函式程式設計 HOWTO

作者:

A. M. Kuchling

發佈版本:

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 iterators and generators and relevant library modules such as itertools and functools.

簡介

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 疊代器.

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, such as printing to the screen or writing to a disk file. Another example is a call to the print() or time.sleep() function, neither of which returns a useful value. Both are called only 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:

• 形式可證明性 (Formal provability)。

• 模組化 (Modularity)。

• 可組合性 (Composability)。

• 容易除錯與測試。

形式可證明性

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.

模組化

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.

容易除錯與測試

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.

可組合性

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.

疊代器

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 __next__() that takes no arguments and always returns the next element of the stream. If there are no more elements in the stream, __next__() must raise the 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 iter() function takes an arbitrary object and tries to return an iterator that will return the object's contents or elements, raising 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 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
<...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 for statement. In the statement for X in Y, Y must be an iterator or some object for which 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 list() or 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 max() and 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; max(), 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 __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 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 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 values() or items() methods to get an appropriate iterator.

The 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 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)
2
3
5
7
11
13

產生器運算式與串列綜合運算式

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', ' \n', '']

>>> # 產生器運算式 -- 回傳疊代器
>>> stripped_iter = (line.strip() for line in line_list)

>>> # 串列綜合運算式 -- 回傳串列
>>> 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