Functional programming in Python, Part 1
Making more out of your favorite scripting language
This content is part # of # in the series: Charming Python
This content is part of the series: Charming Python
Stay tuned for additional content in this series.
We'd better start with the hardest question: "What is functional programming (FP), anyway?" One answer would be to say that FP is what you do when you program in languages like Lisp, Scheme, Haskell, ML, OCAML, Clean, Mercury, or Erlang (or a few others). That is a safe answer, but not one that clarifies very much. Unfortunately, it is hard to get a consistent opinion on just what FP is, even from functional programmers themselves. A story about elephants and blind men seems apropos here. It is also safe to contrast FP with "imperative programming" (what you do in languages like C, Pascal, C++, Java, Perl, Awk, TCL, and most others, at least for the most part).
Personally, I would roughly characterize functional programming as having at least several of the following characteristics. Languages that get called functional make these things easy, and make other things either hard or impossible:
- Functions are first class (objects). That is, everything you can do with "data" can be done with functions themselves (such as passing a function to another function).
- Recursion is used as a primary control structure. In some languages, no other "loop" construct exists.
- There is a focus on LISt Processing (for example, the name
Lisp). Lists are often used with recursion on sub-lists as a substitute for loops.
- "Pure" functional languages eschew side-effects. This excludes the almost ubiquitous pattern in imperative languages of assigning first one, then another value to the same variable to track the program state.
- FP either discourages or outright disallows statements, and instead works with the evaluation of expressions (in other words, functions plus arguments). In the pure case, one program is one expression (plus supporting definitions).
- FP worries about what is to be computed rather than how it is to be computed.
- Much FP utilizes "higher order" functions (in other words, functions that operate on functions that operate on functions).
Advocates of functional programming argue that all these characteristic make for more rapidly developed, shorter, and less bug-prone code. Moreover, high theorists of computer science, logic, and math find it a lot easier to prove formal properties of functional languages and programs than of imperative languages and programs.
Inherent Python functional capabilities
Python has had most of the characteristics of FP listed above since Python 1.0. But as with most Python features, they have been present in a very mixed language. Much as with Python's OOP features, you can use what you want and ignore the rest (until you need it later). With Python 2.0, a very nice bit of "syntactic sugar" was added with list comprehensions. While list comprehensions add no new capability, they make a lot of the old capabilities look a lot nicer.
The basic elements of FP in Python are the functions
filter(), and the operator
lambda. In Python 1.x, the
apply() function also
comes in handy for direct application of one function's list return value
to another function. Python 2.0 provides an improved syntax for this
purpose. Perhaps surprisingly, these very few functions (and the basic
operators) are almost sufficient to write any Python program;
specifically, the flow control statements (
def) can all be handled in a functional
style using exclusively the FP functions and operators. While actually
eliminating all flow control commands in a program is probably only useful
for entering an "obfuscated Python" contest (with code that will look a
lot like Lisp), it is worth understanding how FP expresses flow control
with functions and recursion.
Eliminating flow control statements
The first thing to think about in our elimination exercise is the fact
that Python "short circuits" evaluation of Boolean expressions. This
provides an expression version of
else blocks (assuming each block calls one function, which is
always possible to arrange). Here's how:
Listing 1. "Short-circuit" conditional calls in Python
# Normal statement-based flow control if <cond1>: func1() elif <cond2>: func2() else: func3() # Equivalent "short circuit" expression (<cond1> and func1()) or (<cond2> and func2()) or (func3()) # Example "short circuit" expression >>> x = 3 >>> def pr(s): return s >>> (x==1 and pr('one')) or (x==2 and pr('two')) or (pr('other')) 'other' >>> x = 2 >>> (x==1 and pr('one')) or (x==2 and pr('two')) or (pr('other')) 'two'
Our expression version of conditional calls might seem to be nothing but a
parlor trick; however, it is more interesting when we notice that the
lambda operator must return an expression. Since -- as we
have shown -- expressions can contain conditional blocks via
lambda expression is fully general in
expressing conditional return values. Building on our example:
Listing 2. Lambda with short-circuiting in Python
>>> pr = lambda s:s >>> namenum = lambda x: (x==1 and pr("one")) \ .... or (x==2 and pr("two")) \ .... or (pr("other")) >>> namenum(1) 'one' >>> namenum(2) 'two' >>> namenum(3) 'other'
Functions as first class objects
The above examples have already shown the first class status of functions
in Python, but in a subtle way. When we create a function object
lambda operation, we have something entirely
general. As such, we were able to bind our objects to the names "pr" and
"namenum", in exactly the same way we might have bound the number 23 or
the string "spam" to those names. But just as we can use the number 23
without binding it to any name (in other words, as a function argument),
we can use the function object we created with
binding it to any name. A function is simply another value we might do
something with in Python.
The main thing we do with our first class objects, is pass them to our FP
filter(). Each of these functions accepts a function object
as its first argument.
map()performs the passed function on each corresponding item in the specified list(s), and returns a list of results.
reduce()performs the passed function on each subsequent item and an internal accumulator of a final result; for example,
reduce(lambda n,m:n*m, range(1,10))means "factorial of 10" (in other words, multiply each item by the product of previous multiplications).
filter()uses the passed function to "evaluate" each item in a list, and return a winnowed list of the items that pass the function test.
We also often pass function objects to our own custom functions, but usually those amount to combinations of the mentioned built-ins.
By combining these three FP built-in functions, a surprising range of "flow" operations can be performed (all without statements, only expressions).
Functional looping in Python
Replacing loops is as simple as was replacing conditional blocks.
for can be directly translated to
map(). As with
our conditional execution, we will need to simplify statement blocks to
single function calls (we are getting close to being able to do this
Listing 3. Replacing loops
for e in lst: func(e) # statement-based loop map(func,lst) # map()-based loop
By the way, a similar technique is available for a functional approach to
sequential program flow. That is, imperative programming mostly consists
of statements that amount to "do this, then do that, then do the other
map() lets us do just this:
Listing 4. Map-based action sequence
# let's create an execution utility function do_it = lambda f: f() # let f1, f2, f3 (etc) be functions that perform actions map(do_it, [f1,f2,f3]) # map()-based action sequence
In general, the whole of our main program can be a
expression with a list of functions to execute to complete the program.
Another handy feature of first class functions is that you can put them in
while is slightly more complicated, but is still
possible to do directly:
Listing 5. Functional 'while' looping in Python
# statement-based while loop while <cond>: <pre-suite> if <break_condition>: breakelse: <suite> # FP-style recursive while loop def while_block(): <pre-suite> if <break_condition>: return 1 else: <suite> return 0 while_FP = lambda: (<cond> and while_block()) or while_FP() while_FP()
Our translation of
while still requires a
while_block() function that may itself contain statements
rather than just expressions. But we might be able to apply further
eliminations to that function (such as short circuiting the
if/else in the template). Also, it is hard for <cond>
to be useful with the usual tests, such as
since the loop body (by design) cannot change any variable values (well,
globals could be modified in
while_block()). One way to add a
more useful condition is to let
while_block() return a more
interesting value, and compare that return for a termination condition. It
is worth looking at a concrete example of eliminating statements:
Listing 6. Functional 'echo' loop in Python
# imperative version of "echo()" def echo_IMP(): while 1: x = raw_input("IMP -- ") if x == 'quit': breakelseprint x echo_IMP() # utility function for "identity with side-effect" def monadic_print(x): print x return x # FP version of "echo()" echo_FP = lambda: monadic_print(raw_input("FP -- "))=='quit' or echo_FP() echo_FP()
What we have accomplished is that we have managed to express a little
program that involves I/O, looping, and conditional statements as a pure
expression with recursion (in fact, as a function object that can be
passed elsewhere if desired). We do still utilize the utility
monadic_print(), but this function is completely
general, and can be reused in every functional program expression we might
create later (it's a one-time cost). Notice that any expression containing
monadic_print(x)evaluates to the same thing as
if it had simply contained
x. FP (particularly Haskell) has
the notion of a "monad" for a function that "does nothing, and has a
side-effect in the process."
After all this work in getting rid of perfectly sensible statements and substituting obscure nested expressions for them, a natural question is "Why?!" All of my descriptions of FP are achieved in Python. But the most important characteristic—and the one likely to be concretely useful—is the elimination of side-effects (or at least their containment to special areas like monads). A very large percentage of program errors—and the problem that drives programmers to debuggers—occur because variables obtain unexpected values during the course of program execution. Functional programs bypass this particular issue by simply not assigning values to variables at all.
Let's look at a fairly ordinary bit of imperative code. The goal here is to print out a list of pairs of numbers whose product is more than 25. The numbers that make up the pairs are themselves taken from two other lists. This sort of thing is moderately similar to things that programmers actually do in segments of their programs. An imperative approach to the goal might look like:
Listing 7. Imperative Python code for "print big products"
# Nested loop procedural style for finding big products xs = (1,2,3,4) ys = (10,15,3,22) bigmuls =  # ...more stuff... for x in xs: for y in ys: # ...more stuff... if x*y > 25: bigmuls.append((x,y)) # ...more stuff... # ...more stuff... print bigmuls
This project is small enough that nothing is likely to go wrong. But
perhaps our goal is embedded in code that accomplishes a number of other
goals at the same time. The sections commented with "more stuff" are the
places where side-effects are likely to lead to bugs. At any of these
points, the variables
y might acquire
unexpected values in the hypothetical abbreviated code. Furthermore, after
this bit of code is done, all the variables have values that may or may
not be expected and wanted by later code. Obviously, encapsulation in
functions/instances and care regarding scope can be used to guard against
this type of error. And you can always
del your variables
when you are done with them. But in practice, the types of errors
indicated are common.
A functional approach to our goal eliminates these side-effect errors altogether. A possible bit of code is:
Listing 8. Functional approach to our goal
bigmuls = lambda xs,ys: filter(lambda (x,y):x*y > 25, combine(xs,ys)) combine = lambda xs,ys: map(None, xs*len(ys), dupelms(ys,len(xs))) dupelms = lambda lst,n: reduce(lambda s,t:s+t, map(lambda l,n=n: [l]*n, lst)) print bigmuls((1,2,3,4),(10,15,3,22))
We bind our anonymous (
lambda) function objects to names in
the example, but that is not strictly necessary. We could instead simply
nest the definitions. For readability we do it this way; but also because
combine() is a nice utility function to have anyway (produces
a list of all pairs of elements from two input lists).
dupelms() in turn is mostly just a way of helping out
combine(). Even though this functional example is more
verbose than the imperative example, once you consider the utility
functions for reuse, the new code in
bigmuls() itself is
probably slightly less than in the imperative version.
The real advantage of this functional example is that absolutely no
variables change any values within it. There are no
possible unanticipated side-effects on later code (or
from earlier code). Obviously, the lack of side-effects, in itself, does
not guarantee that the code is correct, but it is nonetheless an
advantage. Notice, however, that Python (unlike many functional languages)
does not prevent rebinding of the names
starts meaning something different later in the program, all bets are off.
You could work up a Singleton class to contain this type of immutable
bindings (as, say,
s.bigmuls and so on); but this column does
not have room for that.
One thing distinctly worth noticing is that our particular goal is tailor-made for a new feature of Python 2. Rather than either the imperative or functional examples given, the best (and functional) technique is:
print [(x,y) for x in (1,2,3,4) for y in (10,15,3,22) if x*y > 25]
I've shown ways to replace just about every Python flow-control construct with a functional equivalent (sparing side-effects in the process). Translating a particular program efficiently takes some additional thinking, but we have seen that the functional built-ins are general and complete. In later columns, we will look at more advanced techniques for functional programming; and hopefully we will be able to explore some more of the pros and cons of functional styles.