Related
I would like to put an int into a string. This is what I am doing at the moment:
num = 40
plot.savefig('hanning40.pdf') #problem line
I have to run the program for several different numbers, so I'd like to do a loop. But inserting the variable like this doesn't work:
plot.savefig('hanning', num, '.pdf')
How do I insert a variable into a Python string?
See also
If you tried using + to concatenate a number with a string (or between strings, etc.) and got an error message, see How can I concatenate str and int objects?.
If you are trying to assemble a URL with variable data, do not use ordinary string formatting, because it is error-prone and more difficult than necessary. Specialized tools are available. See Add params to given URL in Python.
If you are trying to assemble a SQL query, do not use ordinary string formatting, because it is a major security risk. This is the cause of "SQL injection" which costs real companies huge amounts of money every year. See for example Python: best practice and securest way to connect to MySQL and execute queries for proper techniques.
If you just want to print (output) the string, you can prepare it this way first, or if you don't need the string for anything else, print each piece of the output individually using a single call to print. See How can I print multiple things (fixed text and/or variable values) on the same line, all at once? for details on both approaches.
Using f-strings:
plot.savefig(f'hanning{num}.pdf')
This was added in 3.6 and is the new preferred way.
Using str.format():
plot.savefig('hanning{0}.pdf'.format(num))
String concatenation:
plot.savefig('hanning' + str(num) + '.pdf')
Conversion Specifier:
plot.savefig('hanning%s.pdf' % num)
Using local variable names (neat trick):
plot.savefig('hanning%(num)s.pdf' % locals())
Using string.Template:
plot.savefig(string.Template('hanning${num}.pdf').substitute(locals()))
See also:
Fancier Output Formatting - The Python Tutorial
Python 3's f-Strings: An Improved String Formatting Syntax (Guide) - RealPython
With the introduction of formatted string literals ("f-strings" for short) in Python 3.6, it is now possible to write this with a briefer syntax:
>>> name = "Fred"
>>> f"He said his name is {name}."
'He said his name is Fred.'
With the example given in the question, it would look like this
plot.savefig(f'hanning{num}.pdf')
plot.savefig('hanning(%d).pdf' % num)
The % operator, when following a string, allows you to insert values into that string via format codes (the %d in this case). For more details, see the Python documentation:
printf-style String Formatting
You can use + as the normal string concatenation function as well as str().
"hello " + str(10) + " world" == "hello 10 world"
In general, you can create strings using:
stringExample = "someString " + str(someNumber)
print(stringExample)
plot.savefig(stringExample)
If you would want to put multiple values into the string you could make use of format
nums = [1,2,3]
plot.savefig('hanning{0}{1}{2}.pdf'.format(*nums))
Would result in the string hanning123.pdf. This can be done with any array.
Special cases
Depending on why variable data is being used with strings, the general-purpose approaches may not be appropriate.
If you need to prepare an SQL query
Do not use any of the usual techniques for assembling a string. Instead, use your SQL library's functionality for parameterized queries.
A query is code, so it should not be thought about like normal text. Using the library will make sure that any inserted text is properly escaped. If any part of the query could possibly come from outside the program in any way, that is an opportunity for a malevolent user to perform SQL injection. This is widely considered one of the important computer security problems, costing real companies huge amounts of money every year and causing problems for countless customers. Even if you think you know the data is "safe", there is no real upside to using any other approach.
The syntax will depend on the library you are using and is outside the scope of this answer.
If you need to prepare a URL query string
See Add params to given URL in Python. Do not do it yourself; there is no practical reason to make your life harder.
Writing to a file
While it's possible to prepare a string ahead of time, it may be simpler and more memory efficient to just write each piece of data with a separate .write call. Of course, non-strings will still need to be converted to string before writing, which may complicate the code. There is not a one-size-fits-all answer here, but choosing badly will generally not matter very much.
If you are simply calling print
The built-in print function accepts a variable number of arguments, and can take in any object and stringify it using str. Before trying string formatting, consider whether simply passing multiple arguments will do what you want. (You can also use the sep keyword argument to control spacing between the arguments.)
# display a filename, as an example
print('hanning', num, '.pdf', sep='')
Of course, there may be other reasons why it is useful for the program to assemble a string; so by all means do so where appropriate.
It's important to note that print is a special case. The only functions that work this way are ones that are explicitly written to work this way. For ordinary functions and methods, like input, or the savefig method of Matplotlib plots, we need to prepare a string ourselves.
Concatenation
Python supports using + between two strings, but not between strings and other types. To work around this, we need to convert other values to string explicitly: 'hanning' + str(num) + '.pdf'.
Template-based approaches
Most ways to solve the problem involve having some kind of "template" string that includes "placeholders" that show where information should be added, and then using some function or method to add the missing information.
f-strings
This is the recommended approach when possible. It looks like f'hanning{num}.pdf'. The names of variables to insert appear directly in the string. It is important to note that there is not actually such a thing as an "f-string"; it's not a separate type. Instead, Python will translate the code ahead of time:
>>> def example(num):
... return f'hanning{num}.pdf'
...
>>> import dis
>>> dis.dis(example)
2 0 LOAD_CONST 1 ('hanning')
2 LOAD_FAST 0 (num)
4 FORMAT_VALUE 0
6 LOAD_CONST 2 ('.pdf')
8 BUILD_STRING 3
10 RETURN_VALUE
Because it's a special syntax, it can access opcodes that aren't used in other approaches.
str.format
This is the recommended approach when f-strings aren't possible - mainly, because the template string needs to be prepared ahead of time and filled in later. It looks like 'hanning{}.pdf'.format(num), or 'hanning{num}.pdf'.format(num=num)'. Here, format is a method built in to strings, which can accept arguments either by position or keyword.
Particularly for str.format, it's useful to know that the built-in locals, globals and vars functions return dictionaries that map variable names to the contents of those variables. Thus, rather than something like '{a}{b}{c}'.format(a=a, b=b, c=c), we can use something like '{a}{b}{c}'.format(**locals()), unpacking the locals() dict.
str.format_map
This is a rare variation on .format. It looks like 'hanning{num}.pdf'.format_map({'num': num}). Rather than accepting keyword arguments, it accepts a single argument which is a mapping.
That probably doesn't sound very useful - after all, rather than 'hanning{num}.pdf'.format_map(my_dict), we could just as easily write 'hanning{num}.pdf'.format(**my_dict). However, this is useful for mappings that determine values on the fly, rather than ordinary dicts. In these cases, unpacking with ** might not work, because the set of keys might not be determined ahead of time; and trying to unpack keys based on the template is unwieldy (imagine: 'hanning{num}.pdf'.format(num=my_mapping[num]), with a separate argument for each placeholder).
string.Formatter
The string standard library module contains a rarely used Formatter class. Using it looks like string.Formatter().format('hanning{num}.pdf', num=num). The template string uses the same syntax again. This is obviously clunkier than just calling .format on the string; the motivation is to allow users to subclass Formatter to define a different syntax for the template string.
All of the above approaches use a common "formatting language" (although string.Formatter allows changing it); there are many other things that can be put inside the {}. Explaining how it works is beyond the scope of this answer; please consult the documentation. Do keep in mind that literal { and } characters need to be escaped by doubling them up. The syntax is presumably inspired by C#.
The % operator
This is a legacy way to solve the problem, inspired by C and C++. It has been discouraged for a long time, but is still supported. It looks like 'hanning%s.pdf' % num, for simple cases. As you'd expect, literal '%' symbols in the template need to be doubled up to escape them.
It has some issues:
It seems like the conversion specifier (the letter after the %) should match the type of whatever is being interpolated, but that's not actually the case. Instead, the value is converted to the specified type, and then to string from there. This isn't normally necessary; converting directly to string works most of the time, and converting to other types first doesn't help most of the rest of the time. So 's' is almost always used (unless you want the repr of the value, using 'r'). Despite that, the conversion specifier is a mandatory part of the syntax.
Tuples are handled specially: passing a tuple on the right-hand side is the way to provide multiple arguments. This is an ugly special case that's necessary because we aren't using function-call syntax. As a result, if you actually want to format a tuple into a single placeholder, it must be wrapped in a 1-tuple.
Other sequence types are not handled specially, and the different behaviour can be a gotcha.
string.Template
The string standard library module contains a rarely used Template class. Instances provide substitute and safe_substitute methods that work similarly to the built-in .format (safe_substitute will leave placeholders intact rather than raising an exception when the arguments don't match). This should also be considered a legacy approach to the problem.
It looks like string.Template('hanning$num.pdf').substitute(num=num), and is inspired by traditional Perl syntax. It's obviously clunkier than the .format approach, since a separate class has to be used before the method is available. Braces ({}) can be used optionally around the name of the variable, to avoid ambiguity. Similarly to the other methods, literal '$' in the template needs to be doubled up for escaping.
I had a need for an extended version of this: instead of embedding a single number in a string, I needed to generate a series of file names of the form 'file1.pdf', 'file2.pdf' etc. This is how it worked:
['file' + str(i) + '.pdf' for i in range(1,4)]
You can make dict and substitute variables in your string.
var = {"name": "Abdul Jalil", "age": 22}
temp_string = "My name is %(name)s. I am %(age)s years old." % var
Is there a way to check satisfiability of a python string like 'p or p -> p' in Z3 if you do not know the variable names before hand?
For example I have seen this:
p = Bool('p')
solve(Implies(Or(p, p), p))
However I cannot define the variables in Z3 in advance because the proposition is given to me as a string. How can I do this with z3?
I have also seen python's eval function but it seems I need to have the variable names defined in z3 of that prior too
Some questions to ponder: What would be the meaning of that string? What if it has syntax-errors in it? How do you discern what are the valid operators/variables? Do you allow just booleans, or other sorts as well? What about grouping, precedence, and associativity of operators?
Bottom line, if you want to go directly from a string, you really have no choice but to agree on a syntax and a semantics of what those strings mean. And the only way to do that is to write a parser for those strings, and "interpret" that result in the z3 context.
One choice is to "stick" to SMTLib, i.e., ask your input to be well-formatted SMTLib scripts. If you go with this choice, then z3 already have a built-in parser for them that you can readily use. See here: https://z3prover.github.io/api/html/namespacez3py.html#a09fe122cbfbc6d3fa30a79850b2a2414 But I'm pretty sure you'll find this rather ugly and not quite what you wanted. But this is the only "out-of-the-box" solution.
The proper way to handle this issue is to write a basic parser over boolean-expressions, whose syntax (and to some extent semantics) you'll have freedom to define however way you want. Also, this isn't a particularly difficult thing to do. If you're doing this in Python, you can use ply (https://www.dabeaz.com/ply/), or go with a hand-written recursive-descent parser (https://www.booleanworld.com/building-recursive-descent-parsers-definitive-guide/).
Feel free to explore and ask further questions; though make sure to tag them appropriately if it's about parsing strings in Python; which really have nothing to do with z3/z3py.
I would like to put an int into a string. This is what I am doing at the moment:
num = 40
plot.savefig('hanning40.pdf') #problem line
I have to run the program for several different numbers, so I'd like to do a loop. But inserting the variable like this doesn't work:
plot.savefig('hanning', num, '.pdf')
How do I insert a variable into a Python string?
See also
If you tried using + to concatenate a number with a string (or between strings, etc.) and got an error message, see How can I concatenate str and int objects?.
If you are trying to assemble a URL with variable data, do not use ordinary string formatting, because it is error-prone and more difficult than necessary. Specialized tools are available. See Add params to given URL in Python.
If you are trying to assemble a SQL query, do not use ordinary string formatting, because it is a major security risk. This is the cause of "SQL injection" which costs real companies huge amounts of money every year. See for example Python: best practice and securest way to connect to MySQL and execute queries for proper techniques.
If you just want to print (output) the string, you can prepare it this way first, or if you don't need the string for anything else, print each piece of the output individually using a single call to print. See How can I print multiple things (fixed text and/or variable values) on the same line, all at once? for details on both approaches.
Using f-strings:
plot.savefig(f'hanning{num}.pdf')
This was added in 3.6 and is the new preferred way.
Using str.format():
plot.savefig('hanning{0}.pdf'.format(num))
String concatenation:
plot.savefig('hanning' + str(num) + '.pdf')
Conversion Specifier:
plot.savefig('hanning%s.pdf' % num)
Using local variable names (neat trick):
plot.savefig('hanning%(num)s.pdf' % locals())
Using string.Template:
plot.savefig(string.Template('hanning${num}.pdf').substitute(locals()))
See also:
Fancier Output Formatting - The Python Tutorial
Python 3's f-Strings: An Improved String Formatting Syntax (Guide) - RealPython
With the introduction of formatted string literals ("f-strings" for short) in Python 3.6, it is now possible to write this with a briefer syntax:
>>> name = "Fred"
>>> f"He said his name is {name}."
'He said his name is Fred.'
With the example given in the question, it would look like this
plot.savefig(f'hanning{num}.pdf')
plot.savefig('hanning(%d).pdf' % num)
The % operator, when following a string, allows you to insert values into that string via format codes (the %d in this case). For more details, see the Python documentation:
printf-style String Formatting
You can use + as the normal string concatenation function as well as str().
"hello " + str(10) + " world" == "hello 10 world"
In general, you can create strings using:
stringExample = "someString " + str(someNumber)
print(stringExample)
plot.savefig(stringExample)
If you would want to put multiple values into the string you could make use of format
nums = [1,2,3]
plot.savefig('hanning{0}{1}{2}.pdf'.format(*nums))
Would result in the string hanning123.pdf. This can be done with any array.
Special cases
Depending on why variable data is being used with strings, the general-purpose approaches may not be appropriate.
If you need to prepare an SQL query
Do not use any of the usual techniques for assembling a string. Instead, use your SQL library's functionality for parameterized queries.
A query is code, so it should not be thought about like normal text. Using the library will make sure that any inserted text is properly escaped. If any part of the query could possibly come from outside the program in any way, that is an opportunity for a malevolent user to perform SQL injection. This is widely considered one of the important computer security problems, costing real companies huge amounts of money every year and causing problems for countless customers. Even if you think you know the data is "safe", there is no real upside to using any other approach.
The syntax will depend on the library you are using and is outside the scope of this answer.
If you need to prepare a URL query string
See Add params to given URL in Python. Do not do it yourself; there is no practical reason to make your life harder.
Writing to a file
While it's possible to prepare a string ahead of time, it may be simpler and more memory efficient to just write each piece of data with a separate .write call. Of course, non-strings will still need to be converted to string before writing, which may complicate the code. There is not a one-size-fits-all answer here, but choosing badly will generally not matter very much.
If you are simply calling print
The built-in print function accepts a variable number of arguments, and can take in any object and stringify it using str. Before trying string formatting, consider whether simply passing multiple arguments will do what you want. (You can also use the sep keyword argument to control spacing between the arguments.)
# display a filename, as an example
print('hanning', num, '.pdf', sep='')
Of course, there may be other reasons why it is useful for the program to assemble a string; so by all means do so where appropriate.
It's important to note that print is a special case. The only functions that work this way are ones that are explicitly written to work this way. For ordinary functions and methods, like input, or the savefig method of Matplotlib plots, we need to prepare a string ourselves.
Concatenation
Python supports using + between two strings, but not between strings and other types. To work around this, we need to convert other values to string explicitly: 'hanning' + str(num) + '.pdf'.
Template-based approaches
Most ways to solve the problem involve having some kind of "template" string that includes "placeholders" that show where information should be added, and then using some function or method to add the missing information.
f-strings
This is the recommended approach when possible. It looks like f'hanning{num}.pdf'. The names of variables to insert appear directly in the string. It is important to note that there is not actually such a thing as an "f-string"; it's not a separate type. Instead, Python will translate the code ahead of time:
>>> def example(num):
... return f'hanning{num}.pdf'
...
>>> import dis
>>> dis.dis(example)
2 0 LOAD_CONST 1 ('hanning')
2 LOAD_FAST 0 (num)
4 FORMAT_VALUE 0
6 LOAD_CONST 2 ('.pdf')
8 BUILD_STRING 3
10 RETURN_VALUE
Because it's a special syntax, it can access opcodes that aren't used in other approaches.
str.format
This is the recommended approach when f-strings aren't possible - mainly, because the template string needs to be prepared ahead of time and filled in later. It looks like 'hanning{}.pdf'.format(num), or 'hanning{num}.pdf'.format(num=num)'. Here, format is a method built in to strings, which can accept arguments either by position or keyword.
Particularly for str.format, it's useful to know that the built-in locals, globals and vars functions return dictionaries that map variable names to the contents of those variables. Thus, rather than something like '{a}{b}{c}'.format(a=a, b=b, c=c), we can use something like '{a}{b}{c}'.format(**locals()), unpacking the locals() dict.
str.format_map
This is a rare variation on .format. It looks like 'hanning{num}.pdf'.format_map({'num': num}). Rather than accepting keyword arguments, it accepts a single argument which is a mapping.
That probably doesn't sound very useful - after all, rather than 'hanning{num}.pdf'.format_map(my_dict), we could just as easily write 'hanning{num}.pdf'.format(**my_dict). However, this is useful for mappings that determine values on the fly, rather than ordinary dicts. In these cases, unpacking with ** might not work, because the set of keys might not be determined ahead of time; and trying to unpack keys based on the template is unwieldy (imagine: 'hanning{num}.pdf'.format(num=my_mapping[num]), with a separate argument for each placeholder).
string.Formatter
The string standard library module contains a rarely used Formatter class. Using it looks like string.Formatter().format('hanning{num}.pdf', num=num). The template string uses the same syntax again. This is obviously clunkier than just calling .format on the string; the motivation is to allow users to subclass Formatter to define a different syntax for the template string.
All of the above approaches use a common "formatting language" (although string.Formatter allows changing it); there are many other things that can be put inside the {}. Explaining how it works is beyond the scope of this answer; please consult the documentation. Do keep in mind that literal { and } characters need to be escaped by doubling them up. The syntax is presumably inspired by C#.
The % operator
This is a legacy way to solve the problem, inspired by C and C++. It has been discouraged for a long time, but is still supported. It looks like 'hanning%s.pdf' % num, for simple cases. As you'd expect, literal '%' symbols in the template need to be doubled up to escape them.
It has some issues:
It seems like the conversion specifier (the letter after the %) should match the type of whatever is being interpolated, but that's not actually the case. Instead, the value is converted to the specified type, and then to string from there. This isn't normally necessary; converting directly to string works most of the time, and converting to other types first doesn't help most of the rest of the time. So 's' is almost always used (unless you want the repr of the value, using 'r'). Despite that, the conversion specifier is a mandatory part of the syntax.
Tuples are handled specially: passing a tuple on the right-hand side is the way to provide multiple arguments. This is an ugly special case that's necessary because we aren't using function-call syntax. As a result, if you actually want to format a tuple into a single placeholder, it must be wrapped in a 1-tuple.
Other sequence types are not handled specially, and the different behaviour can be a gotcha.
string.Template
The string standard library module contains a rarely used Template class. Instances provide substitute and safe_substitute methods that work similarly to the built-in .format (safe_substitute will leave placeholders intact rather than raising an exception when the arguments don't match). This should also be considered a legacy approach to the problem.
It looks like string.Template('hanning$num.pdf').substitute(num=num), and is inspired by traditional Perl syntax. It's obviously clunkier than the .format approach, since a separate class has to be used before the method is available. Braces ({}) can be used optionally around the name of the variable, to avoid ambiguity. Similarly to the other methods, literal '$' in the template needs to be doubled up for escaping.
I had a need for an extended version of this: instead of embedding a single number in a string, I needed to generate a series of file names of the form 'file1.pdf', 'file2.pdf' etc. This is how it worked:
['file' + str(i) + '.pdf' for i in range(1,4)]
You can make dict and substitute variables in your string.
var = {"name": "Abdul Jalil", "age": 22}
temp_string = "My name is %(name)s. I am %(age)s years old." % var
I am trying to find the right language to describe the following concept. Maybe someone can help me out.
This is a general question about programming but I'll use Python and R for examples.
In Python, we can put something in a dictionary like this
myData = {}
myData["myField"] = 14
In R, for example, using the data.table package, we could write something like
data = data.table(x = c(1, 2, 3))
data[,myField: = x^2]
These do different things but compare the second line of each of them. In Python, the "myField" is a string. In the R data.table example, there is no string. The R example is kinda nice because it saves you typing but then it gives you trouble if want to write a program where myField is a variable. In Python that is trivial because you can just do
myData[myVariable] = 14
with myVariable being defined as another string. In R, you can do this too but have to use a different syntax which means you have to know two completely different syntactical ways of programming it.
My question: What is this called? I know it has something to do with scoping rules, (perhaps meta programming?), but can't figure out the right language for it. Anyone?
I believe this programming language "feature" is known as "bare strings".
PHP also has (deprecated) support for this: Why is $foo[bar] wrong?
It's widely considered to be a pretty terrible idea because of the risk of overlap with variable or constant names, and should definitely be avoided in production code. However, JavaScript has an interesting twist on the idea that avoids those issues:
var obj = { key: "value" };
You can define the keys on inline objects without using quotation marks. This works because you can't do it the other way - the key is parsed as a string, never a variable name. I've found this to be a pretty useful tradeoff in programs where you only use predefined keys in dictionaries. The Python version, for reference, requires the quotation marks, but allows you to use a variable, as you demonstrated:
obj = { "key": "value", key_var: "value" }
I'm not sure if this is what you're asking, but, in your Python example, the "myField" in myData["myField"] is a string literal -- i.e., you're hard-coding in the key value. Similarly, if you defined a Python function
def myFun(a):
# magic happens
and you invoked the function as myFun("goober"), you'd be passing in a string literal ("goober"), as opposed to defining a variable b = "goober" then passing in the variable as myFun(b).
Your question seems related to the definition/use of (unevaluated) symbols in Lisp (and related languages, and also Mathematica), c.f. the answers here
I'm trying to create a calculator program in which the user can type an equation and get an answer. I don't want the full code for this, I just need help with a specific part.
The approach I am trying to take is to have the user input the equation as a string (raw_input) and then I am trying to convert the numbers from their input to integers. After that I need to know how I can get the operands to do what I want them to do depending on which operand the user uses and where it is in the equation.
What are some methods I might use to accomplish this task?
Here is basically what I have right now:
equation_number = raw_input("\nEnter your equation now: ")
[int(d) for d in equation_number if d.isdigit()]
Those lines are just for collecting input and attempting to convert the numbers into integers. Unfortunately, it does not seem to be working very well and .isdigit will only work for positive numbers anyway.
Edit- aong152 mentioned recursive parsing, which I looked into, and it appears to have desirable results:
http://blog.erezsh.com/how-to-write-a-calculator-in-70-python-lines-by-writing-a-recursive-descent-parser/
However, I do not understand the code that the author of this post is using, could anyone familiarize me with the basics of recursive parsing?
The type of program you are trying to make is probably more complicated than you think
The first step would be separating the string into each argument.
Let's say that the user inputs:
1+2.0+3+4
Before you can even convert to ints, you are going to need to split the string up into its components:
1
+
2.0
+
3
+
4
This will require a recursive parser, which (seeing as you are new to python) maybe be a bit of a hurdle.
Assuming that you now have each part seperately as strings,
float("2.0") = 2.0
int(2.0) = 2
Here is a helper function
def num (s):
try:
return int(s)
except exceptions.ValueError:
return int(float(s))
instead of raw_input just use input because raw_input returns a string and input returns ints
This is a very simple calculator:
def calculate():
x = input("Equation: ")
print x
while True:
calculate()
the function takes the input and prints it then the while loop executes it again
im not sure if this is what you want but here you go and also you should make a way to end the loop
After using raw_input() you can use eval() on the result to compute the value of this string. eval() evaluates any valid Python expression and returns the outcome.
But I think this is not to your liking. You probably want to do more by yourself.
So I think you should have a look at the re module to split the input using regular expressions into tokens (sth like numbers and operators). After this you should write a parser which gets the token stream as input. You should decide whether this parser shall just return the computed value (e. g. a number) or maybe an abstract syntax tree, i. e. a data structure which represents the expression in an object-oriented (instead of character-oriented) way. Such an Absy could then be evaluated to get the final result.
Are you familiar with regular expressions? If not, it's probably a good idea to first learn about them. They are the weak, non-recursive cousin of parsing. Don't go deep, just understand the building blocks — A then B, A many times, A or B.
The blog post you found is hard because it implements the parsing by hand. It's using recursive descent, which is the only way to write a parser by hand and keep your sanity, but it's still tricky.
What people do most of the time is only write a high level grammar and use a library (or code generator) to do the hard work of parsing.
Indeed he had an earlier post where he uses a library:
http://blog.erezsh.com/how-to-write-a-calculator-in-50-python-lines-without-eval/
At least the beginning should be very easy. Things to pay attention to:
How precedence arises from the structure of the grammar — add consists of muls, not vice versa.
The moment he adds a rule for parentheses:
atom: neg | number | '(' add ')';
This is where it really becomes recursive!
6-2-1 should parse as (6-2)-1, not 6-(2-1). He doesn't discuss it, but if you look
carefully, it also arises from the structure of the grammar. Don't waste tome on this; just know for future reference that this is called associativity.
The result of parsing is a tree. You can then compute its value in a bottom-up manner.
In the "Calculating!" chapter he does that, but the in a sort of magic way.
Don't worry about that.
To build a calculator yourself, I suggest you strip the problem as much as possible.
Recognizing where numbers end etc. is a bit messy. It could be part of the grammar, or done by a separate pass called lexer or tokenizer.
I suggest you skip it — require the user to type spaces around all operators and parens. Or just assume you're already given a list of the form [2.0, "*", "(", 3.0, "+", -1.0, ")"].
Start with a trivial parser(tokens) function that only handles 3-element expressions — [number, op, number].
Return a single number, the result of the computation. (I previously said parsers output a tree which is processed later. Don't worry about that, returning a number is simpler.)
Write a function that expects either a number or parentheses — in the later case it calls parser().
>>> number_or_expr([1.0, "rest..."])
(1.0, ["rest..."])
>>> number_or_expr(["(", 2.0, "+", 2.0, ")", "rest..."])
(4.0, ["rest..."])
Note that I'm now returning a second value - the remaining part of the input. Change parser() to also use this convention.
Now Rewrite parser() to call number_or_expr() instead of directly assuming tokens[0] and tokens[2] are numbers.
Viola! You now have a (mutually) recursive calculator that can compute anything — it just has to be written in verbose style with parens around everything.
Now stop and admire your code, for at least a day :-) It's still simple but has the essential recursive nature of parsing. And the code structure reflects the grammar 1:1 (which is the nice property of recursive descent. You don't want to know how the other algorithms look).
From here there many improvements possible — support 2+2+2, allow (1), precedence... — but there are 2 ways to go about it:
Improve your code step by step. You'll have to refactor a lot.
Stop working hard and use a parsing library, e.g. pyparsing.
This will allow you to experiment with grammar changes faster.