I have taught myself python in quite a haphazard way. So my question perhaps won't be very pythonic.
When I write functions in classes, I often lose overview of what each function does. I do try to name them properly. But still, they are sometimes smaller parts of code where it seems arbitrary in which functions to put them. So whenever I want to make changes, I still need to go through the entire code in order to figure out how my functions actually flow.
From what I understand, we have objects and we have functions, and these are our units for structuring our code. But this only gives you a flat structure. It doesn't allow you to do any kind of nesting, like in a tree diagram, over multiple levels. Especially, the code in my file doesn't automatically water itself so that the functions that are called first and more often automatically further up on the top, whereas helper functions would be automatically further down in the document, or even nested.
In fact, even being able to visually nest lower-order subroutines "inside" a higher-order function that calls it would seem helpful. But it's not something that would be supported by Python's syntax. (Plus, it wouldn't quite suffice, because a sub-routine might be used by several higher-order functions.)
I imagine it would be useful to see all functions in my code visualized as a tree, or as a concept map:
Where each function is a dot. And calling order visualized by arrows. This way, I would also easily see which functions are more central, and which are more outliers, or even orphaned.
Yet perhaps this isn't even a case for another tool. Perhaps this is more a case of me not understanding proper coding. Perhaps there is something I can do differently in order to get the kind of intuitive overview over how my program works, without needing another tool.
Firstly, I am not quite sure why this isn't asked more often. Reading code is not intuitive, at all! We should be able to visualize the evolution of a process or function so well that close to every one will be able to understand its behavior. In the 60s and so, people had to be reasonably sure their programs would run, because getting access to the computer would take time; today we execute or compile our program, run tests if we have them, and get to know immediately whether it works. What happened is there is less mental effort now, we execute a bit less code in our heads, and the computer a bit more. But we must still think of how the program behaves midst execution in order to debug. For the future, it would be nice if the computer could just tell us how the program behaves.
You propose looking at a sort of tree of the program as a resolute, and after all, the abstract syntax tree is literally a tree, but I don't think this is what we ought to spend our efforts on when it comes to visualizing systems. What would be preferable is if we could look at an interactive view of how the problem changes its intermediate data-structures as a function of time.
Currently, we have debuggers--but that's akin to looking at the issue by asking what a function is at many values, when we would much rather look at its graph. A lot of programming is done by doing something you feel is right, observing if the behavior correct, if it's not correct then we make modifications by reacting and correcting said behavior.
Bret Victor in his essay, Learnable Programming, discusses this topic. I highly recommend it, even though it won't help you right now, maybe you can help others in the future by making these ideas more prevalent.
Onwards, then to where I tell you what you can do right now. In his book Clean Code, Robert C. Martin proposes structuring code much like how a newspaper is laid out.
Think of a well-written newspaper article. You read it vertically. At the top you expect a headline that will tell you what the story is about and allows you to decide whether it is something you want to read. The first paragraph gives you a synopsis of the whole story, hiding all the details while giving you the broad-brush concepts. As you continue downward, the details increase until you have all the dates, names, quotes, claims, and other minutia.
What is proposed, is to organize your program top-down, with higher level procedures that call mid-level procedures, which in turn call the lower level procedures. At any place, it should be obvious that (1) you are at the appropriate level of abstraction, and (2) you are looking at the part of the program implementing the behavior you seek to modify.
This means storing state at the level where it belongs, and exposing it anywhere else. Procedures should take only the parameters they need, because more parameters means you must also think about more parameters when reasoning about the code.
This is the primary reason for decomposing procedures into smaller procedures. For example, here some code I've written previously. It's not perfect, but you can see very clearly which part of the program you need to go to if you want to change anything.
Of course, higher order procedures are listed before any other. I'm telling you what I'm going to do, before I show you how I do it.
function formatLinks(matches, stripped) {
let formatted_links = []
for (match of matches) {
let diff = difference(match, stripped)
if (isSimpleLink(diff)) {
formatted_links.push(formatAsSimpleLink(diff))
} else if (hasPrefix(diff)) {
formatted_links.push(formatAsPrefixedLink(diff))
} else if (hasSuffix(diff)) {
formatted_links.push(formatAsSuffixedLink(diff))
}
}
// There might be multiple links within a word
// in which case we join them and strip any duplicated parts
// (which are otherwise interpreted as suffixes)
if (formatted_links.length > 1) {
return combineLinks(formatted_links)
}
// Default case
return formatted_links[0]
}
If JavaScript was a typed language, and if we could see an image of the decisions made in the code, as a factor of input and time, this could be even better.
I think Quokka.js and VS Code Debug Visualizer are both doing interesting work in this sector.
I need a module or strategy for detecting that a piece of data is written in a programming language, not syntax highlighting where the user specifically chooses a syntax to highlight. My question has two levels, I would greatly appreciate any help, so:
Is there any package in python that receives a string(piece of data) and returns if it belongs to any programming language syntax ?
I don't necessarily need to recognize the syntax, but know if the string is source code or not at all.
Any clues are deeply appreciated.
Maybe you can use existing multi-language syntax highlighters. Many of them can detect language a file is written in.
You could have a look at methods around baysian filtering.
My answer somewhat depends on the amount of code you're going to be given. If you're going to be given 30+ lines of code, it should be fairly easy to identify some unique features of each language that are fairly common. For example, tell the program that if anything matches an expression like from * import * then it's Python (I'm not 100% sure that phrasing is unique to Python, but you get the gist). Other things you could look at that are usually slightly different would be class definition (i.e. Python always starts with 'class', C will start with a definition of the return so you could check to see if there is a line that starts with a data type and has the formatting of a method declaration), conditionals are usually formatted slightly differently, etc, etc. If you wanted to make it more accurate, you could introduce some sort of weighting system, features that are more unique and less likely to be the result of a mismatched regexp get a higher weight, things that are commonly mismatched get a lower weight for the language, and just calculate which language has the highest composite score at the end. You could also define features that you feel are 100% unique, and tell it that as soon as it hits one of those, to stop parsing because it knows the answer (things like the shebang line).
This would, of course, involve you knowing enough about the languages you want to identify to find unique features to look for, or being able to find people that do know unique structures that would help.
If you're given less than 30 or so lines of code, your answers from parsing like that are going to be far less accurate, in that case the easiest best way to do it would probably be to take an appliance similar to Travis, and just run the code in each language (in a VM of course). If the code runs successfully in a language, you have your answer. If not, you would need a list of errors that are "acceptable" (as in they are errors in the way the code was written, not in the interpreter). It's not a great solution, but at some point your code sample will just be too short to give an accurate answer.
At work we used to program our Python in a pretty standard OO way. Lately, a couple guys got on the functional bandwagon. And their code now contains lots more lambdas, maps and reduces. I understand that functional languages are good for concurrency but does programming Python functionally really help with concurrency? I am just trying to understand what I get if I start using more of Python's functional features.
Edit: I've been taken to task in the comments (in part, it seems, by fanatics of FP in Python, but not exclusively) for not providing more explanations/examples, so, expanding the answer to supply some.
lambda, even more so map (and filter), and most especially reduce, are hardly ever the right tool for the job in Python, which is a strongly multi-paradigm language.
lambda main advantage (?) compared to the normal def statement is that it makes an anonymous function, while def gives the function a name -- and for that very dubious advantage you pay an enormous price (the function's body is limited to one expression, the resulting function object is not pickleable, the very lack of a name sometimes makes it much harder to understand a stack trace or otherwise debug a problem -- need I go on?!-).
Consider what's probably the single most idiotic idiom you sometimes see used in "Python" (Python with "scare quotes", because it's obviously not idiomatic Python -- it's a bad transliteration from idiomatic Scheme or the like, just like the more frequent overuse of OOP in Python is a bad transliteration from Java or the like):
inc = lambda x: x + 1
by assigning the lambda to a name, this approach immediately throws away the above-mentioned "advantage" -- and doesn't lose any of the DISadvantages! For example, inc doesn't know its name -- inc.__name__ is the useless string '<lambda>' -- good luck understanding a stack trace with a few of these;-). The proper Python way to achieve the desired semantics in this simple case is, of course:
def inc(x): return x + 1
Now inc.__name__ is the string 'inc', as it clearly should be, and the object is pickleable -- the semantics are otherwise identical (in this simple case where the desired functionality fits comfortably in a simple expression -- def also makes it trivially easy to refactor if you need to temporarily or permanently insert statements such as print or raise, of course).
lambda is (part of) an expression while def is (part of) a statement -- that's the one bit of syntax sugar that makes people use lambda sometimes. Many FP enthusiasts (just as many OOP and procedural fans) dislike Python's reasonably strong distinction between expressions and statements (part of a general stance towards Command-Query Separation). Me, I think that when you use a language you're best off using it "with the grain" -- the way it was designed to be used -- rather than fighting against it; so I program Python in a Pythonic way, Scheme in a Schematic (;-) way, Fortran in a Fortesque (?) way, and so on:-).
Moving on to reduce -- one comment claims that reduce is the best way to compute the product of a list. Oh, really? Let's see...:
$ python -mtimeit -s'L=range(12,52)' 'reduce(lambda x,y: x*y, L, 1)'
100000 loops, best of 3: 18.3 usec per loop
$ python -mtimeit -s'L=range(12,52)' 'p=1' 'for x in L: p*=x'
100000 loops, best of 3: 10.5 usec per loop
so the simple, elementary, trivial loop is about twice as fast (as well as more concise) than the "best way" to perform the task?-) I guess the advantages of speed and conciseness must therefore make the trivial loop the "bestest" way, right?-)
By further sacrificing compactness and readability...:
$ python -mtimeit -s'import operator; L=range(12,52)' 'reduce(operator.mul, L, 1)'
100000 loops, best of 3: 10.7 usec per loop
...we can get almost back to the easily obtained performance of the simplest and most obvious, compact, and readable approach (the simple, elementary, trivial loop). This points out another problem with lambda, actually: performance! For sufficiently simple operations, such as multiplication, the overhead of a function call is quite significant compared to the actual operation being performed -- reduce (and map and filter) often forces you to insert such a function call where simple loops, list comprehensions, and generator expressions, allow the readability, compactness, and speed of in-line operations.
Perhaps even worse than the above-berated "assign a lambda to a name" anti-idiom is actually the following anti-idiom, e.g. to sort a list of strings by their lengths:
thelist.sort(key=lambda s: len(s))
instead of the obvious, readable, compact, speedier
thelist.sort(key=len)
Here, the use of lambda is doing nothing but inserting a level of indirection -- with no good effect whatsoever, and plenty of bad ones.
The motivation for using lambda is often to allow the use of map and filter instead of a vastly preferable loop or list comprehension that would let you do plain, normal computations in line; you still pay that "level of indirection", of course. It's not Pythonic to have to wonder "should I use a listcomp or a map here": just always use listcomps, when both appear applicable and you don't know which one to choose, on the basis of "there should be one, and preferably only one, obvious way to do something". You'll often write listcomps that could not be sensibly translated to a map (nested loops, if clauses, etc), while there's no call to map that can't be sensibly rewritten as a listcomp.
Perfectly proper functional approaches in Python often include list comprehensions, generator expressions, itertools, higher-order functions, first-order functions in various guises, closures, generators (and occasionally other kinds of iterators).
itertools, as a commenter pointed out, does include imap and ifilter: the difference is that, like all of itertools, these are stream-based (like map and filter builtins in Python 3, but differently from those builtins in Python 2). itertools offers a set of building blocks that compose well with each other, and splendid performance: especially if you find yourself potentially dealing with very long (or even unbounded!-) sequences, you owe it to yourself to become familiar with itertools -- their whole chapter in the docs makes for good reading, and the recipes in particular are quite instructive.
Writing your own higher-order functions is often useful, especially when they're suitable for use as decorators (both function decorators, as explained in that part of the docs, and class decorators, introduced in Python 2.6). Do remember to use functools.wraps on your function decorators (to keep the metadata of the function getting wrapped)!
So, summarizing...: anything you can code with lambda, map, and filter, you can code (more often than not advantageously) with def (named functions) and listcomps -- and usually moving up one notch to generators, generator expressions, or itertools, is even better. reduce meets the legal definition of "attractive nuisance"...: it's hardly ever the right tool for the job (that's why it's not a built-in any more in Python 3, at long last!-).
FP is important not only for concurrency; in fact, there's virtually no concurrency in the canonical Python implementation (maybe 3.x changes that?). in any case, FP lends itself well to concurrency because it leads to programs with no or fewer (explicit) states. states are troublesome for a few reasons. one is that they make distributing the computation hard(er) (that's the concurrency argument), another, far more important in most cases, is the tendency to inflict bugs. the biggest source of bugs in contemporary software is variables (there's a close relationship between variables and states). FP may reduce the number of variables in a program: bugs squashed!
see how many bugs can you introduce by mixing the variables up in these versions:
def imperative(seq):
p = 1
for x in seq:
p *= x
return p
versus (warning, my.reduce's parameter list differs from that of python's reduce; rationale given later)
import operator as ops
def functional(seq):
return my.reduce(ops.mul, 1, seq)
as you can see, it's a matter of fact that FP gives you fewer opportunities to shoot yourself in the foot with a variables-related bug.
also, readability: it may take a bit of training, but functional is way easier to read than imperative: you see reduce ("ok, it's reducing a sequence to a single value"), mul ("by multiplication"). wherease imperative has the generic form of a for cycle, peppered with variables and assignments. these for cycles all look the same, so to get an idea of what's going on in imperative, you need to read almost all of it.
then there's succintness and flexibility. you give me imperative and I tell you I like it, but want something to sum sequences as well. no problem, you say, and off you go, copy-pasting:
def imperative(seq):
p = 1
for x in seq:
p *= x
return p
def imperative2(seq):
p = 0
for x in seq:
p += x
return p
what can you do to reduce the duplication? well, if operators were values, you could do something like
def reduce(op, seq, init):
rv = init
for x in seq:
rv = op(rv, x)
return rv
def imperative(seq):
return reduce(*, 1, seq)
def imperative2(seq):
return reduce(+, 0, seq)
oh wait! operators provides operators that are values! but.. Alex Martelli condemned reduce already... looks like if you want to stay within the boundaries he suggests, you're doomed to copy-pasting plumbing code.
is the FP version any better? surely you'd need to copy-paste as well?
import operator as ops
def functional(seq):
return my.reduce(ops.mul, 1, seq)
def functional2(seq):
return my.reduce(ops.add, 0, seq)
well, that's just an artifact of the half-assed approach! abandoning the imperative def, you can contract both versions to
import functools as func, operator as ops
functional = func.partial(my.reduce, ops.mul, 1)
functional2 = func.partial(my.reduce, ops.add, 0)
or even
import functools as func, operator as ops
reducer = func.partial(func.partial, my.reduce)
functional = reducer(ops.mul, 1)
functional2 = reducer(ops.add, 0)
(func.partial is the reason for my.reduce)
what about runtime speed? yes, using FP in a language like Python will incur some overhead. here i'll just parrot what a few professors have to say about this:
premature optimization is the root of all evil.
most programs spend 80% of their runtime in 20% percent of their code.
profile, don't speculate!
I'm not very good at explaining things. Don't let me muddy the water too much, read the first half of the speech John Backus gave on the occasion of receiving the Turing Award in 1977. Quote:
5.1 A von Neumann Program for Inner Product
c := 0
for i := I step 1 until n do
c := c + a[i] * b[i]
Several properties of this program are
worth noting:
Its statements operate on an invisible "state" according to complex
rules.
It is not hierarchical. Except for the right side of the assignment
statement, it does not construct
complex entities from simpler ones.
(Larger programs, however, often do.)
It is dynamic and repetitive. One must mentally execute it to
understand it.
It computes word-at-a-time by repetition (of the assignment) and by
modification (of variable i).
Part of the data, n, is in the program; thus it lacks generality and
works only for vectors of length n.
It names its arguments; it can only be used for vectors a and b.
To become general, it requires a
procedure declaration. These involve
complex issues (e.g., call-by-name
versus call-by-value).
Its "housekeeping" operations are represented by symbols in
scattered places (in the for statement
and the subscripts in the assignment).
This makes it impossible to
consolidate housekeeping operations,
the most common of all, into single,
powerful, widely useful operators.
Thus in programming those operations
one must always start again at square
one, writing "for i := ..." and
"for j := ..." followed by
assignment statements sprinkled with
i's and j's.
I program in Python everyday, and I have to say that too much 'bandwagoning' toward OO or functional could lead toward missing elegant solutions. I believe that both paradigms have their advantages to certain problems - and I think that's when you know what approach to use. Use a functional approach when it leaves you with a clean, readable, and efficient solution. Same goes for OO.
And that's one of the reasons I love Python - the fact that it is multi-paradigm and lets the developer choose how to solve his/her problem.
This answer is completely re-worked. It incorporates a lot of observations from the other answers.
As you can see, there is a lot of strong feelings surrounding the use of functional programming constructs in Python. There are three major groups of ideas here.
First, almost everybody but the people who are most wedded to the purest expression of the functional paradigm agree that list and generator comprehensions are better and clearer than using map or filter. Your colleagues should be avoiding the use of map and filter if you are targeting a version of Python new enough to support list comprehensions. And you should be avoiding itertools.imap and itertools.ifilter if your version of Python is new enough for generator comprehensions.
Secondly, there is a lot of ambivalence in the community as a whole about lambda. A lot of people are really annoyed by a syntax in addition to def for declaring functions, especially one that involves a keyword like lambda that has a rather strange name. And people are also annoyed that these small anonymous functions are missing any of the nice meta-data that describes any other kind of function. It makes debugging harder. Lastly the small functions declared by lambda are often not terribly efficient as they require the overhead of a Python function call each time they are invoked, which is frequently in an inner loop.
Lastly, most (meaning > 50%, but most likely not 90%) people think that reduce is a little strange and obscure. I myself admit to having print reduce.__doc__ whenever I want to use it, which isn't all that often. Though when I see it used, the nature of the arguments (i.e. function, list or iterator, scalar) speak for themselves.
As for myself, I fall in the camp of people who think the functional style is often very useful. But balancing that thought is the fact that Python is not at heart a functional language. And overuse of functional constructs can make programs seem strangely contorted and difficult for people to understand.
To understand when and where the functional style is very helpful and improves readability, consider this function in C++:
unsigned int factorial(unsigned int x)
{
int fact = 1;
for (int i = 2; i <= n; ++i) {
fact *= i;
}
return fact
}
This loop seems very simple and easy to understand. And in this case it is. But its seeming simplicity is a trap for the unwary. Consider this alternate means of writing the loop:
unsigned int factorial(unsigned int n)
{
int fact = 1;
for (int i = 2; i <= n; i += 2) {
fact *= i--;
}
return fact;
}
Suddenly, the loop control variable no longer varies in an obvious way. You are reduced to looking through the code and reasoning carefully about what happens with the loop control variable. Now this example is a bit pathological, but there are real-world examples that are not. And the problem is with the fact that the idea is repeated assignment to an existing variable. You can't trust the variable's value is the same throughout the entire body of the loop.
This is a long recognized problem, and in Python writing a loop like this is fairly unnatural. You have to use a while loop, and it just looks wrong. Instead, in Python you would write something like this:
def factorial(n):
fact = 1
for i in xrange(2, n):
fact = fact * i;
return fact
As you can see, the way you talk about the loop control variable in Python is not amenable to fooling with it inside the loop. This eliminates a lot of the problems with 'clever' loops in other imperative languages. Unfortunately, it's an idea that's semi-borrowed from functional languages.
Even this lends itself to strange fiddling. For example, this loop:
c = 1
for i in xrange(0, min(len(a), len(b))):
c = c * (a[i] + b[i])
if i < len(a):
a[i + 1] = a[a + 1] + 1
Oops, we again have a loop that is difficult to understand. It superficially resembles a really simple and obvious loop, and you have to read it carefully to realize that one of the variables used in the loop's computation is being messed with in a way that will effect future runs of the loop.
Again, a more functional approach to the rescue:
from itertools import izip
c = 1
for ai, bi in izip(a, b):
c = c * (ai + bi)
Now by looking at the code we have some strong indication (partly by the fact that the person is using this functional style) that the lists a and b are not modified during the execution of the loop. One less thing to think about.
The last thing to be worried about is c being modified in strange ways. Perhaps it is a global variable and is being modified by some roundabout function call. To rescue us from this mental worry, here is a purely function approach:
from itertools import izip
c = reduce(lambda x, ab: x * (ab[0] + ab[1]), izip(a, b), 1)
Very concise, and the structure tells us that x is purely an accumulator. It is a local variable everywhere it appear. The final result is unambiguously assigned to c. Now there is much less to worry about. The structure of the code removes several classes of possible error.
That is why people might choose a functional style. It is concise and clear, at least if you understand what reduce and lambda do. There are large classes of problems that could afflict a program written in a more imperative style that you know won't afflict your functional style program.
In the case of factorial, there is a very simple and clear way to write this function in Python in a functional style:
import operator
def factorial(n):
return reduce(operator.mul, xrange(2, n+1), 1)
The question, which seems to be mostly ignored here:
does programming Python functionally really help with concurrency?
No. The value FP brings to concurrency is in eliminating state in computation, which is ultimately responsible for the hard-to-grasp nastiness of unintended errors in concurrent computation. But it depends on the concurrent programming idioms not themselves being stateful, something that doesn't apply to Twisted. If there are concurrency idioms for Python that leverage stateless programming, I don't know of them.
Here's a short summary of positive answers when/why to program functionally.
List comprehensions were imported from Haskell, a FP language. They are Pythonic. I'd prefer to write
y = [i*2 for i in k if i % 3 == 0]
than to use an imperative construct (loop).
I'd use lambda when giving a complicated key to sort, like list.sort(key=lambda x: x.value.estimate())
It's cleaner to use higher-order functions than to write code using OOP's design patterns like visitor or abstract factory
People say that you should program Python in Python, C++ in C++ etc. That's true, but certainly you should be able to think in different ways at the same thing. If while writing a loop you know that you're really doing reducing (folding), then you'll be able to think on a higher level. That cleans your mind and helps to organize. Of course lower-level thinking is important too.
You should NOT overuse those features - there are many traps, see Alex Martelli's post. I'd subjectively say the most serious danger is that excessive use of those features will destroy readability of your code, which is a core attribute of Python.
The standard functions filter(), map() and reduce() are used for various operations on a list and all of the three functions expect two arguments: A function and a list
We could define a separate function and use it as an argument to filter() etc., and its probably a good idea if that function is used several times, or if the function is too complex to be written in a single line. However, if it's needed only once and it's quite simple, it's more convenient to use a lambda construct to generate a (temporary) anonymous function and pass it to filter().
This helps in readability and compact code.
Using these function, would also turn out to be efficient, because the looping on the elements of the list is done in C, which is a little bit faster than looping in python.
And object oriented way is forcibly needed when states are to be maintained, apart from abstraction, grouping, etc., If the requirement is pretty simple, I would stick with functional than to Object Oriented programming.
Map and Filter have their place in OO programming. Right next to list comprehensions and generator functions.
Reduce less so. The algorithm for reduce can rapidly suck down more time than it deserves; with a tiny bit of thinking, a manually-written reduce-loop will be more efficient than a reduce which applies a poorly-thought-out looping function to a sequence.
Lambda never. Lambda is useless. One can make the argument that it actually does something, so it's not completely useless. First: Lambda is not syntactic "sugar"; it makes things bigger and uglier. Second: the one time in 10,000 lines of code that think you need an "anonymous" function turns into two times in 20,000 lines of code, which removes the value of anonymity, making it into a maintenance liability.
However.
The functional style of no-object-state-change programming is still OO in nature. You just do more object creation and fewer object updates. Once you start using generator functions, much OO programming drifts in a functional direction.
Each state change appears to translate into a generator function that builds a new object in the new state from old object(s). It's an interesting world view because reasoning about the algorithm is much, much simpler.
But that's no call to use reduce or lambda.
I'm in the process of writing a small, rule-based 'math' engine. I realize this is unclear, so I'll provide a small example.
Let's say you have some variable a, that holds an integer. You also have some functions you can apply to the number, i.e.
sqr - square the number
flp - flip the bits of the number
dec - decrement the number
inc - increment the number
You can then say, do_formula(a, "2sqr+inc+flp"). If a were 3, it'd square it twice (81), increment it (82), and flip the bits of it (~82 -- which is -83, if dealing with signed integers, I believe).
What would be the best way of parsing the formula? It's relatively simple, and I'm thinking of making all the opcodes be 3 characters... would it be overkill to use Lex? Should I just write a simple home-brewed solution or use something else entirely?
I realize the above example is silly; I'm not building a calculator that'll do that, but it illustrates what I'm trying to do well enough.
If your grammar isn't super-complex and you don't mind doing it in Python, pyparsing could be just what the doctor ordered. I implemented something fairly similar for parsing chemical equations and it took me an hour or so to do it. I'd add the code here, but it wouldn't be particularly relevant.
Yes, seems like an overkill in this case. Just split the string on '=", and then apply the operations one after another. Thank god for dictionaries and functions as first-class citizen your engine can be written in 0.5 - 1 pages of code.
dct = {'sqr' : lambda a: a * a, ...}
ntimes, op = token[:-3], token[-3:]
ntimes = 0 if len(ntimes) == 0 else int(ntimes)
..
dct[op](a)
It really depends on how big your project is going to end up being: If you're looking at creating a new language or something that's parsing more interesting grammars than just + then I'd say lex would be a fun and entertaining way to spend an afternoon.
On the other hand, writing your own parser is extremely informative and not particularly hard if you've really thought out the grammar beforehand.
The question really ends up being which language to do the parsing in? Haskell would be a really fun choice and provided a lot of interesting revelations for me when I wrote my first parser a couple years ago.
What's your host language? For Ruby, I really like treetop. It's a bit hard to get started, but I've used it with success for parsing more complicated math expressions.
If you have some free time and want to learn a new programming paradigm, give Prolog a spin!