Purere

Purere is a python regex library written fully in python. It compiles regex patterns into a python functions.

Purere passes all tests from the CPython test set for re (only skipping some tests involving implementation details). It also works with pypy3.

Why?

Mostly curiosity. Building a regex engine is fun, and purere is actually quite fast for a pure python libary. On some rather evil inputs it even outperforms other backtracking algorithms due to smarter caching (see the Design section below).

However, having a Python only version of the standard library can be useful when porting python to new platforms where we can not use a c compiler.

Usage

Not in PyPi yet, but after cloning you may

pip install .

After which your normal python code should work with the drop in replacement

import purere as re

If you want to generate python code that can be run standalone, you may use the functions purere.get_headers() and purere.compile_to_py(pattern,flags=0,name='regex'). The first of these should be included once in the generated python code and defines the classes for Pattern and Match. The second is called for each pattern that you want to compile to code. pattern and flags have the same meaning as normal. name is the name of the resulting pattern in the scope of the code.

Development status

Everything that re can do is supported appart from the re.L flag, i.e.:

ASCII, Unicode and byte-like strings
Ignore case mode I, multi-line mode M, and Dot-all mode M.
All character categories: \d\D\s\S\w\W.
Repetition using *, +, ? and {min,max}, including non-greedy variants
All AT codes: $ and ^, \A, \Z, \b, \B
Non-capturing grouping using (?:...), Capturing groups, group references, conditional matching depending on group ref (e.g. (?(1)a|b))
All types of asserts, also called look-ahead/look-behind.

The L locale flag will never be implemented. Usage is discouraged for re and we will not be implementing it. Full Unicode support is available and should be used.

TODO:

Full independence from stdlib. The only non optional dependence currently is enum, which is used for the flags. We might roll our own simpler funciton at some point.

Known implementation differences to re regarding matching:

For Unicode patterns we define \d using python's isnumerical(), which is not the same behavior as CPython's re. This means we match all nummerical unicode characters, while re is stricter. To get the original behavior there is an option purere.STRICTUNI that can be passed, in this case unicodedata is used to define '\d'.

Some minor implementation details that do not change matching behavior and that you will probably not notice every:

Match objects are not cached and hence copying them gives back a different object, where CPython gives an exact copy for some reason.
Buffers containing the bytes that are matched by finditer are not locked as pure python code can not do this. In general the behavior of finditer on a changing string is undefined and not tested.
If a compiled pattern is given to purere.compile, as well as flags, then no error is raised. Instead, the pattern is recompiled with the new flags if needed.
Debug output shows the generated python code.

Design

This library uses backtracking but takes inspiration from finite automata implementations to avoid exponential behavior on certain patterns. See also Russ Cox their great articles on regex https://swtch.com/~rsc/regexp/ for a more detailed explanation of this problem.

Compile Time Overview

To avoid re-implementing the parsing of the pattern, the pure python parts of CPython's sre are reused. In particular, sre_parse parses the regex and sre_compile compiles it to instructions that would normally be fed to a virtual machine implemented by _sre.c. We leave this mostly intact but, slightly get in the middle to refactor the results to fit our needs. This refactoring is done in proccess.py. For consistency reasons, compatibility with pypy, and to allow us to re-implement the few lines of code from _sre.c that are used in sre_compile.py, we include a copy of CPython's implementation for their files which have been kept mostly the same. Purere runs fine if the standard library version is used in CPython's.

We do not implement a VM. Instead the resulting code is taken by compiler.py and converted to standalone python code for this specific pattern. First we make all jump locations absolute jumps and then split the code into parts such that all jumps are to the beginning of a part. This allows us to number the parts and change the definition of the jumps once again so they reference part numbers.

With this in hand python code is generated from the VM code for each of the parts in topy.py. A very simple part that only matches the letters a-z might look like:

...
if part == 1:
 if pos>=len(s): break
 if not('a' <= s[pos] <= 'z'): break
 part += 1
...

This is then placed in a big while True: loop consisting of many if part == <some part number>: statements for the many parts. Some boiler plate code is added and the whole thing is compiled using exec. An example for a simple regex is given below.

Runtime Overview

Let us now switch to what happens when matching, i.e., in the generated python code. To main variables are present and correspond to the current state of algorithm, the aforementioned part denotes the part, and pos denotes the position in the string that is being matched. As we implement a backtracking algorithm, a stack is kept of 'states' to jump to if the current branch does not work out, i.e., a list of (part,pos) pairs. In reality there are more parts of the state that we need to keep on the stack, but we will discuss these later. To ease this jumping back the while True: loop sits in another while stack: loop. When a break occurs in the inner loop a new value is taken from the stack and the inner loop starts again. To avoid double work a set done is kept that tracks states that are already visited as visiting them again will result in the same negative result. Some parts of the state are not added to done as their value does not influence the final result (whether there will be a match). If we at some point encounter the end of the code then we return the found match. If the stack is empty before this happens then we return None and conclude that there was no match.

If there are no additional parts of state to track, then the time complexity is roughly O(p^2s), where p is the number of parts and s is the length of the string. The square on p comes from the fact that we have to check p if-statements in the loop. We could improve this to log(p) by nesting the if-statements in a binary-tree fashion but as p is often very small this will not change much.

Specifics

Now for some specifics on certain aspects of regex.

Groups

Non-capturing groups are easy to implement and can mostly be ignored as sre_compile takes care of this. A bit more care needs to be taken to implement capturing groups and their related operations. Simple capture groups are simple enough, we just keep a tuple marks that contains all the starting and ending spots, and keep this in the stack as well. We do not add this to our definition of done, as the position of the marks can not change the final result of the regex. An exception to this is when the groups are referenced later with a back-reference, as now the specifics of the marks matters for the matching result. For these groups a second tuple smarks is kept that is added to the stack and to done.

Loops

All loops are split in a required part and an optional (possible infinite) part. For example a+ becomes aa* and a{3,6} becomes a{3}a{0,3}. Infinite loops are easy to handle and are rewritten as a branch between a part of the code that tries to match the loop content, and then jumps back to the start, and the part of the code after the loop.

Smaller non-infinite loops (like a{0,3}) are unrolled, effectively using part as a loop counter. For larger loop we do add separate loop counter that keeps track of where we are in the loop. The structure for optional finite loops is the same as their infinite counterpart, but the jump back after matching the content is now conditioned on the counters value. For required loops, like a{25}, the structure is even simpler, we keep jumping back to the start until the counter is at a certain value.

Loop counters are added to both the stack and to done.

Look-ahead & look-behind

Together known as ASSERT instructions, these form the big brother of AT instructions. They check for a match but then return to the original pos in the list. As these can possibly be nested we keep a seperate assert_stack of all currently active asserts containing the pos value that should be jumped back to after a successfull assert, and the length of the main stack before the assert started, so we can trow away any open branches of a finished assert.

For positive asserts we simply pop the assert stack if the end is reached, set the old position back and reset the stack to its old value. If a possitive assert fails then at some point the last of its branches will be poped of the stack, after this the algorithm just contnues as normal and pops the branch that was on top of the stack before the assert started, which is exactly the behavior we want if the assert fails. The only bookkeeping here is to ass a marker to the stack that signals that the assert_stack should be poped as an assert ended.

For negative asserts, i.e., we do not want to match here now, we need a bit more work, but not much. We simply push the position to go to after the assert did not match (which is a succesful-negative-assert) onto the stack, as then the assert failing brings us there automaticly. On the other hand, if we reach the end of the assert, then the assert did miatch, which is not what we want, so we pop the previous stack length of the assert_stack and jump back to the last branch before the assert started.

Example result

As an ilustration of the above, the regex (cool|awesome)* is compiled to the following VM code, where jumps are given by line numbers:

01: LS_BRANCH [10]
02: MARK 0
03: LS_BRANCH [5]
04: LITERALS [99, 111, 111, 108]
05: ABS_JUMP 9
06: LITERALS [97, 119, 101, 115, 111, 109, 101]
07: ABS_JUMP 9
08: MARK 1
09: ABS_JUMP 1
10: SUCCESS

Here the MARK codes denote the start and end of groups. The LS_BRANCH instructions take a list of lines to branch to (and also step to the next line first), LITERALS checks for the existence of a string of characters in the string, and ABS_JUMP simply jumps to a line.

This is then compiled into a python function as below. The code is slightly cleaned up to remove parts that are needed in general but do not get used in the simple regex above. Also, note that at this point line numbers have been converted in numbers of parts of the VM code that form a logical block.

def regex(s, pos = 0, endpos = None, full = False):
 # Regex: '(cool|awesome)*'
 endpos = len(s) if endpos is None else min(endpos,len(s))
 marks = (None,)*2
 stack = [(0,pos,marks)]
 done = set()
 while stack:
  part,pos,marks = stack.pop()
  if (part,pos) in done:
   continue

  while True:
   if part == 0:
    done.add((part,pos))
    stack.append((3,pos,marks))
    # ^  [LS_BRANCH, [3]]
    marks = marks[:0]+ (pos,) +marks[1:]
    # ^  [MARK, 0]
    stack.append((1,pos,marks))
    # ^  [LS_BRANCH, [1]]
    if not(pos+4 <= endpos) or s[pos:pos+4] != 'cool': break
    pos += 4
    # ^  [LITERALS, [99, 111, 111, 108]]
    part = 2
    # ^  [ABS_JUMP, 2]
   
   if part == 1:
    done.add((part,pos))
    if not(pos+7 <= endpos) or s[pos:pos+7] != 'awesome': break
    pos += 7
    # ^  [LITERALS, [97, 119, 101, 115, 111, 109, 101]]
    part = 2
    # ^  [ABS_JUMP, 2]
   
   if part == 2:
    done.add((part,pos))
    marks = marks[:1]+ (pos,) +marks[2:]
    # ^  [MARK, 1]
    part = 0
    continue
    # ^  [ABS_JUMP, 0]
   
   if part == 3:
    done.add((part,pos))
    if ((full and pos == endpos) or not full):
     return True,pos,marks,done
    else:
     break
    # ^  [SUCCESS]
 return None, None, None, done

Benchmarking

(Relative) speed will highly depend on the system, python version, and the benchmarks used. Some benchmarks are included and can be run with pytest to get a rough idea:

pytest tests/test_speed.py -rP

We get about a factor 10 slowdown in compilation when using CPython (compared to using re). As for matching time, it really depends on the input. We are particulairly slow in two cases:

Matching single character repeats like .*.
Matching huge texts with a regex that does not start with a string prefix (for example [ab]cd does not start with a string prefix, while ab[cd] starts with the prefix ab)

Both cases are slower because searching long inputs with a loop in python can never beat a loop in C. However, if the pattern always starts the same, then find() is used to only try an match at those positions where the pattern might be. For reasonable patterns the slowdown with CPython is mostly between 6 and 20 times.

Development

Poetry is used for package management. Apart from that, only pytest is needed to run the tests and there are no runtime dependencies. To install pytest and setup a virtual envoirment run poetry install. To run the tests run poetry run pytest.

Name

The name is a reference to the pure python nature and the Dutch word for 'to mash' (which is what my head feels like when I work with regex).

jorants/purere