What you can generate and how

Most things should be easy to generate and everything should be possible.

To support this principle Hypothesis provides strategies for most of built-in types with arguments to constrain or adjust the output, as well as higher-order strategies that can be composed to generate more complex types.

This document is a guide to what strategies are available for generating data and how to build them. Strategies have a variety of other important internal features, such as how they simplify, but the data they can generate is the only public part of their API.

Functions for building strategies are all available in the hypothesis.strategies module. The salient functions from it are as follows:

hypothesis.strategies.nothing()[source]

This strategy never successfully draws a value and will always reject on an attempt to draw.

hypothesis.strategies.just(value)[source]

Return a strategy which only generates value.

Note: value is not copied. Be wary of using mutable values.

hypothesis.strategies.none()[source]

Return a strategy which only generates None.

hypothesis.strategies.one_of(*args)[source]

Return a strategy which generates values from any of the argument strategies.

This may be called with one iterable argument instead of multiple strategy arguments. In which case one_of(x) and one_of(*x) are equivalent.

hypothesis.strategies.integers(min_value=None, max_value=None)[source]

Returns a strategy which generates integers (in Python 2 these may be ints or longs).

If min_value is not None then all values will be >= min_value. If max_value is not None then all values will be <= max_value

hypothesis.strategies.booleans()[source]

Returns a strategy which generates instances of bool.

hypothesis.strategies.floats(min_value=None, max_value=None, allow_nan=None, allow_infinity=None)[source]

Returns a strategy which generates floats.

  • If min_value is not None, all values will be >= min_value.
  • If max_value is not None, all values will be <= max_value.
  • If min_value or max_value is not None, it is an error to enable allow_nan.
  • If both min_value and max_value are not None, it is an error to enable allow_infinity.

Where not explicitly ruled out by the bounds, all of infinity, -infinity and NaN are possible values generated by this strategy.

hypothesis.strategies.complex_numbers()[source]

Returns a strategy that generates complex numbers.

hypothesis.strategies.tuples(*args)[source]

Return a strategy which generates a tuple of the same length as args by generating the value at index i from args[i].

e.g. tuples(integers(), integers()) would generate a tuple of length two with both values an integer.

hypothesis.strategies.sampled_from(elements)[source]

Returns a strategy which generates any value present in the iterable elements.

Note that as with just, values will not be copied and thus you should be careful of using mutable data.

hypothesis.strategies.lists(elements=None, min_size=None, average_size=None, max_size=None, unique_by=None, unique=False)[source]

Returns a list containing values drawn from elements length in the interval [min_size, max_size] (no bounds in that direction if these are None). If max_size is 0 then elements may be None and only the empty list will be drawn.

average_size may be used as a size hint to roughly control the size of list but it may not be the actual average of sizes you get, due to a variety of factors.

If unique is True (or something that evaluates to True), we compare direct object equality, as if unique_by was lambda x: x. This comparison only works for hashable types.

if unique_by is not None it must be a function returning a hashable type when given a value drawn from elements. The resulting list will satisfy the condition that for i != j, unique_by(result[i]) != unique_by(result[j]).

hypothesis.strategies.sets(elements=None, min_size=None, average_size=None, max_size=None)[source]

This has the same behaviour as lists, but returns sets instead.

Note that Hypothesis cannot tell if values are drawn from elements are hashable until running the test, so you can define a strategy for sets of an unhashable type but it will fail at test time.

hypothesis.strategies.frozensets(elements=None, min_size=None, average_size=None, max_size=None)[source]

This is identical to the sets function but instead returns frozensets.

hypothesis.strategies.iterables(elements=None, min_size=None, average_size=None, max_size=None, unique_by=None, unique=False)[source]

This has the same behaviour as lists, but returns iterables instead.

Some iterables cannot be indexed (e.g. sets) and some do not have a fixed length (e.g. generators). This strategy produces iterators, which cannot be indexed and do not have a fixed length. This ensures that you do not accidentally depend on sequence behaviour.

hypothesis.strategies.fixed_dictionaries(mapping)[source]

Generate a dictionary of the same type as mapping with a fixed set of keys mapping to strategies. mapping must be a dict subclass.

Generated values have all keys present in mapping, with the corresponding values drawn from mapping[key]. If mapping is an instance of OrderedDict the keys will also be in the same order, otherwise the order is arbitrary.

hypothesis.strategies.dictionaries(keys, values, dict_class=<type 'dict'>, min_size=None, average_size=None, max_size=None)[source]

Generates dictionaries of type dict_class with keys drawn from the keys argument and values drawn from the values argument.

The size parameters have the same interpretation as for lists.

hypothesis.strategies.streaming(elements)[source]

Generates an infinite stream of values where each value is drawn from elements.

The result is iterable (the iterator will never terminate) and indexable.

Deprecated since version 3.15.0: Use data() instead.

hypothesis.strategies.characters(whitelist_categories=None, blacklist_categories=None, blacklist_characters=None, min_codepoint=None, max_codepoint=None, whitelist_characters=None)[source]

Generates unicode text type (unicode on python 2, str on python 3) characters following specified filtering rules.

When no filtering rules are specifed, any character can be produced.

If min_codepoint or max_codepoint is specifed, then only characters having a codepoint in that range will be produced.

If whitelist_categories is specified, then only characters from those Unicode categories will be produced. This is a further restriction, characters must also satisfy min_codepoint and max_codepoint.

If blacklist_categories is specified, then any character from those categories will not be produced. This is a further restriction, characters that match both whitelist_categories and blacklist_categories will not be produced.

If whitelist_characters is specified, then any additional characters in that list will also be produced.

If blacklist_characters is specified, then any characters in that list will be not be produced. Any overlap between whitelist_characters and blacklist_characters will raise an exception.

hypothesis.strategies.text(alphabet=None, min_size=None, average_size=None, max_size=None)[source]

Generates values of a unicode text type (unicode on python 2, str on python 3) with values drawn from alphabet, which should be an iterable of length one strings or a strategy generating such. If it is None it will default to generating the full unicode range. If it is an empty collection this will only generate empty strings.

min_size, max_size and average_size have the usual interpretations.

hypothesis.strategies.binary(min_size=None, average_size=None, max_size=None)[source]

Generates the appropriate binary type (str in python 2, bytes in python 3).

min_size, average_size and max_size have the usual interpretations.

hypothesis.strategies.randoms()[source]

Generates instances of Random (actually a Hypothesis specific RandomWithSeed class which displays what it was initially seeded with)

hypothesis.strategies.random_module()[source]

If your code depends on the global random module then you need to use this.

It will explicitly seed the random module at the start of your test so that tests are reproducible. The value it passes you is an opaque object whose only useful feature is that its repr displays the random seed. It is not itself a random number generator. If you want a random number generator you should use the randoms() strategy which will give you one.

hypothesis.strategies.builds(target, *args, **kwargs)[source]

Generates values by drawing from args and kwargs and passing them to target in the appropriate argument position.

e.g. builds(target, integers(), flag=booleans()) would draw an integer i and a boolean b and call target(i, flag=b).

If target has type annotations, they will be used to infer a strategy for required arguments that were not passed to builds. You can also tell builds to infer a strategy for an optional argument by passing the special value hypothesis.infer as a keyword argument to builds, instead of a strategy for that argument to target.

hypothesis.strategies.from_type(thing)[source]

Looks up the appropriate search strategy for the given type.

from_type is used internally to fill in missing arguments to builds() and can be used interactively to explore what strategies are available or to debug type resolution.

You can use register_type_strategy() to handle your custom types, or to globally redefine certain strategies - for example excluding NaN from floats, or use timezone-aware instead of naive time and datetime strategies.

The resolution logic may be changed in a future version, but currently tries these four options:

  1. If thing is in the default lookup mapping or user-registered lookup, return the corresponding strategy. The default lookup covers all types with Hypothesis strategies, including extras where possible.
  2. If thing is from the typing module, return the corresponding strategy (special logic).
  3. If thing has one or more subtypes in the merged lookup, return the union of the strategies for those types that are not subtypes of other elements in the lookup.
  4. Finally, if thing has type annotations for all required arguments, it is resolved via builds().
hypothesis.strategies.fractions(min_value=None, max_value=None, max_denominator=None)[source]

Returns a strategy which generates Fractions.

If min_value is not None then all generated values are no less than min_value.

If max_value is not None then all generated values are no greater than max_value.

If max_denominator is not None then the absolute value of the denominator of any generated values is no greater than max_denominator. Note that max_denominator must be at least 1.

hypothesis.strategies.decimals(min_value=None, max_value=None, allow_nan=None, allow_infinity=None, places=None)[source]

Generates instances of decimals.Decimal, which may be:

  • A finite rational number, between min_value and max_value.
  • Not a Number, if allow_nan is True. None means “allow NaN, unless min__value and max_value are not None”.
  • Positive or negative infinity, if max_value and min_value respectively are None, and allow_infinity is not False. None means “allow infinity, unless excluded by the min and max values”.

Note that where floats have one NaN value, Decimals have four: signed, and either quiet or signalling. See the decimal module docs for more information on special values.

If places is not None, all finite values drawn from the strategy will have that number of digits after the decimal place.

hypothesis.strategies.recursive(base, extend, max_leaves=100)[source]

base: A strategy to start from.

extend: A function which takes a strategy and returns a new strategy.

max_leaves: The maximum number of elements to be drawn from base on a given run.

This returns a strategy S such that S = extend(base | S). That is, values maybe drawn from base, or from any strategy reachable by mixing applications of | and extend.

An example may clarify: recursive(booleans(), lists) would return a strategy that may return arbitrarily nested and mixed lists of booleans. So e.g. False, [True], [False, []], [[[[True]]]], are all valid values to be drawn from that strategy.

hypothesis.strategies.permutations(values)[source]

Return a strategy which returns permutations of the collection “values”.

hypothesis.strategies.datetimes(min_datetime=datetime.datetime(1, 1, 1, 0, 0), max_datetime=datetime.datetime(9999, 12, 31, 23, 59, 59, 999999), timezones=none())[source]

A strategy for generating datetimes, which may be timezone-aware.

This strategy works by drawing a naive datetime between min_datetime and max_datetime, which must both be naive (have no timezone).

timezones must be a strategy that generates tzinfo objects (or None, which is valid for naive datetimes). A value drawn from this strategy will be added to a naive datetime, and the resulting tz-aware datetime returned.

Note

tz-aware datetimes from this strategy may be ambiguous or non-existent due to daylight savings, leap seconds, timezone and calendar adjustments, etc. This is intentional, as malformed timestamps are a common source of bugs.

hypothesis.extra.timezones() requires the pytz package, but provides all timezones in the Olsen database. If you also want to allow naive datetimes, combine strategies like none() | timezones().

Alternatively, you can create a list of the timezones you wish to allow (e.g. from the standard library, datetutil, or pytz) and use sampled_from(). Ensure that simple values such as None or UTC are at the beginning of the list for proper minimisation.

hypothesis.strategies.dates(min_date=datetime.date(1, 1, 1), max_date=datetime.date(9999, 12, 31))[source]

A strategy for dates between min_date and max_date.

hypothesis.strategies.times(min_time=datetime.time(0, 0), max_time=datetime.time(23, 59, 59, 999999), timezones=none())[source]

A strategy for times between min_time and max_time.

The timezones argument is handled as for datetimes().

hypothesis.strategies.timedeltas(min_delta=datetime.timedelta(-999999999), max_delta=datetime.timedelta(999999999, 86399, 999999))[source]

A strategy for timedeltas between min_delta and max_delta.

hypothesis.strategies.composite(f)[source]

Defines a strategy that is built out of potentially arbitrarily many other strategies.

This is intended to be used as a decorator. See the full documentation for more details about how to use this function.

hypothesis.strategies.shared(base, key=None)[source]

Returns a strategy that draws a single shared value per run, drawn from base. Any two shared instances with the same key will share the same value, otherwise the identity of this strategy will be used. That is:

>>> s = integers()  # or any other strategy
>>> x = shared(s)
>>> y = shared(s)

In the above x and y may draw different (or potentially the same) values. In the following they will always draw the same:

>>> x = shared(s, key="hi")
>>> y = shared(s, key="hi")
hypothesis.strategies.choices()[source]

Strategy that generates a function that behaves like random.choice.

Will note choices made for reproducibility.

Deprecated since version 3.15.0: Use data() with sampled_from() instead.

hypothesis.strategies.uuids()[source]

Returns a strategy that generates UUIDs.

All returned values from this will be unique, so e.g. if you do lists(uuids()) the resulting list will never contain duplicates.

hypothesis.strategies.runner(default=not_set)[source]

A strategy for getting “the current test runner”, whatever that may be. The exact meaning depends on the entry point, but it will usually be the associated ‘self’ value for it.

If there is no current test runner and a default is provided, return that default. If no default is provided, raises InvalidArgument.

hypothesis.strategies.data()[source]

This isn’t really a normal strategy, but instead gives you an object which can be used to draw data interactively from other strategies.

It can only be used within @given, not find(). This is because the lifetime of the object cannot outlast the test body.

See the rest of the documentation for more complete information.

hypothesis.strategies.register_type_strategy(custom_type, strategy)[source]

Add an entry to the global type-to-strategy lookup.

This lookup is used in builds() and @given.

builds() will be used automatically for classes with type annotations on __init__ , so you only need to register a strategy if one or more arguments need to be more tightly defined than their type-based default, or if you want to supply a strategy for an argument with a default value.

strategy may be a search strategy, or a function that takes a type and returns a strategy (useful for generic types).

hypothesis.strategies.deferred(definition)[source]

A deferred strategy allows you to write a strategy that references other strategies that have not yet been defined. This allows for the easy definition of recursive and mutually recursive strategies.

The definition argument should be a zero-argument function that returns a strategy. It will be evaluated the first time the strategy is used to produce an example.

Example usage:

>>> import hypothesis.strategies as st
>>> x = st.deferred(lambda: st.booleans() | st.tuples(x, x))
>>> x.example()
(False, (False, True))
>>> x.example()
True

Mutual recursion also works fine:

>>> a = st.deferred(lambda: st.booleans() | b)
>>> b = st.deferred(lambda: st.tuples(a, a))
>>> a.example()
(((True, True), False), True)
>>> b.example()
(((( False, ((True, False), (True, True))), True), False), True)

Adapting strategies

Often it is the case that a strategy doesn’t produce exactly what you want it to and you need to adapt it. Sometimes you can do this in the test, but this hurts reuse because you then have to repeat the adaption in every test.

Hypothesis gives you ways to build strategies from other strategies given functions for transforming the data.

Mapping

Map is probably the easiest and most useful of these to use. If you have a strategy s and a function f, then an example s.map(f).example() is f(s.example()), i.e. we draw an example from s and then apply f to it.

e.g.:

>>> lists(integers()).map(sorted).example()
[-224, -222, 16, 159, 120699286316048]

Note that many things that you might use mapping for can also be done with builds().

Filtering

filter lets you reject some examples. s.filter(f).example() is some example of s such that f(example) is truthy.

>>> integers().filter(lambda x: x > 11).example()
1609027033942695427531
>>> integers().filter(lambda x: x > 11).example()
251

It’s important to note that filter isn’t magic and if your condition is too hard to satisfy then this can fail:

>>> integers().filter(lambda x: False).example()
Traceback (most recent call last):
  ...
hypothesis.errors.NoExamples: Could not find any valid examples in 20 tries

In general you should try to use filter only to avoid corner cases that you don’t want rather than attempting to cut out a large chunk of the search space.

A technique that often works well here is to use map to first transform the data and then use filter to remove things that didn’t work out. So for example if you wanted pairs of integers (x,y) such that x < y you could do the following:

>>> tuples(integers(), integers()).map(
... lambda x: tuple(sorted(x))).filter(lambda x: x[0] != x[1]).example()
(180, 241)

Chaining strategies together

Finally there is flatmap. Flatmap draws an example, then turns that example into a strategy, then draws an example from that strategy.

It may not be obvious why you want this at first, but it turns out to be quite useful because it lets you generate different types of data with relationships to eachother.

For example suppose we wanted to generate a list of lists of the same length:

>>> rectangle_lists = integers(min_value=0, max_value=10).flatmap(
... lambda n: lists(lists(integers(), min_size=n, max_size=n)))
>>> find(rectangle_lists, lambda x: True)
[]
>>> find(rectangle_lists, lambda x: len(x) >= 10)
[[], [], [], [], [], [], [], [], [], []]
>>> find(rectangle_lists, lambda t: len(t) >= 3 and len(t[0]) >= 3)
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]
>>> find(rectangle_lists, lambda t: sum(len(s) for s in t) >= 10)
[[0], [0], [0], [0], [0], [0], [0], [0], [0], [0]]

In this example we first choose a length for our tuples, then we build a strategy which generates lists containing lists precisely of that length. The finds show what simple examples for this look like.

Most of the time you probably don’t want flatmap, but unlike filter and map which are just conveniences for things you could just do in your tests, flatmap allows genuinely new data generation that you wouldn’t otherwise be able to easily do.

(If you know Haskell: Yes, this is more or less a monadic bind. If you don’t know Haskell, ignore everything in these parentheses. You do not need to understand anything about monads to use this, or anything else in Hypothesis).

Recursive data

Sometimes the data you want to generate has a recursive definition. e.g. if you wanted to generate JSON data, valid JSON is:

  1. Any float, any boolean, any unicode string.
  2. Any list of valid JSON data
  3. Any dictionary mapping unicode strings to valid JSON data.

The problem is that you cannot call a strategy recursively and expect it to not just blow up and eat all your memory. The other problem here is that not all unicode strings display consistently on different machines, so we’ll restrict them in our doctest.

The way Hypothesis handles this is with the recursive() function which you pass in a base case and a function that given a strategy for your data type returns a new strategy for it. So for example:

>>> from string import printable; from pprint import pprint
>>> json = recursive(none() | booleans() | floats() | text(printable),
... lambda children: lists(children) | dictionaries(text(printable), children))
>>> pprint(json.example())
{'': 'Me$',
 "\r5qPZ%etF:vL'9gC": False,
 '$KsT(( J/(wQ': [],
 '0)G&31': False,
 '7': [],
 'C.i]A-I': {':?Xh>[;': None,
             'YHT\r!\x0b': -6.801160220000663e+18,
...
>>> pprint(json.example())
[{"7_8'qyb": None,
  ':': -0.3641507440748771,
  'TI_^\n>L{T\x0c': -0.0,
  'ZiOqQ\t': 'RKT*a]IjI/Zx2HB4ODiSUN)LsZ',
  'n;E^^6|9=@g@@BmAi': '7j5\\'},
 True]
>>> pprint(json.example())
[]

That is, we start with our leaf data and then we augment it by allowing lists and dictionaries of anything we can generate as JSON data.

The size control of this works by limiting the maximum number of values that can be drawn from the base strategy. So for example if we wanted to only generate really small JSON we could do this as:

>>> small_lists = recursive(booleans(), lists, max_leaves=5)
>>> small_lists.example()
True
>>> small_lists.example()
[True, False]
>>> small_lists.example()
True

Composite strategies

The @composite decorator lets you combine other strategies in more or less arbitrary ways. It’s probably the main thing you’ll want to use for complicated custom strategies.

The composite decorator works by giving you a function as the first argument that you can use to draw examples from other strategies. For example, the following gives you a list and an index into it:

>>> @composite
... def list_and_index(draw, elements=integers()):
...     xs = draw(lists(elements, min_size=1))
...     i = draw(integers(min_value=0, max_value=len(xs) - 1))
...     return (xs, i)

draw(s) is a function that should be thought of as returning s.example(), except that the result is reproducible and will minimize correctly. The decorated function has the initial argument removed from the list, but will accept all the others in the expected order. Defaults are preserved.

>>> list_and_index()
list_and_index()
>>> list_and_index().example()
([215, 112], 0)

>>> list_and_index(booleans())
list_and_index(elements=booleans())
>>> list_and_index(booleans()).example()
([False, False], 1)

Note that the repr will work exactly like it does for all the built-in strategies: It will be a function that you can call to get the strategy in question, with values provided only if they do not match the defaults.

You can use assume inside composite functions:

@composite
def distinct_strings_with_common_characters(draw):
    x = draw(text(), min_size=1)
    y = draw(text(alphabet=x))
    assume(x != y)
    return (x, y)

This works as assume normally would, filtering out any examples for which the passed in argument is falsey.

Drawing interactively in tests

There is also the data() strategy, which gives you a means of using strategies interactively. Rather than having to specify everything up front in @given you can draw from strategies in the body of your test:

@given(data())
def test_draw_sequentially(data):
    x = data.draw(integers())
    y = data.draw(integers(min_value=x))
    assert x < y

If the test fails, each draw will be printed with the falsifying example. e.g. the above is wrong (it has a boundary condition error), so will print:

Falsifying example: test_draw_sequentially(data=data(...))
Draw 1: 0
Draw 2: 0

As you can see, data drawn this way is simplified as usual.

Test functions using the data() strategy do not support explicit @example(...)s. In this case, the best option is usually to construct your data with @composite or the explicit example, and unpack this within the body of the test.

Optionally, you can provide a label to identify values generated by each call to data.draw(). These labels can be used to identify values in the output of a falsifying example.

For instance:

@given(data())
def test_draw_sequentially(data):
    x = data.draw(integers(), label='First number')
    y = data.draw(integers(min_value=x), label='Second number')
    assert x < y

will produce the output:

Falsifying example: test_draw_sequentially(data=data(...))
Draw 1 (First number): 0
Draw 2 (Second number): 0