# Reducing Failure-Inducing Inputs¶

A standard problem in debugging is this: Your program fails after processing some large input. Only a part of this input, however, is responsible for the failure. Reducing the input to a failure-inducing minimum not only eases debugging – it also helps in understanding why and when the program fails. In this chapter, we present techniques that automatically reduce and simplify failure-inducing inputs to a minimum, notably the popular Delta Debugging technique.

from bookutils import YouTubeVideo


Prerequisites

• Using the "delta debugging" technique for reduction has no specific prerequisites.
• To understand the DeltaDebugger implementation, reading the chapter on tracing is recommended.

This chapter is adapted from a similar chapter in "The Fuzzing Book". The material has been adapted to be independent from the fuzzingbook infrastructure, to build on general delta debugging (dd), and to provide a simpler invocation interface.

## Synopsis¶

>>> from debuggingbook.DeltaDebugger import <identifier>


and then make use of the following features.

A reducer takes a failure-inducing input and reduces it to the minimum that still reproduces the failure. This chapter provides a DeltaDebugger class that implements such a reducer.

Here is a simple example: An arithmetic expression causes an error in the Python interpreter:

>>> def myeval(inp: str) -> Any:
>>>     return eval(inp)

>>> with ExpectError(ZeroDivisionError):
>>>     myeval('1 + 2 * 3 / 0')

Traceback (most recent call last):
File "<ipython-input-1-93ec01ccd5a1>", line 2, in <module>
myeval('1 + 2 * 3 / 0')
File "<ipython-input-1-79b898a76dcc>", line 2, in myeval
return eval(inp)
File "<string>", line 1, in <module>
ZeroDivisionError: division by zero (expected)


Can we reduce this input to a minimum? Delta Debugging is a simple and robust reduction algorithm. We provide a DeltaDebugger class that is used in conjunction with a (failing) function call:

with DeltaDebugger() as dd:
fun(args...)
dd


The class automatically determines minimal arguments that cause the function to fail with the same exception as the original. Printing out the class object reveals the minimized call.

>>> with DeltaDebugger() as dd:
>>>     myeval('1 + 2 * 3 / 0')
>>> dd

myeval(inp='3/0')


The input is reduced to the maximum: We get the essence of the division by zero.

There also is an interface to access the reduced input(s) programmatically. The method min_args() returns a dictionary in which all function arguments are minimized:

>>> dd.min_args()

{'inp': '3/0'}


In contrast, max_args() returns a dictionary in which all function arguments are maximized, but still pass:

>>> dd.max_args()

{'inp': '1 + 2 * 3  '}


The method min_arg_diff() returns a triple of

• passing input,
• failing input, and
• their minimal failure-inducing difference:
>>> dd.min_arg_diff()

({'inp': ' 3 '}, {'inp': ' 3 /0'}, {'inp': '/0'})


And you can also access the function itself, as well as its original arguments.

>>> dd.function().__name__, dd.args()

('myeval', {'inp': '1 + 2 * 3 / 0'})


DeltaDebugger processes (i.e., minimizes or maximizes) all arguments that support a len() operation and that can be indexed – notably strings and lists. If a function has multiple arguments, all arguments that can be processed will be processed.

This chapter also provides a number of superclasses to DeltaDebugger, notably CallCollector, which obtains the first function call for DeltaDebugger. CallReducer classes allow for implementing alternate call reduction strategies.

## Why Reducing?¶

A common problem in debugging is that given an input, only a small part of that input may be responsible for the failure. A central part of debugging is to identify these parts – and to simplify (or reduce) the input to a minimal form that reproduces the failure – but does and contains as little else as possible.

Here's an example of such a situation. We have a mystery() method that – given its code – can occasionally fail. But under which circumstances does this actually happen? We have deliberately obscured the exact condition in order to make this non-obvious.

import bookutils

import Tracer

from bookutils import quiz

def mystery(inp: str) -> None:
x = inp.find(chr(0o17 + 0o31))
y = inp.find(chr(0o27 + 0o22))
if x >= 0 and y >= 0 and x < y:
raise ValueError("Invalid input")
else:
pass


To find an input that causes the function to fail, let us fuzz it – that is, feed it with random inputs – until we find a failing input. There's entire books about fuzzing; but here, a very simple fuzz() function for this purpose will already suffice.

To build a fuzzer, we need random inputs – and thus a source for randomness. The function random.randrange(a, b) returns a random number in the range (a, b).

import random

random.randrange(32, 128)

107


We can use random.randrange() to compose random (printable) characters:

def fuzz() -> str:
length = random.randrange(10, 70)
fuzz = ""
for i in range(length):
fuzz += chr(random.randrange(32, 127))
return fuzz


Here are some random strings produced by our fuzz() function:

for i in range(6):
print(repr(fuzz()))

'N&+slk%hyp5'
"'@[3(rW*M5W]tMFPU4\\P@tz%[X?uo\\1?b4T;1bDeYtHx #UJ5"
'w}pMmPodJM,_%%BC~dYN6*g|Y*Ou9I<P94}7,99ivb(9=%jJj*Y*d~OLXk!;J'
"!iOU8]hqg00?u(c);>:\\=V<ZV1=*g#UJA'No5QZ)~--[})Sdv#m*L"
'0iHh[-MzS.U.X}fG7aA:G<bEI\'Ofn[",Mx{@jfto}i3D?7%V7XdtO6BjYEa#Il)~]'
"Eh7h)ChX0G*m,|sosJ.mu/\\c'EpaPi0(n{"


Let us now use fuzz() to find an input where mistery() fails:

while True:
fuzz_input = fuzz()
try:
mystery(fuzz_input)
except ValueError:
break


This is an input that causes mystery() to fail:

failing_input = fuzz_input
failing_input

'V"/+!aF-(V4EOz*+s/Q,7)2@0_'

len(failing_input)

26

from ExpectError import ExpectError

with ExpectError(ValueError):
mystery(failing_input)

Traceback (most recent call last):
File "<ipython-input-1-4e5dc18f5c4d>", line 2, in <module>
mystery(failing_input)
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


Something in this input causes mystery() to fail. But what is it?

## Manual Input Reduction¶

One important step in the debugging process is reduction – that is, to identify those circumstances of a failure that are relevant for the failure to occur, and to omit (if possible) those parts that are not. As Kernighan and Pike [Kernighan et al, 1999] put it:

For every circumstance of the problem, check whether it is relevant for the problem to occur. If it is not, remove it from the problem report or the test case in question.

Specifically for inputs, they suggest a divide and conquer process:

Proceed by binary search. Throw away half the input and see if the output is still wrong; if not, go back to the previous state and discard the other half of the input.

This is something we can easily try out, using our last generated input:

failing_input

'V"/+!aF-(V4EOz*+s/Q,7)2@0_'


For instance, we can see whether the error still occurs if we only feed in the first half:

half_length = len(failing_input) // 2   # // is integer division
first_half = failing_input[:half_length]
first_half

'V"/+!aF-(V4EO'

with ExpectError(ValueError):
mystery(first_half)


Nope – the first half alone does not suffice. Maybe the second half?

second_half = failing_input[half_length:]
assert first_half + second_half == failing_input
second_half

'z*+s/Q,7)2@0_'

with ExpectError(ValueError):
mystery(second_half)


This did not go so well either. We may still proceed by cutting away smaller chunks – say, one character after another. If our test is deterministic and easily repeated, it is clear that this process eventually will yield a reduced input. But still, it is a rather inefficient process, especially for long inputs. What we need is a strategy that effectively minimizes a failure-inducing input – a strategy that can be automated.

## Delta Debugging¶

One strategy to effectively reduce failure-inducing inputs is delta debugging [Zeller et al, 2002]. Delta Debugging implements the "binary search" strategy, as listed above, but with a twist: If neither half fails (also as above), it keeps on cutting away smaller and smaller chunks from the input, until it eliminates individual characters. Thus, after cutting away the first half, we cut away the first quarter, the second quarter, and so on.

Let us illustrate this on our example, and see what happens if we cut away the first quarter.

quarter_length = len(failing_input) // 4
input_without_first_quarter = failing_input[quarter_length:]
input_without_first_quarter

'F-(V4EOz*+s/Q,7)2@0_'

with ExpectError(ValueError):
mystery(input_without_first_quarter)

Traceback (most recent call last):
File "<ipython-input-1-93dfdcc38bb3>", line 2, in <module>
mystery(input_without_first_quarter)
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


Ah! This has failed, and reduced our failing input by 25%. Let's remove another quarter.

input_without_first_and_second_quarter = failing_input[quarter_length * 2:]
input_without_first_and_second_quarter

'Oz*+s/Q,7)2@0_'

with ExpectError(ValueError):
mystery(input_without_first_and_second_quarter)


This is not too surprising, as we had that one before:

second_half

'z*+s/Q,7)2@0_'

input_without_first_and_second_quarter

'Oz*+s/Q,7)2@0_'


How about removing the third quarter, then?

input_without_first_and_third_quarter = failing_input[quarter_length:
quarter_length * 2] + failing_input[quarter_length * 3:]
input_without_first_and_third_quarter

'F-(V4EQ,7)2@0_'

with ExpectError(ValueError):
mystery(input_without_first_and_third_quarter)

Traceback (most recent call last):
File "<ipython-input-1-8ab1da14a84d>", line 2, in <module>
mystery(input_without_first_and_third_quarter)
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


Yes! This has succeeded. Our input is now 50% smaller.

We have now tried to remove pieces that make up $\frac{1}{2}$ and $\frac{1}{4}$ of the original failing string. In the next iteration, we would go and remove even smaller pieces – $\frac{1}{8}$, $\frac{1}{16}$ and so on. We continue until we are down to $\frac{1}{26}$ – that is, individual characters.

However, this is something we happily let a computer do for us – and this is what the Delta Debugging algorithm does. Delta Debugging implements the strategy sketched above: It first removes larger chunks of size $\frac{1}{2}$; if this does not fail, then we proceed to chunks of size $\frac{1}{4}$, then $\frac{1}{8}$ and so on.

Our ddmin() implementation uses the exact same Python code as Zeller in [Zeller et al, 2002]; the only difference is that it has been adapted to work on Python 3. The variable n (initially 2) indicates the granularity – in each step, chunks of size $\frac{1}{n}$ are cut away. If none of the test fails (some_complement_is_failing is False), then n is doubled – until it reaches the length of the input.

PASS = 'PASS'
FAIL = 'FAIL'
UNRESOLVED = 'UNRESOLVED'

def ddmin(test: Callable, inp: Sequence, *test_args: Any) -> Sequence:
"""Reduce the input inp, using the outcome of test(fun, inp)."""
assert test(inp, *test_args) != PASS

n = 2     # Initial granularity
while len(inp) >= 2:
start = 0
subset_length = int(len(inp) / n)
some_complement_is_failing = False

while start < len(inp):
complement = (inp[:int(start)] + inp[int(start + subset_length):])

if test(complement, *test_args) == FAIL:
inp = complement
n = max(n - 1, 2)
some_complement_is_failing = True
break

start += subset_length

if not some_complement_is_failing:
if n == len(inp):
break
n = min(n * 2, len(inp))

return inp


To see how ddmin() works, let us run it on our failing input. We need to define a test function that returns PASS or FAIL, depending on the test outcome. This generic_test() assumes that the function fails if it raises an exception (such as an AssertException), and passes otherwise. The optional argument expected_exc specifies the name of exception to be checked for; this ensures we reduce only for the kind of error raised in the original failure.

def generic_test(inp: Sequence, fun: Callable,
expected_exc: Optional[Type] = None) -> str:
result = None
detail = ""
try:
result = fun(inp)
outcome = PASS
except Exception as exc:
detail = f" ({type(exc).__name__}: {str(exc)})"
if expected_exc is None:
outcome = FAIL
elif type(exc) == type(expected_exc) and str(exc) == str(expected_exc):
outcome = FAIL
else:
outcome = UNRESOLVED

print(f"{fun.__name__}({repr(inp)}): {outcome}{detail}")
return outcome


We can now invoke ddmin() in our setting. With each step, we see how the remaining input gets smaller and smaller, until only two characters remain:

ddmin(generic_test, failing_input, mystery, ValueError('Invalid input'))

mystery('V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
mystery('z*+s/Q,7)2@0_'): PASS
mystery('V"/+!aF-(V4EO'): PASS
mystery('F-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
mystery('Oz*+s/Q,7)2@0_'): PASS
mystery('F-(V4EQ,7)2@0_'): FAIL (ValueError: Invalid input)
mystery(',7)2@0_'): PASS
mystery('F-(V4EQ'): PASS
mystery('V4EQ,7)2@0_'): PASS
mystery('F-(Q,7)2@0_'): FAIL (ValueError: Invalid input)
mystery('Q,7)2@0_'): PASS
mystery('F-()2@0_'): FAIL (ValueError: Invalid input)
mystery('2@0_'): PASS
mystery('F-()'): FAIL (ValueError: Invalid input)
mystery('()'): FAIL (ValueError: Invalid input)
mystery(')'): PASS
mystery('('): PASS

'()'


Now we know why mystery() fails – it suffices that the input contains two matching parentheses. Delta Debugging determines this in 25 steps. Its result is 1-minimal, meaning that every character contained is required to produce the error; removing any (as seen in the last two tests, above) no longer causes the test to fail. This property is guaranteed by the delta debugging algorithm, which in its last stage always tries to delete characters one by one.

A reduced test case such as the one above has many advantages:

• A reduced test case reduces the cognitive load of the programmer. The test case is shorter and focused, and thus does not burden the programmer with irrelevant details. A reduced input typically leads to shorter executions and smaller program states, both of which reduce the search space as it comes to understanding the bug. In our case, we have eliminated lots of irrelevant input – only the two characters the reduced input contains are relevant.

• A reduced test case is easier to communicate. All one needs here is the summary: mystery() fails on "()", which is much better than mystery() fails on a 4100-character input (attached).

• A reduced test case helps in identifying duplicates. If similar bugs have been reported already, and all of them have been reduced to the same cause (namely that the input contains matching parentheses), then it becomes obvious that all these bugs are different symptoms of the same underlying cause – and would all be resolved at once with one code fix.

How effective is delta debugging? In the best case (when the left half or the right half fails), the number of tests is logarithmic proportional to the length $n$ of an input (i.e., $O(\log_2 n)$); this is the same complexity as binary search. In the worst case, though, delta debugging can require a number of tests proportional to $n^2$ (i.e., $O(n^2)$) – this happens in the case when we are down to character granularity, and we have to repeatedly tried to delete all characters, only to find that deleting the last character results in a failure [Zeller et al, 2002]. (This is a pretty pathological situation, though.)

In general, delta debugging is a robust algorithm that is easy to implement, easy to deploy, and easy to use – provided that the underlying test case is deterministic and runs quickly enough to warrant a number of experiments. In general, any debugging task should start with simplifying the test case as much as possible – and this is where delta debugging can help.

As defined above, using ddmin() still requires the developer to set up a special testing function – and writing or using even a generic tester (like generic_test()) takes some effort. We want to simplify the setup such that only two lines of Python is required.

Our aim is to have a DeltaDebugger class that we can use in conjunction with a failing (i.e., exception raising) function call:

with DeltaDebugger() as dd:
mystery(failing_input)
dd


Here, at the end of the with statement, printing out dd shows us the minimal input that causes the failure.

Our interface consist of six building blocks:

1. We collect the name and args of the first call in the with body, as well as the exception it raises.
2. We set up an infrastructure such that we can repeat calls with different arguments.
3. We make sure that multiple tests with the same arguments can return outcomes from a cache.
4. We create a DeltaDebugger class that implements the general Delta Debugging algorithm – an algorithm than can minimize failing inputs as well as maximize passing inputs.
5. We provide an infrastructure that applies Delta Debugging on multiple arguments.
6. Finally, custom methods like min_args() allow to invoke delta debugging on arguments.

#### Collecting a Call¶

We start by creating an infrastructure that collects a call. The CallCollector class saves the first call observed in _function, _args, and _exception attributes, respectively; it then turns tracing off.

import sys

from types import FunctionType, FrameType, TracebackType

from StackInspector import StackInspector

class NoCallError(ValueError):
pass

class CallCollector(StackInspector):
"""
Collect an exception-raising function call f().
Use as with CallCollector(): f()
"""

def __init__(self) -> None:
"""Initialize collector"""
self.init()

def init(self) -> None:
"""Reset for new collection."""
self._function: Optional[Callable] = None
self._args: Dict[str, Any] = {}
self._exception: Optional[BaseException] = None
self.original_trace_function: Optional[Callable] = None

def traceit(self, frame: FrameType, event: str, arg: Any) -> None:
"""Tracing function. Collect first call, then turn tracing off."""
if event == 'call':
name = frame.f_code.co_name
if name.startswith('__'):
# Internal function
return
if self._function is not None:
return

func = self.search_func(name, frame)
if func:
self._function = func
else:
# Create new function from given code
self._function = self.create_function(frame)

self._args = {}  # Create a local copy of args
for var in frame.f_locals:
if var in frame.f_code.co_freevars:
continue  # Local var, not an argument
self._args[var] = frame.f_locals[var]

# Turn tracing off
sys.settrace(self.original_trace_function)

def after_collection(self) -> None:
"""Called after collection. To be defined in subclasses."""
pass

def args(self) -> Dict[str, Any]:
"""Return the dictionary of collected arguments."""
return self._args

def function(self) -> Callable:
"""Return the function called."""
if self._function is None:
raise NoCallError("No function call collected")
return self._function

def exception(self) -> Optional[BaseException]:
"""Return the exception produced, or None if none."""
return self._exception

def format_call(self, args: Optional[Dict[str, Any]] = None) -> str:
...

def format_exception(self, exc: Optional[BaseException] = None) -> str:
...

def call(self, new_args: Optional[Dict[str, Any]] = None) -> Any:
...


A CallCollector is used like a Tracer from the chapter on tracing, using a with block to collect a single function call.

class CallCollector(CallCollector):
def __enter__(self) -> Any:
"""Called at begin of with block. Turn tracing on."""
self.init()
self.original_trace_function = sys.gettrace()
sys.settrace(self.traceit)
return self

def __exit__(self, exc_tp: Type, exc_value: BaseException,
exc_traceback: TracebackType) -> Optional[bool]:
"""Called at end of with block. Turn tracing off."""
sys.settrace(self.original_trace_function)

if not self._function:
if exc_tp:
return False  # re-raise exception
else:
raise NoCallError("No call collected")

if self.is_internal_error(exc_tp, exc_value, exc_traceback):
return False  # Re-raise exception

self._exception = exc_value
self.after_collection()
return True  # Ignore exception


Here are the attributes as collected by CallCollector for our mystery() function. Note that the mystery() exception is "swallowed" by the CallCollector.

with CallCollector() as call_collector:
mystery(failing_input)

call_collector.function()

<function __main__.mystery(inp:str) -> None>

call_collector.args()

{'inp': 'V"/+!aF-(V4EOz*+s/Q,7)2@0_'}

call_collector.exception()

ValueError('Invalid input')


If an error occurs before the first function call takes place, the exception is simply re-raised.

with ExpectError(NameError):
with CallCollector() as c:
some_error()

Traceback (most recent call last):
File "<ipython-input-1-b98195fc9313>", line 3, in <module>
some_error()  # type: ignore
NameError: name 'some_error' is not defined (expected)


#### Repeating a Call¶

Our second step is an infrastructure such that we can call the function collected earlier with alternate arguments. We can call the function directly via the collected _function attribute:

call_collector.function()("foo")

with ExpectError(ValueError):
call_collector.function()(failing_input)

Traceback (most recent call last):
File "<ipython-input-1-2c94675c1637>", line 2, in <module>
call_collector.function()(failing_input)
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


We can also provide the arguments collected during the call:

with ExpectError(ValueError):
call_collector.function()(**call_collector.args())

Traceback (most recent call last):
File "<ipython-input-1-f4fc9b38eb41>", line 2, in <module>
call_collector.function()(**call_collector.args())
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


Our call() method calls the collected function using this construct. It also allows to change individual arguments by providing a new_args dictionary of variable names to new values.

class CallCollector(CallCollector):
def call(self, new_args: Optional[Dict[str, Any]] = None) -> Any:
"""
Call collected function. If new_args is given,
override arguments from its {var: value} entries.
"""

if new_args is None:
new_args = {}

args = {}  # Create local copy
for var in self.args():
args[var] = self.args()[var]
for var in new_args:
args[var] = new_args[var]

return self.function()(**args)


Using simply call() without arguments reproduces the failure:

with CallCollector() as call_collector:
mystery(failing_input)
with ExpectError(ValueError):
call_collector.call()

Traceback (most recent call last):
File "<ipython-input-1-b941b6b99692>", line 4, in <module>
call_collector.call()
File "<ipython-input-1-107a8504cab5>", line 17, in call
return self.function()(**args)
File "<ipython-input-1-fd984d68a269>", line 5, in mystery
raise ValueError("Invalid input")
ValueError: Invalid input (expected)


We can also supply alternate arguments (and get alternate outcomes):

call_collector.call({'inp': 'foo'})


We close with two helper functions that come handy for logging and error messages:

class CallCollector(CallCollector):
def format_call(self, args: Optional[Dict[str, Any]] = None) -> str:
"""Return a string representing a call of the function with given args."""
if args is None:
args = self.args()
return self.function().__name__ + "(" + \
", ".join(f"{arg}={repr(args[arg])}" for arg in args) + ")"

def format_exception(self, exc: Optional[BaseException] = None) -> str:
"""Return a string representing the given exception."""
if exc is None:
exc = self.exception()
s = type(exc).__name__
if str(exc):
s += ": " + str(exc)
return s

with CallCollector() as call_collector:
mystery(failing_input)

call_collector.format_call()

'mystery(inp=\'V"/+!aF-(V4EOz*+s/Q,7)2@0_\')'

call_collector.format_exception()

'ValueError: Invalid input'


#### Testing, Logging, and Caching¶

Our next to last step is an infrastructure that implements delta debugging for the collected call.

We first introduce a CallReducer class as an abstract superclass for all kinds of reducers. Its run() method tests the function and returns PASS, FAIL, or UNRESOLVED. As with generic_test(), above, we check for exception type and exact error message.

class CallReducer(CallCollector):
def __init__(self, *, log: Union[bool, int] = False) -> None:
"""Initialize. If log is True, enable logging."""
super().__init__()
self.log = log
self.reset()

def reset(self) -> None:
"""Reset the number of tests."""
self.tests = 0

def run(self, args: Dict[str, Any]) -> str:
"""
Run collected function with args. Return
* PASS if no exception occurred
* FAIL if the collected exception occurred
* UNRESOLVED if some other exception occurred.
Not to be used directly; can be overloaded in subclasses.
"""
try:
result = self.call(args)
except Exception as exc:
self.last_exception = exc
if (type(exc) == type(self.exception()) and
str(exc) == str(self.exception())):
return FAIL
else:
return UNRESOLVED  # Some other failure

self.last_result = result
return PASS


The test() method runs a single test (with logging, if wanted); the reduce_arg() method will eventually reduce an input to the minimum.

class CallReducer(CallReducer):
def test(self, args: Dict[str, Any]) -> str:
"""Like run(), but also log detail and keep statistics."""
outcome = self.run(args)
if outcome == PASS:
detail = ""
else:
detail = f" ({self.format_exception(self.last_exception)})"

self.tests += 1
if self.log:
print(f"Test #{self.tests} {self.format_call(args)}: {outcome}{detail}")

return outcome

def reduce_arg(self, var_to_be_reduced: str, args: Dict[str, Any]) -> Sequence:
"""
Determine and return a minimal value for var_to_be_reduced.
"""
return args[var_to_be_reduced]


Here's some logging output from the test() function:

with CallReducer(log=True) as reducer:
mystery(failing_input)

reducer.test({'inp': failing_input})
reducer.test({'inp': '123'})
reducer.test({'inp': '123'})

Test #1 mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #2 mystery(inp='123'): PASS
Test #3 mystery(inp='123'): PASS

'PASS'


The CachingCallReducer variant saves test results, such that we don't have to run the same tests again and again:

class CachingCallReducer(CallReducer):
"""Like CallReducer, but cache test outcomes."""

def init(self) -> None:
super().init()
self._cache: Dict[FrozenSet, str] = {}

def test(self, args: Dict[str, Any]) -> str:
# Create a hashable index
try:
index = frozenset((k, v) for k, v in args.items())
except TypeError:
index = frozenset()

if not index:
# Non-hashable value – do not use cache
return super().test(args)

if index in self._cache:
return self._cache[index]

outcome = super().test(args)
self._cache[index] = outcome

return outcome


If we now repeat a test with the same argument, its outcome can be found in the cache:

with CachingCallReducer(log=True) as reducer:
mystery(failing_input)

reducer.test({'inp': failing_input})
reducer.test({'inp': '123'})
reducer.test({'inp': '123'})

Test #1 mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #2 mystery(inp='123'): PASS

'PASS'


#### General Delta Debugging¶

The DeltaDebugger class finally implements Delta Debugging on arguments. Our implementation uses the general dd delta debugging algorithm from [Zeller et al, 2002]. In contrast to ddmin, it returns a pair of a maximized passing input and a minimized failing input. The algorithm can be customized, however, to leave the passing input fixed and only to minimize the failing input (as with ddmin), or vice versa.

Internally, dd does not directly work on a list of elements; instead, it works on sets of indices into such a list. The function to_set() converts a collection into such a set.

def to_set(inp: Sequence) -> Set:
"""Convert inp into a set of indices"""
return set(range(len(inp)))

to_set("abcd")

{0, 1, 2, 3}


The function from_set() converts a set of indices back into the original collection. For this, it uses a function empty() that returns an empty collection that has the same type as the given input inp.

def empty(inp: Any) -> Any:
"""Return an "empty" element of the same type as inp"""
return type(inp)()

empty("abc"), empty([1, 2, 3]), empty({0, -1, -2})

('', [], set())


The function add_to() tries out various ways to add an element to a given collection.

def add_to(collection: Any, elem: Any) -> Any:
"""Add element to collection; return new collection."""
if isinstance(collection, str):
return collection + elem  # Strings

try:  # Lists and other collections
return collection + type(collection)([elem])
except TypeError:
pass

try:  # Sets
return collection | type(collection)([elem])
except TypeError:
pass

raise ValueError("Cannot add element to collection")

add_to("abc", "d"), add_to([1, 2, 3], 4), add_to(set([1, 2, 3]), 4)

('abcd', [1, 2, 3, 4], {1, 2, 3, 4})


Using empty() and add_to(), we can now implement from_set():

def from_set(the_set: Any, inp: Sequence) -> Any:
"""Convert a set of indices into inp back into a collection."""
ret = empty(inp)
for i, c in enumerate(inp):
if i in the_set:

return ret

from_set({1, 2}, "abcd")

'bc'


To split a set of elements into n subsets of equal size, we use this helper function, based on this discussion in StackOverflow.

def split(elems: Any, n: int) -> List:
assert 1 <= n <= len(elems)

k, m = divmod(len(elems), n)
try:
subsets = list(elems[i * k + min(i, m):(i + 1) * k + min(i + 1, m)]
for i in range(n))
except TypeError:
# Convert to list and back
subsets = list(type(elems)(
list(elems)[i * k + min(i, m):(i + 1) * k + min(i + 1, m)])
for i in range(n))

assert len(subsets) == n
assert sum(len(subset) for subset in subsets) == len(elems)
assert all(len(subset) > 0 for subset in subsets)

return subsets

for n in range(1, 8):
print(split([1, 2, 3, 4, 5, 6, 7], n))

[[1, 2, 3, 4, 5, 6, 7]]
[[1, 2, 3, 4], [5, 6, 7]]
[[1, 2, 3], [4, 5], [6, 7]]
[[1, 2], [3, 4], [5, 6], [7]]
[[1, 2], [3, 4], [5], [6], [7]]
[[1, 2], [3], [4], [5], [6], [7]]
[[1], [2], [3], [4], [5], [6], [7]]

split("abcd", 3)

['ab', 'c', 'd']

split({1, 2, 3, 4, 5, 6, 7}, 3)

[{1, 2, 3}, {4, 5}, {6, 7}]


With these, we can now implement general delta debugging. Our implementation follows [Zeller et al, 2002] with the following optimizations:

• We can control whether only to minimize or to maximize ("mode")
• The operations "Reduce to subset" and "Increase to subset" are only taken while the number of subsets is still 2.
class DeltaDebugger(CachingCallReducer):
def dd(self, var_to_be_reduced: str, fail_args: Dict[str, Any],
*, mode: str = '-') -> Tuple[Sequence, Sequence, Sequence]:
"""General Delta Debugging.
var_to_be_reduced - the name of the variable to reduce.
fail_args - a dict of (failure-inducing) function arguments,
with fail_args[var_to_be_reduced] - the input to apply dd on.
mode- how the algorithm should operate:
'-' (default): minimize input (ddmin),
'+': maximizing input (ddmax),
'+-': minimizing pass/fail difference (dd)
Returns a triple (pass, fail, diff) with
* maximized passing input (pass),
* minimized failing input (fail), and
* their difference diff
(elems that are in fail, but not in pass).
"""
def test(c: Set) -> str:
# Set up args
test_args = {}
for var in fail_args:
test_args[var] = fail_args[var]
test_args[var_to_be_reduced] = from_set(c, fail_inp)
return self.test(test_args)

def ret(c_pass: Set, c_fail: Set) -> \
Tuple[Sequence, Sequence, Sequence]:
return (from_set(c_pass, fail_inp),
from_set(c_fail, fail_inp),
from_set(c_fail - c_pass, fail_inp))

n = 2  # Initial granularity

fail_inp = fail_args[var_to_be_reduced]

c_pass = to_set([])
c_fail = to_set(fail_inp)
offset = 0

minimize_fail = '-' in mode
maximize_pass = '+' in mode

while True:
if self.log > 1:
print("Passing input:", repr(from_set(c_pass, fail_inp)))
print("Failing input:", repr(from_set(c_fail, fail_inp)))

delta = c_fail - c_pass
if len(delta) < n:
return ret(c_pass, c_fail)

deltas = split(delta, n)

j = 0
while j < n:
i = (j + offset) % n
next_c_pass = c_pass | deltas[i]
next_c_fail = c_fail - deltas[i]

if minimize_fail and n == 2 and test(next_c_pass) == FAIL:
if self.log > 1:
print("Reduce to subset")
c_fail = next_c_pass
# n = 2
offset = 0
break
elif maximize_pass and n == 2 and test(next_c_fail) == PASS:
if self.log > 1:
print("Increase to subset")
c_pass = next_c_fail
# n = 2
offset = 0
break
elif minimize_fail and test(next_c_fail) == FAIL:
if self.log > 1:
print("Reduce to complement")
c_fail = next_c_fail
n = max(n - 1, 2)
offset = i
break
elif maximize_pass and test(next_c_pass) == PASS:
if self.log > 1:
print("Increase to complement")
c_pass = next_c_pass
n = max(n - 1, 2)
offset = i
break
else:
j += 1  # choose next subset

if j >= n:  # no reduction found
if n >= len(delta):
return ret(c_pass, c_fail)

n = min(n + 2, len(delta))


By default, dd() minimizes inputs – just like ddmin().

with DeltaDebugger() as dd:
mystery(failing_input)


Its output is a triple of maximized passing input (if wanted), minimized failing input, and difference. Here is this triple for mystery(), just as with ddmin():

mystery_pass, mystery_fail, mystery_diff = dd.dd('inp', {'inp': failing_input})


The first element (mystery_pass) is the maximal passing input:

mystery_pass

''


The second element (mystery_fail) is the minimal failing input:

mystery_fail

'()'


And the third element (mystery_diff) is the difference between the two:

mystery_diff

'()'


Note that we will introduce more comfortable APIs later.

We can follow the operation of dd() by increasing the logging level. We see how with every test, the difference between the passing and the failing input gets smaller and smaller.

with DeltaDebugger(log=2) as dd:
mystery(failing_input)

dd.dd('inp', {'inp': failing_input})

Passing input: ''
Failing input: 'V"/+!aF-(V4EOz*+s/Q,7)2@0_'
Test #1 mystery(inp='V"/+!aF-(V4EO'): PASS
Test #2 mystery(inp='z*+s/Q,7)2@0_'): PASS
Passing input: ''
Failing input: 'V"/+!aF-(V4EOz*+s/Q,7)2@0_'
Test #3 mystery(inp='-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '-(V4EOz*+s/Q,7)2@0_'
Test #4 mystery(inp='*+s/Q,7)2@0_'): PASS
Test #5 mystery(inp='-(V4EOz7)2@0_'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '-(V4EOz7)2@0_'
Test #6 mystery(inp='7)2@0_'): PASS
Test #7 mystery(inp='-(V4EOz'): PASS
Passing input: ''
Failing input: '-(V4EOz7)2@0_'
Test #8 mystery(inp='-(V47)2@0_'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '-(V47)2@0_'
Test #9 mystery(inp='-(V4@0_'): PASS
Test #10 mystery(inp='-(V47)2'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '-(V47)2'
Test #11 mystery(inp='-7)2'): PASS
Test #12 mystery(inp='(V4'): PASS
Passing input: ''
Failing input: '-(V47)2'
Test #13 mystery(inp='-47)2'): PASS
Test #14 mystery(inp='-(V7)2'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '-(V7)2'
Test #15 mystery(inp='-(V2'): PASS
Test #16 mystery(inp='(V7)'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '(V7)'
Test #17 mystery(inp='7)'): PASS
Test #18 mystery(inp='(V'): PASS
Passing input: ''
Failing input: '(V7)'
Test #19 mystery(inp='(7)'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '(7)'
Test #20 mystery(inp='()'): FAIL (ValueError: Invalid input)
Reduce to complement
Passing input: ''
Failing input: '()'
Test #21 mystery(inp=')'): PASS
Test #22 mystery(inp='('): PASS

('', '()', '()')


#### Processing Multiple Arguments¶

What happens if a function has multiple arguments? First, we check if they are reducible – that is, they provide a len() length function and a way to access indexed elements. This holds for all strings and all lists, as well as other ordered collections.

def is_reducible(value: Any) -> bool:
# Return True if value supports len() and indexing.
try:
_ = len(value)
except TypeError:
return False

try:
_ = value[0]
except TypeError:
return False
except IndexError:
return False

return True


Our method process_args() processes recorded call arguments, one after the one, until all are minimized or maximized. Processing them individually (rather than, say, all at once) allows to maintain a stable context during reduction.

This method also does all the housekeeping, checking arguments and results, and raising errors if need be.

class FailureNotReproducedError(ValueError):
pass

class NotFailingError(ValueError):
pass

class DeltaDebugger(DeltaDebugger):
def check_reproducibility(self) -> None:
# Check whether running the function again fails
assert self.function(), \
"No call collected. Use with dd: func() first."
assert self.args(), \
"No arguments collected. Use with dd: func(args) first."

self.reset()
outcome = self.test(self.args())
if outcome == UNRESOLVED:
raise FailureNotReproducedError(
"When called again, " +
self.format_call(self.args()) +
" raised " +
self.format_exception(self.last_exception) +
self.format_exception(self.exception()))

if outcome == PASS:
raise NotFailingError("When called again, " +
self.format_call(self.args()) +
" did not fail")
assert outcome == FAIL

class DeltaDebugger(DeltaDebugger):
def process_args(self, strategy: Callable, **strategy_args: Any) -> \
Tuple[Dict[str, Any], Dict[str, Any], Dict[str, Any]]:
"""
Reduce all reducible arguments, using strategy(var, strategy_args).
"""

pass_args = {}  # Local copy
fail_args = {}  # Local copy
diff_args = {}
for var in self.args():
fail_args[var] = self.args()[var]
diff_args[var] = self.args()[var]
pass_args[var] = self.args()[var]

if is_reducible(pass_args[var]):
pass_args[var] = empty(pass_args[var])

vars_to_be_processed = set(fail_args.keys())

pass_processed = 0
fail_processed = 0

self.check_reproducibility()

# We take turns in processing variables until all are processed
while len(vars_to_be_processed) > 0:
for var in vars_to_be_processed:
if not is_reducible(fail_args[var]):
vars_to_be_processed.remove(var)
break

if self.log:
print(f"Processing {var}...")

maximized_pass_value, minimized_fail_value, diff = \
strategy(var, fail_args, **strategy_args)

if (maximized_pass_value is not None and
len(maximized_pass_value) > len(pass_args[var])):
pass_args[var] = maximized_pass_value
# FIXME: diff_args may not be correct for multiple args
diff_args[var] = diff
if self.log:
print(f"Maximized {var} to",
repr(maximized_pass_value))
vars_to_be_processed = set(fail_args.keys())
pass_processed += 1

if (minimized_fail_value is not None and
len(minimized_fail_value) < len(fail_args[var])):
fail_args[var] = minimized_fail_value
diff_args[var] = diff
if self.log:
print(f"Minimized {var} to",
repr(minimized_fail_value))
vars_to_be_processed = set(fail_args.keys())
fail_processed += 1

vars_to_be_processed.remove(var)
break

assert pass_processed == 0 or self.test(pass_args) == PASS, \
f"{self.format_call(pass_args)} does not pass"
assert fail_processed == 0 or self.test(fail_args) == FAIL, \
f"{self.format_call(fail_args)} does not fail"

if self.log and pass_processed > 0:
print("Maximized passing call to",
self.format_call(pass_args))
if self.log and fail_processed > 0:
print("Minimized failing call to",
self.format_call(fail_args))

return pass_args, fail_args, diff_args


For more housekeeping, we define the after_collection() method that will be invoked at the end of the with block. It checks for a number of additional preconditions.

class DeltaDebugger(DeltaDebugger):
def after_collection(self) -> None:
# Some post-collection checks
if self._function is None:
raise NoCallError("No function call observed")
if self.exception() is None:
raise NotFailingError(
f"{self.format_call()} did not raise an exception")

if self.log:
print(f"Observed {self.format_call()}" +
f" raising {self.format_exception(self.exception())}")


#### Public API¶

We finish the implementation with public methods that allow users to run delta debugging and obtain the diagnostics.

class DeltaDebugger(DeltaDebugger):
def min_args(self) -> Dict[str, Any]:
"""Return 1-minimal arguments."""
pass_args, fail_args, diff = self.process_args(self.dd, mode='-')
return fail_args

class DeltaDebugger(DeltaDebugger):
def max_args(self) -> Dict[str, Any]:
"""Return 1-maximal arguments."""
pass_args, fail_args, diff = self.process_args(self.dd, mode='+')
return pass_args

class DeltaDebugger(DeltaDebugger):
def min_arg_diff(self) -> Tuple[Dict[str, Any], Dict[str, Any], Dict[str, Any]]:
"""Return 1-minimal difference between arguments."""
return self.process_args(self.dd, mode='+-')


The __repr__() method returns a string representation of the minimized call.

class DeltaDebugger(DeltaDebugger):
def __repr__(self) -> str:
"""Return a string representation of the minimized call."""
return self.format_call(self.min_args())


To see how the DeltaDebugger works, let us run it on our failing input. The expected usage is as introduced earlier – we wrap the failing function in a with block, and then print out the debugger to see the reduced arguments. We see that DeltaDebugger easily reduces the arguments to the minimal failure-inducing input:

with DeltaDebugger() as dd:
mystery(failing_input)
dd

mystery(inp='()')


We can turn on logging for DeltaDebugger to see how it proceeds. With each step, we see how the remaining input gets smaller and smaller, until only two characters remain:

with DeltaDebugger(log=True) as dd:
mystery(failing_input)
dd

Observed mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_') raising ValueError: Invalid input
Test #1 mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Processing inp...
Test #2 mystery(inp='V"/+!aF-(V4EO'): PASS
Test #3 mystery(inp='z*+s/Q,7)2@0_'): PASS
Test #4 mystery(inp='-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #5 mystery(inp='*+s/Q,7)2@0_'): PASS
Test #6 mystery(inp='-(V4EOz7)2@0_'): FAIL (ValueError: Invalid input)
Test #7 mystery(inp='7)2@0_'): PASS
Test #8 mystery(inp='-(V4EOz'): PASS
Test #9 mystery(inp='-(V47)2@0_'): FAIL (ValueError: Invalid input)
Test #10 mystery(inp='-(V4@0_'): PASS
Test #11 mystery(inp='-(V47)2'): FAIL (ValueError: Invalid input)
Test #12 mystery(inp='-7)2'): PASS
Test #13 mystery(inp='(V4'): PASS
Test #14 mystery(inp='-47)2'): PASS
Test #15 mystery(inp='-(V7)2'): FAIL (ValueError: Invalid input)
Test #16 mystery(inp='-(V2'): PASS
Test #17 mystery(inp='(V7)'): FAIL (ValueError: Invalid input)
Test #18 mystery(inp='7)'): PASS
Test #19 mystery(inp='(V'): PASS
Test #20 mystery(inp='(7)'): FAIL (ValueError: Invalid input)
Test #21 mystery(inp='()'): FAIL (ValueError: Invalid input)
Test #22 mystery(inp=')'): PASS
Test #23 mystery(inp='('): PASS
Minimized inp to '()'
Minimized failing call to mystery(inp='()')

mystery(inp='()')


It is also possible to access the debugger programmatically:

with DeltaDebugger() as dd:
mystery(failing_input)

dd.args()

{'inp': 'V"/+!aF-(V4EOz*+s/Q,7)2@0_'}

dd.min_args()

{'inp': '()'}


### Quiz

What happens if the function under test does not raise an exception?

Indeed, DeltaDebugger checks if an exception occurs. If not, you obtain a NotFailingError.

with ExpectError(NotFailingError):
mystery("An input that does not fail")

Traceback (most recent call last):
File "<ipython-input-1-5ea55a994fe1>", line 3, in <module>
mystery("An input that does not fail")
File "<ipython-input-1-85c3974b9c66>", line 24, in __exit__
self.after_collection()
File "<ipython-input-1-91e94e1bf173>", line 8, in after_collection
f"{self.format_call()} did not raise an exception")
NotFailingError: mystery(inp='An input that does not fail') did not raise an exception (expected)


Delta Debugging also assumes that the function under test is deterministic. If it occasionally fails and occasionally passes, you will get random results.

## Usage Examples¶

Let us apply DeltaDebugger on a number of examples.

### Reducing remove_html_markup()¶

For our ongoing remove_html_markup() example, we can reduce the failure-inducing input to a minimum, too:

from Assertions import remove_html_markup  # minor dependency

with DeltaDebugger(log=True) as dd:
remove_html_markup('"x > y"')
dd.min_args()

Observed remove_html_markup(s='"x > y"') raising AssertionError
Test #1 remove_html_markup(s='"x > y"'): FAIL (AssertionError)
Processing s...
Test #2 remove_html_markup(s='"x >'): FAIL (AssertionError)
Test #3 remove_html_markup(s='"x'): PASS
Test #4 remove_html_markup(s=' >'): PASS
Test #5 remove_html_markup(s='x >'): PASS
Test #6 remove_html_markup(s='" >'): FAIL (AssertionError)
Test #7 remove_html_markup(s='">'): FAIL (AssertionError)
Test #8 remove_html_markup(s='>'): PASS
Test #9 remove_html_markup(s='"'): PASS
Minimized s to '">'
Minimized failing call to remove_html_markup(s='">')

{'s': '">'}


### Reducing Multiple Arguments¶

If a function has multiple reducible variables, they get reduced in turns. This string_error() function fails whenever s1 is a substring of s2:

def string_error(s1: str, s2: str) -> None:
assert s1 not in s2, "no substrings"


Running DeltaDebugger on string_error shows how first s1 is reduced, then s2, then s1 again.

with DeltaDebugger(log=True) as dd:
string_error("foo", "foobar")

string_error_args = dd.min_args()
string_error_args

Observed string_error(s2='foobar', s1='foo') raising AssertionError: no substrings
Test #1 string_error(s2='foobar', s1='foo'): FAIL (AssertionError: no substrings)
Processing s2...
Test #2 string_error(s2='foo', s1='foo'): FAIL (AssertionError: no substrings)
Test #3 string_error(s2='fo', s1='foo'): PASS
Test #4 string_error(s2='o', s1='foo'): PASS
Test #5 string_error(s2='oo', s1='foo'): PASS
Minimized s2 to 'foo'
Processing s1...
Test #6 string_error(s2='foo', s1='fo'): FAIL (AssertionError: no substrings)
Test #7 string_error(s2='foo', s1='f'): FAIL (AssertionError: no substrings)
Minimized s1 to 'f'
Processing s2...
Test #8 string_error(s2='fo', s1='f'): FAIL (AssertionError: no substrings)
Test #9 string_error(s2='f', s1='f'): FAIL (AssertionError: no substrings)
Minimized s2 to 'f'
Processing s1...
Minimized failing call to string_error(s2='f', s1='f')

{'s2': 'f', 's1': 'f'}


We see that the failure also occurs if both variables contain only one (same) character:

with ExpectError(AssertionError):
string_error(string_error_args['s1'], string_error_args['s2'])

Traceback (most recent call last):
File "<ipython-input-1-94fdeac63d8a>", line 2, in <module>
string_error(string_error_args['s1'], string_error_args['s2'])
File "<ipython-input-1-1cdeb8727e33>", line 2, in string_error
assert s1 not in s2, "no substrings"
AssertionError: no substrings (expected)


### Invoking an Interactive Debugger¶

The results from delta debugging can be immediately used to invoke an nvoke an interactive debugger on the minimized input. To this end, we need to turn the dictionary returned by min_args() into a arguments of the (failing) function call.

Python provides a simple way to turn dictionaries into function calls. The construct

fun(**args)


invokes the function fun, with all parameters assigned from the respective values in the dictionary.

With this, we can immediately invoke a Debugger on the failing run with minimized arguments:

from Debugger import Debugger  # minor dependency

['print', 'quit']

with ExpectError(AssertionError):
with Debugger():
string_error(**string_error_args)

Calling string_error(s2 = 'f', s1 = 'f')

(debugger) print
s2 = 'f'
s1 = 'f'

(debugger) quit
Traceback (most recent call last):
File "<ipython-input-1-f8a0c9a135a8>", line 3, in <module>
string_error(**string_error_args)
File "<ipython-input-1-1cdeb8727e33>", line 2, in string_error
assert s1 not in s2, "no substrings"
AssertionError: no substrings (expected)


### Reducing other Collections¶

Our DeltaDebugger is not limited to strings. It can reduce any argument x for which a len(x) operation and an indexing operation x[i] is defined – notably lists. Here is how to apply DeltaDebugger on a list:

def list_error(l1: List, l2: List, maxlen: int) -> None:
assert len(l1) < len(l2) < maxlen, "invalid string length"

with DeltaDebugger() as dd:
list_error(l1=[1, 2, 3, 4, 5, 6, 7, 8, 9, 10], l2=[1, 2, 3], maxlen=5)
dd

list_error(maxlen=5, l2=[1], l1=[1])


## Debugging Inputs¶

Sometimes, it may be useful to not minimize the input, but rather maximize it – that is, to find the maximum input that does not fail. For instance, you may have an input of which you want to preserve as much as possible – to repair it, or to establish a context that is as close as possible to the real input.

This is possible by using the max_arg() method. It implements the ddmax variant of the general Delta Debugging algorithm [Kirschner et al, 2020]. With each step, it tries to add more and more characters to the passing input until it is 1-maximal – that is, any additional character that would be added from the failing input also would cause the function to fail.

with DeltaDebugger(log=True) as dd:
mystery(failing_input)
max_passing_input = dd.max_args()['inp']
max_passing_input

Observed mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_') raising ValueError: Invalid input
Test #1 mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Processing inp...
Test #2 mystery(inp='z*+s/Q,7)2@0_'): PASS
Test #3 mystery(inp='-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #4 mystery(inp='V"/+!aFz*+s/Q,7)2@0_'): PASS
Test #5 mystery(inp='V"/+!aF4EOz*+s/Q,7)2@0_'): PASS
Test #6 mystery(inp='V"/+!aF-4EOz*+s/Q,7)2@0_'): PASS
Test #7 mystery(inp='V"/+!aF-V4EOz*+s/Q,7)2@0_'): PASS
Maximized inp to 'V"/+!aF-V4EOz*+s/Q,7)2@0_'
Maximized passing call to mystery(inp='V"/+!aF-V4EOz*+s/Q,7)2@0_')

'V"/+!aF-V4EOz*+s/Q,7)2@0_'


Note that this is precisely the failure-inducing input except for one of the parentheses. Adding this single character would cause the input to cause a failure.

## Failure-Inducing Differences¶

If one wants to look for differences that distinguish passing from failing runs, Delta Debugging also has a direct method for this – by both maximizing the passing input and minimizing the failing input until they meet somewhere in the middle. The remaining difference is what makes the difference between passing and failing.

To compute the failure-inducing differences for mystery(), use the min_arg_diff() method:

with DeltaDebugger(log=True) as dd:
mystery(failing_input)
max_passing_args, min_failing_args, diff = dd.min_arg_diff()
max_passing_args['inp'], min_failing_args['inp'], diff['inp']

Observed mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_') raising ValueError: Invalid input
Test #1 mystery(inp='V"/+!aF-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Processing inp...
Test #2 mystery(inp='V"/+!aF-(V4EO'): PASS
Test #3 mystery(inp='z*+s/Q,7)2@0_'): PASS
Test #4 mystery(inp='V"/+!aFz*+s/Q,7)2@0_'): PASS
Test #5 mystery(inp='-(V4EOz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #6 mystery(inp='-(Vz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #7 mystery(inp='(Vz*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Test #8 mystery(inp='(z*+s/Q,7)2@0_'): FAIL (ValueError: Invalid input)
Maximized inp to 'z*+s/Q,7)2@0_'
Minimized inp to '(z*+s/Q,7)2@0_'
Maximized passing call to mystery(inp='z*+s/Q,7)2@0_')
Minimized failing call to mystery(inp='(z*+s/Q,7)2@0_')

('z*+s/Q,7)2@0_', '(z*+s/Q,7)2@0_', '(')


Minimizing failure-inducing differences is especially efficient on large inputs, since the number of differences between a passing and a failing input is much smaller than the inputs themselves. Here is the failure-inducing difference as determined by Delta Debugging:

diff['inp']

'('


## Reducing Program Code¶

One particularly fun application of reducers is on program code. Technically speaking, program code is just another input to a computation; and we can actually automatically determine which minimum of program code is required to produce a failure, using Delta Debugging. Such minimization of code is typically used as it comes to debugging programs that accept code as their input, such as compilers and interpreters. However, it can also pinpoint failure causes in the (input) code itself.

As an example, let us apply Delta Debugging on the code from the chapter on assertions. You do not need to have read the chapter; the important part is that this chapter provides an implementation of remove_html_markup() that we want to use.

import Assertions  # minor dependency


Here is the source code of all the chapter; this is several hundred lines long.

import inspect

assertions_source_lines, _ = inspect.getsourcelines(Assertions)
# print_content("".join(assertions_source_lines), ".py")
assertions_source_lines[:10]

['from bookutils import YouTubeVideo\n',
'\n',
'import bookutils\n',
'\n',
'from bookutils import quiz\n',
'\n',
'import Tracer\n',
'\n',
'from ExpectError import ExpectError\n']

len(assertions_source_lines)

552


We can take this code and execute it. Nothing particular should happen here, as our imports only import definitions of functions, classes, and global variables.

def compile_and_run(lines: List[str]) -> None:
# To execute 'Assertions' in place, we need to define __name__ and __package__
exec("".join(lines), {'__name__': '<string>',
'__package__': 'debuggingbook',
'Any': Any,
'Type': Type,
'TracebackType': TracebackType,
'Optional': Optional},
{})

compile_and_run(assertions_source_lines)

from Assertions import remove_html_markup  # minor dependency


Let us add some code to it – a "My Test" assertion that tests that remove_html_markup(), applied on a string with double quotes, should keep these in place:

def compile_and_test_html_markup_simple(lines: List[str]) -> None:
compile_and_run(lines +
[
'''''',
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
])


This assertion fails. (As always, remove_html_markup() is buggy.)

with ExpectError(AssertionError):
compile_and_test_html_markup_simple(assertions_source_lines)

Traceback (most recent call last):
File "<ipython-input-1-b38cab3f28f5>", line 2, in <module>
compile_and_test_html_markup_simple(assertions_source_lines)
File "<ipython-input-1-c90d70aa6999>", line 5, in compile_and_test_html_markup_simple
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
File "<ipython-input-1-bce9f67e0746>", line 9, in compile_and_run
{})
File "<string>", line 553, in <module>
AssertionError: My Test (expected)


The question we want to address in this section is: Given this assertion, can we automatically determine which part of the Assertions code lines in assertions_source_lines is relevant for producing the failure?

### Reducing Code Lines¶

Since our Assertions source code comes as a list of lines, we can apply our DeltaDebugger on it. The result will be the list of source lines that is necessary to make the assertion fail.

### Quiz

What will the reduced set of lines contain?

Let us see what the DeltaDebugger produces.

with DeltaDebugger(log=False) as dd:
compile_and_test_html_markup_simple(assertions_source_lines)


We get exactly two lines of code:

reduced_lines = dd.min_args()['lines']
len(reduced_lines)

2


And these are:

from bookutils import print_content

print_content("".join(reduced_lines), ".py")

def remove_html_markup(s):  # type: ignore
tag = False


On these lines, our test actually still fails:

with ExpectError(AssertionError):
compile_and_test_html_markup_simple(reduced_lines)

Traceback (most recent call last):
File "<ipython-input-1-a658f339430e>", line 2, in <module>
compile_and_test_html_markup_simple(reduced_lines)
File "<ipython-input-1-c90d70aa6999>", line 5, in compile_and_test_html_markup_simple
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
File "<ipython-input-1-bce9f67e0746>", line 9, in compile_and_run
{})
File "<string>", line 3, in <module>
AssertionError: My Test (expected)


This failure may come as a surprise – remove_html_markup() is reduced to a function which does not even return a value. However, this is how it causes our "My Test" assertion to fail: In Python, a function without an explicit return statement returns None. This value is definitely not the string the "My Test" assertion expects, so it fails.

At the same time, we also have a function test_square_root() which is equally devoid of any meaning – its code line does not even stem from its original implementation. Note, however, how the set of four lines is actually 1-minimal – removing any further line would result in a syntax error.

To ensure we do not remove code that actually would be necessary for normal behavior, let us add another check – one that checks for the normal functionality of remove_html_markup(). If this one fails (say, after the code has been tampered with too much), it raises an exception – but a different one from the original failure:

def compile_and_test_html_markup(lines: List[str]) -> None:
compile_and_run(lines +
[
'',
'''if remove_html_markup('<foo>bar</foo>') != 'bar':\n''',
'''    raise RuntimeError("Missing functionality")\n''',
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
])


On our "reduced" code, we now obtain a different exception.

with ExpectError():
compile_and_test_html_markup(reduced_lines)

Traceback (most recent call last):
File "<ipython-input-1-917a65ea7884>", line 2, in <module>
compile_and_test_html_markup(reduced_lines)
File "<ipython-input-1-7bc7dc1451d4>", line 7, in compile_and_test_html_markup
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
File "<ipython-input-1-bce9f67e0746>", line 9, in compile_and_run
{})
File "<string>", line 4, in <module>
RuntimeError: Missing functionality (expected)


Such an outcome that is different from the original failure causes our DeltaDebugger not treating this as a failure, but rather as a UNRESOLVED outcome, indicating that the test cannot determine whether it passed or failed. The ddmin algorithm treats such unresolved outcomes as if they were passing; hence, the algorithm treats its minimization attempt as unsuccessful.

How does this change things? When we reduce the Assertions source code with the extended assertions, we now get a different result:

with DeltaDebugger(log=False) as dd:
compile_and_test_html_markup(assertions_source_lines)
reduced_assertions_source_lines = dd.min_args()['lines']


Our result actually is the source code of remove_html_markup() – and only the source code. This is a success, as Delta Debugging has eliminated all the other parts of the Assertions source code; these neither contribute to the correct functioning of remove_html_markup(), nor to the failure at hand.

print_content(''.join(reduced_assertions_source_lines), '.py')

def remove_html_markup(s):  # type: ignore
tag = False
quote = False
out = ""
for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif c == '"' or c == "'" and tag:
quote = not quote
elif not tag:
out = out + c
return out


All in all, we have reduced the number of relevant lines in Assertions to about 3% of the original source code.

len(reduced_assertions_source_lines) / len(assertions_source_lines)

0.025362318840579712


The astute reader may notice that remove_html_markup(), as shown above, is slightly different from the original version in the chapter on assertions. Here's the original version for comparison:

remove_html_markup_source_lines, _ = inspect.getsourcelines(Assertions.remove_html_markup)
print_content(''.join(remove_html_markup_source_lines), '.py')

def remove_html_markup(s):  # type: ignore
tag = False
quote = False
out = ""

for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif c == '"' or c == "'" and tag:
quote = not quote
elif not tag:
out = out + c

# postcondition
assert '<' not in out and '>' not in out

return out


### Quiz

In the reduced version, what has changed?

Indeed, Delta Debugging has determined all these as being irrelevant for reproducing the failure – and consequently, has deleted them.

### Reducing Code Characters¶

We can reduce the code further by removing individual characters rather than lines. To this end, we convert our (already reduced) remove_html_markup() code into a list of characters.

reduced_assertions_source_characters = list("".join(reduced_assertions_source_lines))
print(reduced_assertions_source_characters[:30])

['d', 'e', 'f', ' ', 'r', 'e', 'm', 'o', 'v', 'e', '_', 'h', 't', 'm', 'l', '_', 'm', 'a', 'r', 'k', 'u', 'p', '(', 's', ')', ':', ' ', ' ', '#', ' ']


Our compile_and_test_html_markup() works (and fails) as before: It still joins the given strings into one and executes them. (Remember that in Python, "characters" are simply strings of length one.)

with ExpectError(AssertionError):
compile_and_test_html_markup(reduced_assertions_source_characters)

Traceback (most recent call last):
File "<ipython-input-1-9f9e3b457bcf>", line 2, in <module>
compile_and_test_html_markup(reduced_assertions_source_characters)
File "<ipython-input-1-7bc7dc1451d4>", line 7, in compile_and_test_html_markup
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"\n'''
File "<ipython-input-1-bce9f67e0746>", line 9, in compile_and_run
{})
File "<string>", line 17, in <module>
AssertionError: My Test (expected)


Let's see what Delta Debugging makes of that – and also, how long it takes. The Timer class gives us a simple means to measure time.

from Timer import Timer

with DeltaDebugger(log=False) as dd:
compile_and_test_html_markup(reduced_assertions_source_characters)


Here's the reduced result:

with Timer() as t:
further_reduced_assertions_source_characters = dd.min_args()['lines']
print_content("".join(further_reduced_assertions_source_characters), ".py")

def remove_html_markup(s):
tag=False
quote=out=""
for c in s:
if c=='<'and not quote:tag=True
elif c=='>'and not quote:tag=False
elif c=='"'or c==tag:quote
elif not tag:out=out+c
return out


• All superfluous blanks and even newlines have been removed.
• As a curiosity, the initialization of quote and out to "" is now merged into a single (semantics-preserving) statement.
• The semantics and effect of < and > characters is preserved, as mandated by our RuntimeError check.
• Double quotes still have the effect of not being included in the returned value: the remaining quote has no effect.

Semantics-wise, this reduced variant still yields the "original" failure; the biggest semantic differences, though, are in the condition and code associated with double quotes – which actually also is the location of the defect to be fixed. This is how reducing code can also point to not only necessary locations, but also defective locations.

Mind you that reducing code is not cheap, and especially not if you remove by characters. It has taken DeltaDebugger several thousand tests to obtain the result above:

dd.tests

20611


And to do so, it even required several seconds. This may be little for a human, but from a CPU standpoint, this is an enormous effort.

t.elapsed_time()

6.844581562996609


### Reducing Syntax Trees¶

When reducing code (or generally speaking, recursive structures), using a syntactic approach can be a much better alternative to the line-by-line or character-by-character approaches discussed above. The idea is that one represents the input as a tree (rather than a sequence of strings), in which a reducer would work on entire subtrees, deleting or reducing parts of the tree.

We illustrate this concept on syntax trees representing Python code. Python provides us with simple means to interactively convert code into syntax trees (and back again). So, in order to reduce code, we can

1. parse the program code into a syntax tree (called abstract syntax tree or AST);
2. reduce the syntax tree to a minimum, executing it to test reductions; and
3. unparse the tree to obtain textual code again.

Since transformations on the AST are much less likely to produce syntax errors, reducing ASTs is much more efficient than reducing program code as text.

In the chapter on slicing, we already have seen several examples on how to work with ASTs. In our context, an AST also offers additional possibilities for reducing. Notably, instead of just deleting code fragments, we can also replace them with simpler fragments. For instance, we can replace arithmetic expressions with constants, or conditional statements if cond: body with the associated body body.

Let us illustrate how this works, again choosing remove_html_markup() as our ongoing example. One more time, we create a function with associated test.

fun_source = inspect.getsource(remove_html_markup)

print_content(fun_source, '.py')

def remove_html_markup(s):  # type: ignore
tag = False
quote = False
out = ""

for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif c == '"' or c == "'" and tag:
quote = not quote
elif not tag:
out = out + c

# postcondition
assert '<' not in out and '>' not in out

return out


#### From Code to Syntax Trees¶

Let us parse this piece of code into an AST. This is done by the ast.parse() function.

import ast
import astor

fun_tree: ast.Module = ast.parse(fun_source)


The parsed tree contains the function definition:

from bookutils import show_ast

show_ast(fun_tree)


Let us add some tests to this, using the same scheme:

test_source = (
'''if remove_html_markup('<foo>bar</foo>') != 'bar':\n''' +
'''    raise RuntimeError("Missing functionality")\n''' +
'''assert remove_html_markup('"foo"') == '"foo"', "My Test"'''
)

test_tree: ast.Module = ast.parse(test_source)

print_content(astor.to_source(test_tree), '.py')

if remove_html_markup('<foo>bar</foo>') != 'bar':
raise RuntimeError('Missing functionality')
assert remove_html_markup('"foo"') == '"foo"', 'My Test'


We can merge the function definition tree and the test tree into a single one:

import copy

fun_test_tree = copy.deepcopy(fun_tree)
fun_test_tree.body += test_tree.body


Such a tree can be compiled into a code object, using Python's compile() function:

fun_test_code = compile(fun_test_tree, '<string>', 'exec')


and the resulting code object can be executed directly, using the Python exec() function. We see that our test fails as expected.

with ExpectError(AssertionError):
exec(fun_test_code, {}, {})

Traceback (most recent call last):
File "<ipython-input-1-59dfdc161ac5>", line 2, in <module>
exec(fun_test_code, {}, {})
File "<string>", line 3, in <module>
AssertionError: My Test (expected)


#### Traversing Syntax Trees¶

Our goal is now to reduce this tree (or at least the subtree with the function definition) to a minimum. To this end, we manipulate the AST through the Python modules ast and astor. The official Python ast reference is complete, but a bit brief; the documentation "Green Tree Snakes - the missing Python AST docs" provides an excellent introduction.

The two means for exploring and changing ASTs are the classes NodeVisitor and NodeTransformer, respectively. We start with creating a list of all nodes in the tree, using a NodeVisitor subclass.

Its visit() method is called for every node in the tree, which we achieve by having it return self.generic_visit() for the current node. It saves all visited nodes in the _all_nodes attribute.

from ast import NodeTransformer, NodeVisitor, fix_missing_locations, AST

class NodeCollector(NodeVisitor):
"""Collect all nodes in an AST."""
def __init__(self) -> None:
super().__init__()
self._all_nodes: List[AST] = []

def generic_visit(self, node: AST) -> None:
self._all_nodes.append(node)
return super().generic_visit(node)

def collect(self, tree: AST) -> List[AST]:
"""Return a list of all nodes in tree."""
self._all_nodes = []
self.visit(tree)
return self._all_nodes


This is how our NodeCollector() class produces a list of all nodes:

fun_nodes = NodeCollector().collect(fun_tree)
len(fun_nodes)

107

fun_nodes[:30]

[<_ast.Module at 0x7f9899c366d8>,
<_ast.FunctionDef at 0x7f9899c36630>,
<_ast.arguments at 0x7f9899c367b8>,
<_ast.arg at 0x7f9899c36748>,
<_ast.Assign at 0x7f9899c36fd0>,
<_ast.Name at 0x7f9899c365c0>,
<_ast.Store at 0x7f989794e5c0>,
<_ast.NameConstant at 0x7f9899c36390>,
<_ast.Assign at 0x7f9899c36f60>,
<_ast.Name at 0x7f9899c36f98>,
<_ast.Store at 0x7f989794e5c0>,
<_ast.NameConstant at 0x7f9899c36320>,
<_ast.Assign at 0x7f9899c362b0>,
<_ast.Name at 0x7f9899c362e8>,
<_ast.Store at 0x7f989794e5c0>,
<_ast.Str at 0x7f9899c36358>,
<_ast.For at 0x7f9899c363c8>,
<_ast.Name at 0x7f9899c36470>,
<_ast.Store at 0x7f989794e5c0>,
<_ast.Name at 0x7f9899c36400>,
<_ast.If at 0x7f9899c36438>,
<_ast.BoolOp at 0x7f9899c364a8>,
<_ast.And at 0x7f98979520f0>,
<_ast.Compare at 0x7f9899c364e0>,
<_ast.Name at 0x7f9899c36518>,
<_ast.Eq at 0x7f9897956828>,
<_ast.Str at 0x7f9899c367f0>,
<_ast.UnaryOp at 0x7f9899c36588>]


Such a list of nodes is what we can feed into Delta Debugging in order to reduce it. The idea is that with every test, we take the tree and for each node in the tree, we check whether it is still in the list – if not, we remove it. Thus, by reducing the list of nodes, we simultaneously reduce the tree as well.

#### Deleting Nodes¶

In our next step, we write some code that, given such a list of nodes, prunes the tree such that only elements in the list are still contained. To this end, we proceed in four steps:

1. We traverse the original AST, marking all nodes as "to be deleted".
2. We traverse the given list of nodes, clearing their markers.
3. We copy the original tree (including the markers) into a new tree – the one to be reduced.
4. We traverse the new tree, now deleting all marked nodes.

Why do we go through such an extra effort? The reason is that our list of nodes contains references into the original tree – a tree that needs to stay unchanged such that we can reuse it for later. The new tree (the copy) has the same nodes, but at different addresses, so our original references cannot be used anymore. Markers, however, just like any other attributes, are safely copied from the original into the new tree.

The NodeMarker() visitor marks all nodes in a tree:

class NodeMarker(NodeVisitor):
def visit(self, node: AST) -> AST:
node.marked = True
return super().generic_visit(node)


The NodeReducer() transformer reduces all marked nodes. If a method visit_<node class>() is defined, it will be invoked; otherwise, visit_Node() is invoked, which deletes the node (and its subtree) by returning None.

class NodeReducer(NodeTransformer):
def visit(self, node: AST) -> Any:
method = 'visit_' + node.__class__.__name__
visitor = getattr(self, method, self.visit_Node)
return visitor(node)

def visit_Module(self, node: AST) -> Any:
# Can't remove modules
return super().generic_visit(node)

def visit_Node(self, node: AST) -> Any:
"""Default visitor for all nodes"""
if node.marked:
return None  # delete it
return super().generic_visit(node)


Our function copy_and_reduce() puts these pieces together:

def copy_and_reduce(tree: AST, keep_list: List[AST]) -> AST:
"""Copy tree, reducing all nodes that are not in keep_list."""

# Mark all nodes except those in keep_list
NodeMarker().visit(tree)
for node in keep_list:
# print("Clearing", node)
node.marked = False

# Copy tree and delete marked nodes
new_tree = copy.deepcopy(tree)
NodeReducer().visit(new_tree)
return new_tree


Let us apply this in practice. We take the first assignment in our tree...

fun_nodes[4]

<_ast.Assign at 0x7f9899c36fd0>


... whose subtree happens to be the assignment to tag:

astor.to_source(fun_nodes[4])

'tag = False\n'


We keep all nodes except for this one.

keep_list = fun_nodes.copy()
del keep_list[4]


Let us now create a copy of the tree in which the assignment is missing:

new_fun_tree = cast(ast.Module, copy_and_reduce(fun_tree, keep_list))
show_ast(new_fun_tree)


The new tree no longer contains the initial assignment to tag:

print_content(astor.to_source(new_fun_tree), '.py')

def remove_html_markup(s):
quote = False
out = ''
for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif c == '"' or c == "'" and tag:
quote = not quote
elif not tag:
out = out + c
assert '<' not in out and '>' not in out
return out


If we add our tests and then execute this code, we get an error, as tag is now no longer initialized:

new_fun_tree.body += test_tree.body

fun_code = compile(new_fun_tree, "<string>", 'exec')

with ExpectError(UnboundLocalError):
exec(fun_code, {}, {})

Traceback (most recent call last):
File "<ipython-input-1-7b27e77c9f53>", line 2, in <module>
exec(fun_code, {}, {})
File "<string>", line 3, in <module>
File "<string>", line 13, in remove_html_markup
UnboundLocalError: local variable 'tag' referenced before assignment (expected)


If we have no node in the keep list, the whole tree gets deleted:

empty_tree = copy_and_reduce(fun_tree, [])

astor.to_source(empty_tree)

''


#### Reducing Trees¶

We can put all these steps together in a single function. compile_and_test_ast() takes a tree and a list of nodes, reduces the tree to those nodes in the list, and then compiles and runs the reduced AST.

def compile_and_test_ast(tree: ast.Module, keep_list: List[AST],
test_tree: Optional[ast.Module] = None) -> None:
new_tree = cast(ast.Module, copy_and_reduce(tree, keep_list))
# print(astor.to_source(new_tree))

if test_tree is not None:
new_tree.body += test_tree.body

try:
code_object = compile(new_tree, '<string>', 'exec')
except Exception:
raise SyntaxError("Cannot compile")

exec(code_object, {}, {})

with ExpectError(AssertionError):
compile_and_test_ast(fun_tree, fun_nodes, test_tree)

Traceback (most recent call last):
File "<ipython-input-1-5bb5087772bf>", line 2, in <module>
compile_and_test_ast(fun_tree, fun_nodes, test_tree)
File "<ipython-input-1-d2ef90f17ad3>", line 14, in compile_and_test_ast
exec(code_object, {}, {})
File "<string>", line 3, in <module>
AssertionError: My Test (expected)


When we run our delta debugger on the AST, this is the list of remaining nodes we obtain:

with DeltaDebugger() as dd:
compile_and_test_ast(fun_tree, fun_nodes, test_tree)

reduced_nodes = dd.min_args()['keep_list']
len(reduced_nodes)

66


This is the associated tree:

reduced_fun_tree = copy_and_reduce(fun_tree, reduced_nodes)
show_ast(reduced_fun_tree)


And this is its textual representation:

print_content(astor.to_source(reduced_fun_tree), '.py')

def remove_html_markup(s):
tag = False
quote = False
out = ''
for c in s:
if c == '<' and not quote:
tag = True
elif c == '>' and not quote:
tag = False
elif c == '"' or c == "'" and tag:
quote = not quote
elif not tag:
out = out + c
return out

dd.tests

2611


We see that some code was deleted – notably the assertion at the end – but otherwise, our deletion strategy was not particularly effective. This is because in Python, one cannot simply delete the single statement in a controlled body – this raises a syntax error. One would have to replace it with pass (or some other statement with no effect) to stay syntactically valid. Still, the syntax-based reduction would still single out remove_html_markup() from the Assertions source code – and do so even faster, as it would apply on one definition (rather than one line) after another.

#### Transforming Nodes¶

To further boost our syntactic reduction strategy, we implement a set of additional reduction operators. First, as already discussed, we do not simply delete an assignment, but we replace it with a pass statement. To obtain the tree for pass, we simply parse it and access the subtree.

class NodeReducer(NodeReducer):
PASS_TREE = ast.parse("pass").body[0]

def visit_Assign(self, node: ast.Assign) -> AST:
if node.marked:
# Replace by pass
return self.PASS_TREE
return super().generic_visit(node)


In a similar vein, we can replace comparison operators with False:

class NodeReducer(NodeReducer):
FALSE_TREE = ast.parse("False").body[0].value

def visit_Compare(self, node: ast.Compare) -> AST:
if node.marked:
# Replace by False
return self.FALSE_TREE
return super().generic_visit(node)


If we have a Boolean operator, we attempt to replace it with its left operand:

class NodeReducer(NodeReducer):
def visit_BoolOp(self, node: ast.BoolOp) -> AST:
if node.marked:
# Replace by left operator
return node.values[0]
return super().generic_visit(node)


And if we find an If clause, we attempt to replace it by its body:

class NodeReducer(NodeReducer):
def visit_If(self, node: ast.If) -> Union[AST, List[ast.stmt]]:
if node.marked:
# Replace by body
return node.body
return super().generic_visit(node)


Let us try to reduce our code with these additional reducers enabled:

with DeltaDebugger() as dd:
compile_and_test_ast(fun_tree, fun_nodes, test_tree)


This is the reduced code we get. We see that all references to quote have gone, as has the handling of single quotes – none of this is relevant for the failure:

reduced_nodes = dd.min_args()['keep_list']
reduced_fun_tree = copy_and_reduce(fun_tree, reduced_nodes)
print_content(astor.to_source(reduced_fun_tree), '.py')

def remove_html_markup(s):
tag = False
pass
out = ''
for c in s:
if c == '<':
tag = True
elif c == '>':
tag = False
elif c == '"':
pass
elif not tag:
out = out + c
return out


Again, the best insights come from comparing this reduced version to the original implementation – and we learn that the problem is not related to the quote variable, or to the handling of single quotes; the problem is simply that when the input contains double quotes, these are not added to the final string.

With our reduction code, however, we only touch the surface of what could actually be possible. So far, we implement exactly one reduction per node – but of course, there are many alternatives an expression or statement could be reduced to. We will explore some of these in the exercises, below; also be sure to check out the background on code reduction.

## Lessons Learned¶

• Reducing failure-inducing inputs to a minimum is helpful for testing and debugging.
• Delta debugging is a simple and robust algorithm to easily reduce inputs of test cases, as well as their code.
• Precisely specifying failure conditions helps avoiding false diagnoses.

## Next Steps¶

Our next chapter focuses on finding failure-inducing code changes, using delta debugging and version control systems.

## Background¶

The "lexical" delta debugging algorithm discussed here – both in its simplifying ddmin as well as in its general dd form – stem from [Zeller et al, 2002]; actually, ddmin is the exact Python implementation as used by Zeller in 2002. The ddmax variant was first evaluated in [Kirschner et al, 2020]. This chapter is the first to show how both ddmin and ddmax can be implemented as small variations of dd.

The idea of systematically reducing inputs has been discovered a number of times, although not as automatic and generic as delta debugging. [Slutz et al, 1998], for instance, discusses systematic reduction of SQL statements for SQL databases; the general process as manual work is well described by [Kernighan et al, 1999].

The deficits of delta debugging as it comes to syntactically complex inputs were first discussed in compiler testing, and reducing tree inputs rather than string inputs was quickly discovered as an alternative. Hierarchical Delta Debugging (HDD) [Misherghi et al, 2006] applies delta debugging on subtrees of a parse tree, systematically reducing a parse tree to a minimum. Generalized Tree Reduction [Herfert et al, 2017] generalizes this idea to apply arbitrary patterns such as replacing a term by a compatible term in a subtree. Using grammars to reduce inputs was first implemented in the Perses tool [Sun et al, 2018]. A Python implementation of grammar-based input reduction is part of "The Fuzzing Book".

While applying delta debugging to code lines does a decent job, syntactic and especially language-specific approaches can do a much better job for the programming language at hand:

• C-Reduce [Regehr et al, 2012] is a reducer specifically targeting the reduction of programming languages. Besides reductions in the style of delta debugging or tree transformations, C-Reduce comes with more than 30 source-to-source transformations that replace aggregates by scalars, remove function parameters at a definition and all call sites, change functions to return void and deleting all return statements, and many more. While specifically instantiated for the C language (and used for testing C compilers), these principles extend to arbitrary programming languages following an ALGOL-like syntax.

• Kalhauge and Palsberg [Kalhauge et al, 2019] introduce binary reduction of dependency graphs, a general solution for reducing arbitrary inputs with dependencies. Their J-Reduce tool specifically targets Java programs, and again is much faster than delta debugging and achieves a higher reduction rate.

This blog post by David McIver contains lots of insights on how to apply reduction in practice, in particular multiple runs with different abstraction levels.

## Exercises¶

How to best reduce inputs is still an underdeveloped field of research, with lots of opportunities.

### Exercise 1: Advanced Syntactic Code Reduction¶

Extend the code in "Transforming Nodes" such that multiple reduction possibilities for a node are being considered. For instance:

• Replace a BoolOp node by True.
• Replace a BoolOp node by False.
• Replace a BoolOp node by its left operand.
• Replace a BoolOp node by its right operand.

or:

• Replace an If node by its "then" body.
• Replace an If node by its "else" body.

or:

• Replace all instances of a variable by a constant.

or:

• Replace expressions by a constant.

Have a look at the official Python ast reference for a list of nodes (and some ideas on what to replace them by). The documentation "Green Tree Snakes - the missing Python AST docs" provides an excellent introduction on visitors and transformers. Make copious use of AST visualization and tests to ensure your syntax trees are still correct.

Strategy-wise, you should first create a list of possible reductions; and then pass to Delta Debugging a "keep list" of reductions that should not be applied. When Delta Debugging minimizes this list, it will apply as many reductions as possible.