# 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 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`()

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

  Examples from this strategy do not shrink (because there are none).

`hypothesis.strategies.``just`(value)

  Return a strategy which only generates `value`.

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

  If `value` is the result of a callable, you can use `builds(callable)` instead of `just(callable())` to get a fresh value each time.

  Examples from this strategy do not shrink (because there is only one).

`hypothesis.strategies.``none`()

  Return a strategy which only generates None.

  Examples from this strategy do not shrink (because there is only one).

`hypothesis.strategies.``one_of`(*args)

  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.

  Examples from this strategy will generally shrink to ones that come from strategies earlier in the list, then shrink according to behaviour of the strategy that produced them. In order to get good shrinking behaviour, try to put simpler strategies first. e.g. `one_of(none(), text())` is better than `one_of(text(), none())`.

  This is especially important when using recursive strategies. e.g. `x = st.deferred(lambda: st.none() | st.tuples(x, x))` will shrink well, but `x = st.deferred(lambda: st.tuples(x, x) | st.none())` will shrink very badly indeed.

`hypothesis.strategies.``integers`(min_value=None, max_value=None)

  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

  Examples from this strategy will shrink towards being positive (e.g. 1000 is considered simpler than -1) and then towards zero.

`hypothesis.strategies.``booleans`()

  Returns a strategy which generates instances of bool.

  Examples from this strategy will shrink towards False (i.e. shrinking will try to replace True with False where possible).

`hypothesis.strategies.``floats`(min_value=None, max_value=None, allow_nan=None, allow_infinity=None)

  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.

  Examples from this strategy have a complicated and hard to explain shrinking behaviour, but it tries to improve “human readability”. Finite numbers will be preferred to infinity and infinity will be preferred to NaN.

`hypothesis.strategies.``complex_numbers`()

  Returns a strategy that generates complex numbers.

  Examples from this strategy shrink by shrinking their component real and imaginary parts.

`hypothesis.strategies.``tuples`(*args)

  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.

  Examples from this strategy shrink by shrinking their component parts.

`hypothesis.strategies.``sampled_from`(elements)

  Returns a strategy which generates any value present in `elements`.

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

  `sampled_from` supports ordered collections, as well as `Enum` objects. `Flag` objects may also generate any combination of their members.

  Examples from this strategy shrink by replacing them with values earlier in the list. So e.g. sampled_from((10, 1)) will shrink by trying to replace 1 values with 10, and sampled_from((1, 10)) will shrink by trying to replace 10 values with 1.

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

  Returns a list containing values drawn from elements with 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 the 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]).

  Examples from this strategy shrink by trying to remove elements from the list, and by shrinking each individual element of the list.

`hypothesis.strategies.``sets`(elements=None, min_size=None, average_size=None, max_size=None)

  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.

  Examples from this strategy shrink by trying to remove elements from the set, and by shrinking each individual element of the set.

`hypothesis.strategies.``frozensets`(elements=None, min_size=None, average_size=None, max_size=None)

  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)

  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)

  Generates 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.

  Examples from this strategy shrink by shrinking each individual value in the generated dictionary.

`hypothesis.strategies.``dictionaries`(keys, values, dict_class=<class 'dict'>, min_size=None, average_size=None, max_size=None)

  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.

  Examples from this strategy shrink by trying to remove keys from the generated dictionary, and by shrinking each generated key and value.

`hypothesis.strategies.``streaming`(elements)

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

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

  Examples from this strategy shrink by trying to shrink each value drawn.

  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)

  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.

  Examples from this strategy shrink towards smaller codepoints.

`hypothesis.strategies.``text`(alphabet=None, min_size=None, average_size=None, max_size=None)

  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.

  Examples from this strategy shrink towards shorter strings, and with the characters in the text shrinking as per the alphabet strategy.

`hypothesis.strategies.``from_regex`(regex)

  Generates strings that contain a match for the given regex (i.e. ones for which `re.search()` will return a non-None result).

  `regex` may be a pattern or `compiled regex`. Both byte-strings and unicode strings are supported, and will generate examples of the same type.

  You can use regex flags such as `re.IGNORECASE`, `re.DOTALL` or `re.UNICODE` to control generation. Flags can be passed either in compiled regex or inside the pattern with a `(?iLmsux)` group.

  Some regular expressions are only partly supported - the underlying strategy checks local matching and relies on filtering to resolve context-dependent expressions. Using too many of these constructs may cause health-check errors as too many examples are filtered out. This mainly includes (positive or negative) lookahead and lookbehind groups.

  If you want the generated string to match the whole regex you should use boundary markers. So e.g. `r"\A.\Z"` will return a single character string, while `"."` will return any string, and `r"\A.$"` will return a single character optionally followed by a `"\n"`.

  Examples from this strategy shrink towards shorter strings and lower character values.

`hypothesis.strategies.``binary`(min_size=None, average_size=None, max_size=None)

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

  min_size, average_size and max_size have the usual interpretations.

  Examples from this strategy shrink towards smaller strings and lower byte values.

`hypothesis.strategies.``randoms`()

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

  Examples from this strategy shrink to seeds closer to zero.

`hypothesis.strategies.``random_module`()

  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.

  Examples from these strategy shrink to seeds closer to zero.

`hypothesis.strategies.``builds`(target, *args, **kwargs)

  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`.

  Examples from this strategy shrink by shrinking the argument values to the target.

`hypothesis.strategies.``from_type`(thing)

  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 `python: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)

  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. min_value and max_value may be anything accepted by the `Fraction` constructor.

  If max_denominator is not None then the denominator of any generated values is no greater than max_denominator. Note that max_denominator must be None or a positive integer.

  Examples from this strategy shrink towards smaller denominators, then closer to zero.

`hypothesis.strategies.``decimals`(min_value=None, max_value=None, allow_nan=None, allow_infinity=None, places=None)

  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.

  Examples from this strategy do not have a well defined shrink order but try to maximize human readability when shrinking.

`hypothesis.strategies.``recursive`(base, extend, max_leaves=100)

  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 may be 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, []]`, and `[[[[True]]]]` are all valid values to be drawn from that strategy.

  Examples from this strategy shrink by trying to reduce the amount of recursion and by shrinking according to the shrinking behaviour of base and the result of extend.

`hypothesis.strategies.``permutations`(values)

  Return a strategy which returns permutations of the collection `values`.

  Examples from this strategy shrink by trying to become closer to the original order of values.

`hypothesis.strategies.``datetimes`(min_value=datetime.datetime(1, 1, 1, 0, 0), max_value=datetime.datetime(9999, 12, 31, 23, 59, 59, 999999), timezones=none(), min_datetime=None, max_datetime=None)

  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.

  > Examples from this strategy shrink towards midnight on January 1st 2000.

  The following arguments have been renamed:

  > - min_datetime has been renamed to min_value
  > - max_datetime has been renamed to max_value

  Use of the old names has been deprecated and will be removed in a future version of Hypothesis.

`hypothesis.strategies.``dates`(min_value=datetime.date(1, 1, 1), max_value=datetime.date(9999, 12, 31), min_date=None, max_date=None)

  A strategy for dates between `min_date` and `max_date`.

  > Examples from this strategy shrink towards January 1st 2000.

  The following arguments have been renamed:

  > - min_date has been renamed to min_value
  > - max_date has been renamed to max_value

  Use of the old names has been deprecated and will be removed in a future version of Hypothesis.

`hypothesis.strategies.``times`(min_value=datetime.time(0, 0), max_value=datetime.time(23, 59, 59, 999999), timezones=none(), min_time=None, max_time=None)

  A strategy for times between `min_time` and `max_time`.

  > The `timezones` argument is handled as for `datetimes()`.

  > Examples from this strategy shrink towards midnight, with the timezone component shrinking as for the strategy that provided it.

  The following arguments have been renamed:

  > - min_time has been renamed to min_value
  > - max_time has been renamed to max_value

  Use of the old names has been deprecated and will be removed in a future version of Hypothesis.

`hypothesis.strategies.``timedeltas`(min_value=datetime.timedelta(-999999999), max_value=datetime.timedelta(999999999, 86399, 999999), min_delta=None, max_delta=None)

  A strategy for timedeltas between `min_value` and `max_value`.

  > Examples from this strategy shrink towards zero.

  The following arguments have been renamed:

  > - min_delta has been renamed to min_value
  > - max_delta has been renamed to max_value

  Use of the old names has been deprecated and will be removed in a future version of Hypothesis.

`hypothesis.strategies.``composite`(f)

  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.

  Examples from this strategy shrink by shrinking the output of each draw call.

`hypothesis.strategies.``shared`(base, key=None)

  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")

  Examples from this strategy shrink as per their base strategy.

`hypothesis.strategies.``choices`()

  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.

  Examples from this strategy shrink by making each choice function return an earlier value in the sequence passed to it.

`hypothesis.strategies.``uuids`(version=None)

  Returns a strategy that generates `UUIDs`.

  If the optional version argument is given, value is passed through to `UUID` and only UUIDs of that version will be generated.

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

  Examples from this strategy don’t have any meaningful shrink order.

`hypothesis.strategies.``runner`(default=not_set)

  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.

  Examples from this strategy do not shrink (because there is only one).

`hypothesis.strategies.``data`()

  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.

  Examples from this strategy do not shrink (because there is only one), but the result of calls to each draw() call shrink as they normally would.

`hypothesis.strategies.``register_type_strategy`(custom_type, strategy)

  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)

  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, (True, True)), (False, True)), (True, True))
      >>> x.example()
      (True, 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))
      >>> b.example()
      (False, True)

  Examples from this strategy shrink as they normally would from the strategy returned by the definition.

## Shrinking

When using strategies it is worth thinking about how the data shrinks. Shrinking is the process by which Hypothesis tries to produce human readable examples when it finds a failure - it takes a complex example and turns it into a simpler one.

Each strategy defines an order in which it shrinks - you won’t usually need to care about this much, but it can be worth being aware of as it can affect what the best way to write your own strategies is.

The exact shrinking behaviour is not a guaranteed part of the API, but it doesn’t change that often and when it does it’s usually because we think the new way produces nicer examples.

Possibly the most important one to be aware of is `one_of()`, which has a preference for values produced by strategies earlier in its argument list. Most of the others should largely “do the right thing” without you having to think about it.

## 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()
    [-158104205405429173199472404790070005365, -131418136966037518992825706738877085689, -49279168042092131242764306881569217089, 2564476464308589627769617001898573635]

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()
    87034457550488036879331335314643907276
    >>> integers().filter(lambda x: x > 11).example()
    145321388071838806577381808280858991039

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(sorted).filter(lambda x: x[0] < x[1]).example()
    [-145066798798423346485767563193971626126, -19139012562996970506504843426153630262]

### 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 each other.

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())
    {'': 'wkP!4',
     '\nLdy': None,
     '"uHuds:8a{h\\:694K~{mY>a1yA:#CmDYb': {},
     '#1J1': [')gnP',
              inf,
              ['6', 11881275561.716116, "v'A?qyp_sB\n$62g", ''],
              -1e-05,
              'aF\rl',
              [-2.599459969184803e+250, True, True, None],
              [True,
               '9qP\x0bnUJH5',
               3.0741121405774857e-131,
               None,
               '',
               -inf,
               'L&',
               1.5,
               False,
               None]],
     'cx.': None}
    >>> pprint(json.example())
    [5.321430774293539e+16, [], 1.1045114769709281e-125]
    >>> pprint(json.example())
    {'a': []}

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()
    [False, False, True, True, True]
    >>> 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()
    ([-57328788235238539257894870261848707608], 0)

    >>> list_and_index(booleans())
    list_and_index(elements=booleans())
    >>> list_and_index(booleans()).example()
    ([True], 0)

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