# 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.

## Core Strategies

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

`hypothesis.strategies.``binary`(min_size=0, max_size=None)

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

  min_size and max_size have the usual interpretations.

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

`hypothesis.strategies.``booleans`()

  Returns a strategy which generates instances of `python:bool`.

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

`hypothesis.strategies.``builds`(*callable_and_args, **kwargs)

  Generates values by drawing from `args` and `kwargs` and passing them to the callable (provided as the first positional argument) 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 the callable 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 the callable.

  If the callable is a class defined with attrs, missing required arguments will be inferred from the attribute on a best-effort basis, e.g. by checking attrs standard validators. Dataclasses are handled natively by the inference from type hints.

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

`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. Any overlap between `whitelist_categories` and `blacklist_categories` will raise an exception, as each character can only belong to a single class.
  - 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.

  The `_codepoint` arguments must be integers between zero and `python:sys.maxunicode`. The `_characters` arguments must be collections of length-one unicode strings, such as a unicode string.

  The `_categories` arguments must be used to specify either the one-letter Unicode major category or the two-letter Unicode general category. For example, `('Nd', 'Lu')` signifies “Number, decimal digit” and “Letter, uppercase”. A single letter (‘major category’) can be given to match all corresponding categories, for example `'P'` for characters in any punctuation category.

  Examples from this strategy shrink towards the codepoint for `'0'`, or the first allowable codepoint after it if `'0'` is excluded.

`hypothesis.strategies.``complex_numbers`(min_magnitude=0, max_magnitude=None, allow_infinity=None, allow_nan=None)

  Returns a strategy that generates complex numbers.

  This strategy draws complex numbers with constrained magnitudes. The `min_magnitude` and `max_magnitude` parameters should be non-negative `Real` numbers; values of `None` correspond to zero and infinite values respectively.

  If `min_magnitude` is positive or `max_magnitude` is finite, it is an error to enable `allow_nan`. If `max_magnitude` is finite, it is an error to enable `allow_infinity`.

  The magnitude contraints are respected up to a relative error of (around) floating-point epsilon, due to implementation via the system `sqrt` function.

  Examples from this strategy shrink by shrinking their real and imaginary parts, as `floats()`.

  If you need to generate complex numbers with particular real and imaginary parts or relationships between parts, consider using `builds(complex, ...)` or `@composite` respectively.

`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.``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.

  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.

class `hypothesis.strategies.``DataObject`(data)

  This type only exists so that you can write type hints for tests using the `data()` strategy. Do not use it directly!

`hypothesis.strategies.``dates`(min_value=datetime.date(1, 1, 1), max_value=datetime.date(9999, 12, 31))

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

  Examples from this strategy shrink towards January 1st 2000.

`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())

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

  This strategy works by drawing a naive datetime between `min_value` and `max_value`, 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.pytz.timezones()` requires the pytz package, but provides all timezones in the Olsen database. If you want to allow naive datetimes, combine strategies like `none() | timezones()`.

  `hypothesis.extra.dateutil.timezones()` requires the python-dateutil package, and similarly provides all timezones there.

  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.

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

  Generates instances of `python:decimal.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.``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

  Mutual recursion also works fine:

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

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

`hypothesis.strategies.``dictionaries`(keys, values, dict_class=<class 'dict'>, min_size=0, 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.``emails`()

  A strategy for generating email addresses as unicode strings. The address format is specified in RFC 5322#section-3.4.1. Values shrink towards shorter local-parts and host domains.

  This strategy is useful for generating “user data” for tests, as mishandling of email addresses is a common source of bugs.

`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.``floats`(min_value=None, max_value=None, allow_nan=None, allow_infinity=None, width=64, exclude_min=False, exclude_max=False)

  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.

  The width argument specifies the maximum number of bits of precision required to represent the generated float. Valid values are 16, 32, or 64. Passing `width=32` will still use the builtin 64-bit `float` class, but always for values which can be exactly represented as a 32-bit float. Half-precision floats (`width=16`) are only supported on Python 3.6, or if Numpy is installed.

  The exclude_min and exclude_max argument can be used to generate numbers from open or half-open intervals, by excluding the respective endpoints. Attempting to exclude an endpoint which is None will raise an error; use `allow_infinity=False` to generate finite floats. You can however use e.g. `min_value=float("-inf"), exclude_min=True` to exclude only one infinite endpoint.

  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.``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.``from_regex`(regex, fullmatch=False)

  Generates strings that contain a match for the given regex (i.e. ones for which `python: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 `python:re.IGNORECASE` or `python:re.DOTALL` 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"`. Alternatively, passing `fullmatch=True` will ensure that the whole string is a match, as if you had used the `\A` and `\Z` markers.

  Examples from this strategy shrink towards shorter strings and lower character values, with exact behaviour that may depend on the pattern.

`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 five 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, and is not an abstract class, it is resolved via `builds()`.
  5. Because `abstract types` cannot be instantiated, we treat abstract types as the union of their concrete subclasses. Note that this lookup works via inheritance but not via `register`, so you may still need to use `register_type_strategy()`.

  There is a valuable recipe for leveraging `from_type()` to generate “everything except” values from a specified type. I.e.

      def everything_except(excluded_types):
          return (
              from_type(type).flatmap(from_type)
              .filter(lambda x: not isinstance(x, excluded_types))
          )

  For example, `everything_except(int)` returns a strategy that can generate anything that `from_type()` can ever generate, except for instances of `python:int`, and excluding instances of types added via `register_type_strategy()`.

  This is useful when writing tests which check that invalid input is rejected in a certain way.

`hypothesis.strategies.``frozensets`(elements, min_size=0, max_size=None)

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

`hypothesis.strategies.``functions`(like=<function <lambda>>, returns=none())

  A strategy for functions, which can be used in callbacks.

  The generated functions will mimic the interface of `like`, which must be a callable (including a class, method, or function). The return value for the function is drawn from the `returns` argument, which must be a strategy.

  Note that the generated functions do not validate their arguments, and may return a different value if called again with the same arguments.

  Generated functions can only be called within the scope of the `@given` which created them. This strategy does not support `.example()`.

`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 zero, and negative values will also shrink towards positive (i.e. -n may be replaced by +n).

`hypothesis.strategies.``iterables`(elements, min_size=0, 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.``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.``lists`(elements, min_size=0, 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, only the empty list will be drawn.

  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 callable or tuple of callables 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])`.

  If `unique_by` is a tuple of callables the uniqueness will be respective to each callable.

  For example, the following will produce two columns of integers with both columns being unique respectively. .. code-block:: pycon

      >>> twoints = st.tuples(st.integers(), st.integers())
      >>> st.lists(twoints, unique_by=(lambda x: x[0], lambda x: x[1]))

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

`hypothesis.strategies.``none`()

  Return a strategy which only generates None.

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

`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.``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.``permutations`(values)

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

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

`hypothesis.strategies.``random_module`()

  The Hypothesis engine handles PRNG state for the stdlib and Numpy random modules internally, always seeding them to zero and restoring the previous state after the test.

  If having a fixed seed would unacceptably weaken your tests, and you cannot use a `random.Random` instance provided by `randoms()`, this strategy calls `python:random.seed()` with an arbitrary integer and passes you an opaque object whose repr displays the seed value for debugging. If `numpy.random` is available, that state is also managed.

  Examples from these strategy shrink to seeds closer to zero.

`hypothesis.strategies.``randoms`()

  Generates instances of `random.Random`, tweaked to show the seed value in the repr for reproducibility.

  Examples from this strategy shrink to seeds closer to zero.

`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.``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.``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.``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.``sets`(elements, min_size=0, 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.``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.``slices`(size)

  Generates slices that will select indices up to the supplied size

  Generated slices will have start and stop indices that range from 0 to size - 1 and will step in the appropriate direction. Slices should only produce an empty selection if the start and end are the same.

  Examples from this strategy shrink toward 0 and smaller values

`hypothesis.strategies.``text`(alphabet=characters(blacklist_categories=('Cs', )), min_size=0, 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 strings.

  The default alphabet strategy can generate the full unicode range but excludes surrogate characters because they are invalid in the UTF-8 encoding. You can use `characters()` without arguments to find surrogate-related bugs such as bpo-34454.

  `min_size` and `max_size` have the usual interpretations. Note that Python measures string length by counting codepoints: U+00C5 `Å` is a single character, while U+0041 U+030A `Å` is two - the `A`, and a combining ring above.

  Examples from this strategy shrink towards shorter strings, and with the characters in the text shrinking as per the alphabet strategy. This strategy does not `normalize()` examples, so generated strings may be in any or none of the ‘normal forms’.

`hypothesis.strategies.``timedeltas`(min_value=datetime.timedelta(days=-999999999), max_value=datetime.timedelta(days=999999999, seconds=86399, microseconds=999999))

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

  Examples from this strategy shrink towards zero.

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

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

  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.

`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.``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.

## Provisional Strategies

This module contains various provisional APIs and strategies.

It is intended for internal use, to ease code reuse, and is not stable. Point releases may move or break the contents at any time!

Internet strategies should conform to RFC 3986 or the authoritative definitions it links to. If not, report the bug!

class `hypothesis.provisional.``DomainNameStrategy`(max_length=None, max_element_length=None)

`hypothesis.provisional.``domains`(max_length=255, max_element_length=63)

  Generate RFC 1035 compliant fully qualified domain names.

`hypothesis.provisional.``urls`()

  A strategy for RFC 3986, generating http/https URLs.

`hypothesis.provisional.``ip4_addr_strings`()

  A strategy for IPv4 address strings.

  This consists of four strings representing integers [0..255], without zero-padding, joined by dots.

`hypothesis.provisional.``ip6_addr_strings`()

  A strategy for IPv6 address strings.

  This consists of sixteen quads of hex digits (0000 .. FFFF), joined by colons. Values do not currently have zero-segments collapsed.

## 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()
    [-25527, -24245, -23118, -93, -70, -7, 0, 39, 40, 65, 88, 112, 6189, 9480, 19469, 27256, 32526, 1566924430]

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()
    26126
    >>> integers().filter(lambda x: x > 11).example()
    23324

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.Unsatisfiable: 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()
    [-8543729478746591815, 3760495307320535691]

### 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)))
    >>> rectangle_lists.example()
    []
    >>> rectangle_lists.filter(lambda x: len(x) >= 10).example()
    [[], [], [], [], [], [], [], [], [], []]
    >>> rectangle_lists.filter(lambda t: len(t) >= 3 and len(t[0]) >= 3).example()
    [[0, 0, 0], [0, 0, 0], [0, 0, 0]]
    >>> rectangle_lists.filter(lambda t: sum(len(s) for s in t) >= 10).example()
    [[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()` strategy 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, 1) | dictionaries(text(printable), children, min_size=1))
    >>> pprint(json.example())
    [[1.175494351e-38, ']', 1.9, True, False, '.M}Xl', ''], True]
    >>> pprint(json.example())
    {'de(l': None,
     'nK': {'(Rt)': None,
            '+hoZh1YU]gy8': True,
            '8z]EIFA06^l`i^': 'LFE{Q',
            '9,': 'l{cA=/'}}

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]

## 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 converting a function that returns one example into a function that returns a strategy that produces such examples - which you can pass to `@given`, modify with `.map` or `.filter`, and generally use like any other strategy.

It does this by giving you a special function `draw` as the first argument, which can be used just like the corresponding method of the `data()` strategy within a test. In fact, the implementation is almost the same - but defining a strategy with `@composite` makes code reuse easier, and usually improves the display of failing examples.

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()
    ([15949, -35, 21764, 8167, 1607867656, -41, 104, 19, -90, 520116744169390387, 7107438879249457973], 0)

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

This is similar to `@composite`, but even more powerful as it allows you to mix test code with example generation. The downside of this power is that `data()` is incompatible with explicit `@example(...)`s - and the mixed code is often harder to debug when something goes wrong.

If you need values that are affected by previous draws but which don’t depend on the execution of your test, stick to the simpler `@composite`.

    @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.

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