |
| |
| itertools.combinations([1, 2, 3, 4, 5], 3) => |
| (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 4), (1, 3, 5), (1, 4, 5), |
| (2, 3, 4), (2, 3, 5), (2, 4, 5), |
| (3, 4, 5) |
| |
| The elements within each tuple remain in the same order as |
| *iterable* returned them. For example, the number 1 is always before |
| 2, 3, 4, or 5 in the examples above. A similar function, |
| :func:`itertools.permutations(iterable, r=None) <itertools.permutations>`, |
| removes this constraint on the order, returning all possible |
| arrangements of length *r*:: |
| |
| itertools.permutations([1, 2, 3, 4, 5], 2) => |
| (1, 2), (1, 3), (1, 4), (1, 5), |
| (2, 1), (2, 3), (2, 4), (2, 5), |
| (3, 1), (3, 2), (3, 4), (3, 5), |
| (4, 1), (4, 2), (4, 3), (4, 5), |
| (5, 1), (5, 2), (5, 3), (5, 4) |
| |
| itertools.permutations([1, 2, 3, 4, 5]) => |
| (1, 2, 3, 4, 5), (1, 2, 3, 5, 4), (1, 2, 4, 3, 5), |
| ... |
| (5, 4, 3, 2, 1) |
| |
| If you don't supply a value for *r* the length of the iterable is used, |
| meaning that all the elements are permuted. |
| |
| Note that these functions produce all of the possible combinations by |
| position and don't require that the contents of *iterable* are unique:: |
| |
| itertools.permutations('aba', 3) => |
| ('a', 'b', 'a'), ('a', 'a', 'b'), ('b', 'a', 'a'), |
| ('b', 'a', 'a'), ('a', 'a', 'b'), ('a', 'b', 'a') |
| |
| The identical tuple ``('a', 'a', 'b')`` occurs twice, but the two 'a' |
| strings came from different positions. |
| |
| The :func:`itertools.combinations_with_replacement(iterable, r) <itertools.combinations_with_replacement>` |
| function relaxes a different constraint: elements can be repeated |
| within a single tuple. Conceptually an element is selected for the |
| first position of each tuple and then is replaced before the second |
| element is selected. :: |
| |
| itertools.combinations_with_replacement([1, 2, 3, 4, 5], 2) => |
| (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), |
| (2, 2), (2, 3), (2, 4), (2, 5), |
| (3, 3), (3, 4), (3, 5), |
| (4, 4), (4, 5), |
| (5, 5) |
| |
| |
| Grouping elements |
| ----------------- |
| |
| The last function I'll discuss, :func:`itertools.groupby(iter, key_func=None) |
| <itertools.groupby>`, is the most complicated. ``key_func(elem)`` is a function |
| that can compute a key value for each element returned by the iterable. If you |
| don't supply a key function, the key is simply each element itself. |
| |
| :func:`~itertools.groupby` collects all the consecutive elements from the |
| underlying iterable that have the same key value, and returns a stream of |
| 2-tuples containing a key value and an iterator for the elements with that key. |
| |
| :: |
| |
| city_list = [('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL'), |
| ('Anchorage', 'AK'), ('Nome', 'AK'), |
| ('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ'), |
| ... |
| ] |
| |
| def get_state(city_state): |
| return city_state[1] |
| |
| itertools.groupby(city_list, get_state) => |
| ('AL', iterator-1), |
| ('AK', iterator-2), |
| ('AZ', iterator-3), ... |
| |
| where |
| iterator-1 => |
| ('Decatur', 'AL'), ('Huntsville', 'AL'), ('Selma', 'AL') |
| iterator-2 => |
| ('Anchorage', 'AK'), ('Nome', 'AK') |
| iterator-3 => |
| ('Flagstaff', 'AZ'), ('Phoenix', 'AZ'), ('Tucson', 'AZ') |
| |
| :func:`~itertools.groupby` assumes that the underlying iterable's contents will |
| already be sorted based on the key. Note that the returned iterators also use |
| the underlying iterable, so you have to consume the results of iterator-1 before |
| requesting iterator-2 and its corresponding key. |
| |
| |
| The functools module |
| ==================== |
| |
| The :mod:`functools` module in Python 2.5 contains some higher-order functions. |
| A **higher-order function** takes one or more functions as input and returns a |
| new function. The most useful tool in this module is the |
| :func:`functools.partial` function. |
| |
| For programs written in a functional style, you'll sometimes want to construct |
| variants of existing functions that have some of the parameters filled in. |
| Consider a Python function ``f(a, b, c)``; you may wish to create a new function |
| ``g(b, c)`` that's equivalent to ``f(1, b, c)``; you're filling in a value for |
| one of ``f()``'s parameters. This is called "partial function application". |
| |
| The constructor for :func:`~functools.partial` takes the arguments |
| ``(function, arg1, arg2, ..., kwarg1=value1, kwarg2=value2)``. The resulting |
| object is callable, so you can just call it to invoke ``function`` with the |
| filled-in arguments. |
| |
| Here's a small but realistic example:: |
| |
| import functools |
| |
| def log(message, subsystem): |
| """Write the contents of 'message' to the specified subsystem.""" |
| print('%s: %s' % (subsystem, message)) |
| ... |
| |
| server_log = functools.partial(log, subsystem='server') |
| server_log('Unable to open socket') |
| |
| :func:`functools.reduce(func, iter, [initial_value]) <functools.reduce>` |
| cumulatively performs an operation on all the iterable's elements and, |
| therefore, can't be applied to infinite iterables. *func* must be a function |
| that takes two elements and returns a single value. :func:`functools.reduce` |
| takes the first two elements A and B returned by the iterator and calculates |
| ``func(A, B)``. It then requests the third element, C, calculates |
| ``func(func(A, B), C)``, combines this result with the fourth element returned, |
| and continues until the iterable is exhausted. If the iterable returns no |
| values at all, a :exc:`TypeError` exception is raised. If the initial value is |
| supplied, it's used as a starting point and ``func(initial_value, A)`` is the |
| first calculation. :: |
| |
| >>> import operator, functools |
| >>> functools.reduce(operator.concat, ['A', 'BB', 'C']) |
| 'ABBC' |
| >>> functools.reduce(operator.concat, []) |
| Traceback (most recent call last): |
| ... |
| TypeError: reduce() of empty sequence with no initial value |
| >>> functools.reduce(operator.mul, [1, 2, 3], 1) |
| 6 |
| >>> functools.reduce(operator.mul, [], 1) |
| 1 |
| |
| If you use :func:`operator.add` with :func:`functools.reduce`, you'll add up all the |
| elements of the iterable. This case is so common that there's a special |
| built-in called :func:`sum` to compute it: |
| |
| >>> import functools, operator |
| >>> functools.reduce(operator.add, [1, 2, 3, 4], 0) |
| 10 |
| >>> sum([1, 2, 3, 4]) |
| 10 |
| >>> sum([]) |
| 0 |
| |
| For many uses of :func:`functools.reduce`, though, it can be clearer to just |
| write the obvious :keyword:`for` loop:: |
| |
| import functools |
| # Instead of: |
| product = functools.reduce(operator.mul, [1, 2, 3], 1) |
| |
| # You can write: |
| product = 1 |
| for i in [1, 2, 3]: |
| product *= i |
| |
| A related function is :func:`itertools.accumulate(iterable, func=operator.add) |
| <itertools.accumulate>`. It performs the same calculation, but instead of |
| returning only the final result, :func:`accumulate` returns an iterator that |
| also yields each partial result:: |
| |
| itertools.accumulate([1, 2, 3, 4, 5]) => |
| 1, 3, 6, 10, 15 |
| |
| itertools.accumulate([1, 2, 3, 4, 5], operator.mul) => |
| 1, 2, 6, 24, 120 |
| |
| |
| The operator module |
| ------------------- |
| |
| The :mod:`operator` module was mentioned earlier. It contains a set of |
| functions corresponding to Python's operators. These functions are often useful |
| in functional-style code because they save you from writing trivial functions |
| that perform a single operation. |
| |
| Some of the functions in this module are: |
| |
| * Math operations: ``add()``, ``sub()``, ``mul()``, ``floordiv()``, ``abs()``, ... |
| * Logical operations: ``not_()``, ``truth()``. |
| * Bitwise operations: ``and_()``, ``or_()``, ``invert()``. |
| * Comparisons: ``eq()``, ``ne()``, ``lt()``, ``le()``, ``gt()``, and ``ge()``. |
| * Object identity: ``is_()``, ``is_not()``. |
| |
| Consult the operator module's documentation for a complete list. |
| |
| |
| Small functions and the lambda expression |
| ========================================= |
| |
| When writing functional-style programs, you'll often need little functions that |
| act as predicates or that combine elements in some way. |
| |
| If there's a Python built-in or a module function that's suitable, you don't |
| need to define a new function at all:: |
| |
| stripped_lines = [line.strip() for line in lines] |
| existing_files = filter(os.path.exists, file_list) |
| |
| If the function you need doesn't exist, you need to write it. One way to write |
| small functions is to use the :keyword:`lambda` statement. ``lambda`` takes a |
| number of parameters and an expression combining these parameters, and creates |
| an anonymous function that returns the value of the expression:: |
| |
| adder = lambda x, y: x+y |
| |
| print_assign = lambda name, value: name + '=' + str(value) |
| |
| An alternative is to just use the ``def`` statement and define a function in the |
| usual way:: |
| |
| def adder(x, y): |
| return x + y |
| |
| def print_assign(name, value): |
| return name + '=' + str(value) |
| |
| Which alternative is preferable? That's a style question; my usual course is to |
| avoid using ``lambda``. |
| |
| One reason for my preference is that ``lambda`` is quite limited in the |
| functions it can define. The result has to be computable as a single |
| expression, which means you can't have multiway ``if... elif... else`` |
| comparisons or ``try... except`` statements. If you try to do too much in a |
| ``lambda`` statement, you'll end up with an overly complicated expression that's |
| hard to read. Quick, what's the following code doing? :: |
| |
| import functools |
| total = functools.reduce(lambda a, b: (0, a[1] + b[1]), items)[1] |
| |
| You can figure it out, but it takes time to disentangle the expression to figure |
| out what's going on. Using a short nested ``def`` statements makes things a |
| little bit better:: |
| |
| import functools |
| def combine(a, b): |
| return 0, a[1] + b[1] |
| |
| total = functools.reduce(combine, items)[1] |
| |
| But it would be best of all if I had simply used a ``for`` loop:: |
| |
| total = 0 |
| for a, b in items: |
| total += b |
| |
| Or the :func:`sum` built-in and a generator expression:: |
| |
| total = sum(b for a, b in items) |
| |
| Many uses of :func:`functools.reduce` are clearer when written as ``for`` loops. |
| |
| Fredrik Lundh once suggested the following set of rules for refactoring uses of |
| ``lambda``: |
| |
| 1. Write a lambda function. |
| 2. Write a comment explaining what the heck that lambda does. |
| 3. Study the comment for a while, and think of a name that captures the essence |
| of the comment. |
| 4. Convert the lambda to a def statement, using that name. |
| 5. Remove the comment. |
| |
| I really like these rules, but you're free to disagree |
| about whether this lambda-free style is better. |
| |
| |
| Revision History and Acknowledgements |
| ===================================== |
| |
| The author would like to thank the following people for offering suggestions, |
| corrections and assistance with various drafts of this article: Ian Bicking, |
| Nick Coghlan, Nick Efford, Raymond Hettinger, Jim Jewett, Mike Krell, Leandro |
| Lameiro, Jussi Salmela, Collin Winter, Blake Winton. |
| |
| Version 0.1: posted June 30 2006. |
| |
| Version 0.11: posted July 1 2006. Typo fixes. |
| |
| Version 0.2: posted July 10 2006. Merged genexp and listcomp sections into one. |
| Typo fixes. |
| |
| Version 0.21: Added more references suggested on the tutor mailing list. |
| |
| Version 0.30: Adds a section on the ``functional`` module written by Collin |
| Winter; adds short section on the operator module; a few other edits. |
| |
| |
| References |
| ========== |
| |
| General |
| ------- |
| |
| **Structure and Interpretation of Computer Programs**, by Harold Abelson and |
| Gerald Jay Sussman with Julie Sussman. Full text at |
| https://mitpress.mit.edu/sicp/. In this classic textbook of computer science, |
| chapters 2 and 3 discuss the use of sequences and streams to organize the data |
| flow inside a program. The book uses Scheme for its examples, but many of the |
| design approaches described in these chapters are applicable to functional-style |
| Python code. |
| |
| http://www.defmacro.org/ramblings/fp.html: A general introduction to functional |
| programming that uses Java examples and has a lengthy historical introduction. |
| |
| https://en.wikipedia.org/wiki/Functional_programming: General Wikipedia entry |
| describing functional programming. |
| |
| https://en.wikipedia.org/wiki/Coroutine: Entry for coroutines. |
| |
| https://en.wikipedia.org/wiki/Currying: Entry for the concept of currying. |
| |
| Python-specific |
| --------------- |
| |
| http://gnosis.cx/TPiP/: The first chapter of David Mertz's book |
| :title-reference:`Text Processing in Python` discusses functional programming |
| for text processing, in the section titled "Utilizing Higher-Order Functions in |
| Text Processing". |
| |
| Mertz also wrote a 3-part series of articles on functional programming |
| for IBM's DeveloperWorks site; see |
| `part 1 <https://www.ibm.com/developerworks/linux/library/l-prog/index.html>`__, |
| `part 2 <https://www.ibm.com/developerworks/linux/library/l-prog2/index.html>`__, and |
| `part 3 <https://www.ibm.com/developerworks/linux/library/l-prog3/index.html>`__, |
| |
| |
| Python documentation |
| -------------------- |
| |
| Documentation for the :mod:`itertools` module. |
| |
| Documentation for the :mod:`functools` module. |
| |
| Documentation for the :mod:`operator` module. |
| |
| :pep:`289`: "Generator Expressions" |
| |
| :pep:`342`: "Coroutines via Enhanced Generators" describes the new generator |
| features in Python 2.5. |
| |
| .. comment |
| |
| Handy little function for printing part of an iterator -- used |
| while writing this document. |
| |
| import itertools |
| def print_iter(it): |
| slice = itertools.islice(it, 10) |
| for elem in slice[:-1]: |
| sys.stdout.write(str(elem)) |
| sys.stdout.write(', ') |
| print(elem[-1]) |