# What you can generate and how¶

The general philosophy of Hypothesis data generation is that everything should be possible to generate and most things should be easy. Although this is more aspirational than achieved, the state of the art is already pretty good.

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, but the type of data they generate is the only public part of their API.

## Built-in types¶

### Primitives¶

The following “primitive” types all have out of the box high quality strategies written for them which you can get as the result of calling strategy on their type (or using their type in @given).

- int (on python 2.7 this will also generate longs)
- bool
- None
- float
- complex
- Decimal
- Fraction
- Unicode text (str on 3, unicode on 2.7)
- Binary text (bytes on 3, str on 2.7)
- Random

Some examples:

```
>>> strategy(float).example()
1.33e-321
>>> strategy(int).example()
-12576855
```

None is also supported as a convenient alias so you don’t have to use type(None):

```
>>> print(strategy(None).example())
None
```

### Tuples¶

Given values x1, ..., xn, the tuple (x1, ..., xn) gives a strategy which produces a tuple of that length where each coordinate has data drawn from the strategy of the corresponding coordinate. So e.g. strategy((x, y)).example() looks like (strategy(x).example(), strategy(y).example()).

Examples:

```
>>> strategy((int, bool)).example()
(-8, False)
>>> strategy((int, int, int)).example()
(-6, -37837571, -8)
```

The empty tuple gives the strategy that only generates the empty tuple:

```
>>> strategy(()).example()
()
```

collections.namedtuple instances also work out of the box, and in exactly the same way:

```
>>> from collections import namedtuple
>>> T = namedtuple('T', ('a', 'b', 'c'))
>>> strategy(T(int, int, float)).example()
T(a=1572, b=187, c=-1.1575520623614878e-260)
```

### Lists¶

You can generate lists of anything you can generate a strategy of. strategy([x]).example() is a list with zero or more values drawn from strategy(x).example().

e.g.

```
>>> strategy([int]).example()
[-40, -8, -17, -2, 25, -37, 5, 8, -31, -28, -40, -23, -28]
>>> strategy([bool]).example()
[]
>>> strategy([bool]).example()
[False, False, False]
```

The strategy corresponding to a list of multiple elements draws elements from a mix of its contents. So strategy([x, y]).example() would potentially have elements from either strategy(x).example() or strategy(y).example().

e.g.

```
>>> strategy([float, bool]).example()
[]
>>> strategy([float, bool]).example()
[nan, True, nan, -7.2244003034848e-310, -9.90765688276e-312, True, -3e-323]
>>> strategy([float, bool]).example()
[True]
```

An empty list will give you a strategy generating only empty lists:

```
>>> strategy([]).example()
[]
```

### Sets and frozensets¶

Sets and frozensets behave identically to lists:

```
>>> strategy({int}).example()
set()
>>> strategy({int}).example()
{0, 2, -1}
>>> strategy(frozenset({int})).example()
frozenset({-7, -3, -2, -1})
>>> strategy(set()).example()
set()
>>> strategy(frozenset()).example()
frozenset()
```

### Dictionaries¶

Dictionaries with fixed keys work like tuples: They generate the dictionary with those keys, with the examples for the values drawn from the strategy corresponding to the values in the source.

```
>>> strategy({"foo": int, "bar": bool}).example()
{'bar': True, 'foo': -367}
>>> strategy({}).example()
{}
```

## Mixing strategies¶

Given strategies a and b, a | b is a strategy that generates data from either of them:

```
>>> (strategy(int) | strategy(bool)).example()
True
>>> (strategy(int) | strategy(bool)).example()
-7
```

Note that the strategy for [x, y] is the same as the strategy for [x | y] (in fact this is how it is implemented under the hood).

## Special specifiers¶

The module hypothesis.specifiers has a number of types you can use to define more specific strategies for data.

### dictionary¶

The strategy for dictionary instances just gives you dictionaries with fixed keys. If instead you want dictionaries with variable keys you use this function . It takes two arguments - one generates keys, the other values.

```
>>> from hypothesis.specifiers import dictionary
>>> strategy(dictionary(int, int)).example()
{}
>>> strategy(dictionary(int, int)).example()
{20819: -157}
>>> strategy(dictionary(int, int)).example()
{288: 13, 911: 12, -259: 9, -121: -4}
```

It also takes an optional third argument you can use for custom dictionary classes (these don’t have to be dict subtypes, anything that can be build from a list of (key, value) pairs will do):

```
>>> from collections import OrderedDict
>>> strategy(dictionary(int, int, OrderedDict)).example()
OrderedDict([(0, 0), (1, 0)])
>>> strategy(dictionary(int, int, OrderedDict)).example()
OrderedDict()
>>> strategy(dictionary(int, int, OrderedDict)).example()
OrderedDict([(-3, -213), (3, 203), (18, 0)])
```

### one_of¶

one_of takes a collection of values and generates a value from any of them. strategy(one_of((x, y, z))) is the same as strategy(x) | strategy(y) | strategy(z).

```
>>> strategy([one_of((int, bool))]).example()
[-4397, False, -8789, -13191, True, 5800, -16392, True, False, -3042]
```

### Strings from specific alphabets¶

By default Hypothesis generates unicode strings with a very large range of unicode characters. Often what you want is something more specific. Hypothesis provides a strings() specifier which lets you specify the alphabet to draw from.

```
>>> strategy([strings("abc")]).example()
['aaaaacc', 'acacacacaaaabaacc', 'aaacccc', 'cba']
>>> strategy([strings(chr(i) for i in range(128))]).example()
[' rce 13< 61ce8o> e8> 63e >3 c r', 'are<e3nnn1boeno> 3']
```

### Integer ranges¶

specifiers offers two special classes of integer strategy: integers_in_range and integers_from. strategy(integers_in_range(a, b)) generates an integers x such that a <= x <= b:

```
>>> strategy([integers_in_range(0, 1)]).example()
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
>>> strategy([integers_in_range(0, 1)]).example()
[0, 1, 0, 1]
```

integers_from(a) generates integers such that a <= x:

```
>>> strategy([integers_from(10)]).example()
[12, 17]
>>> strategy([integers_from(10)]).example()
[10, 12, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10]
```

### Float ranges¶

Similar to integers_in_range, floats_in_range(a, b) generates a float x such that a <= x <= b:

```
>>> strategy([floats_in_range(0.5, 3)]).example()
[2.604271306355233, 2.0002340854172322, 0.6189895621739885]
```

### just¶

The only example just(x) produces is x.

```
>>> strategy(just(1)).example()
1
```

Note that this returns exactly that value, with no copying:

```
>>> s = strategy(just(object()))
>>> s.example() is s.example()
True
```

This means that you should be careful about using it with mutable objects, as it will be repeatedly passed to test functions which may mutate it.

### sampled_from¶

sampled_from(x) gives a strategy such that strategy(sampled_from(x)).example() in x.

```
>>> x = ["a", "b", "c"]
>>> strategy([sampled_from(x)]).example()
['a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a', 'a']
>>> strategy([sampled_from(x)]).example()
['a', 'c']
>>> strategy([sampled_from(x)]).example()
['a', 'b', 'c', 'a', 'c', 'b']
```

Note that once again these values are not copied, so be careful using this on mutable data.

### Infinite streams¶

Sometimes you need examples of a particular type to keep your test going but you’re not sure how many you’ll need in advance. For this, we have streaming types.

```
>>>> from hypothesis import strategy
>>>> from hypothesis.specifiers import streaming
>>>> x = strategy(streaming(int)).example()
>>>> x
Stream(...)
>>>> x[2]
209
>>>> x
Stream(32, 132, 209, ...)
>>>> x[10]
130
>>>> x
Stream(32, 132, 209, 843, -19, 58, 141, -1046, 37, 243, 130, ...)
```

Think of a Stream as an infinite list where we’ve only evaluated as much as we need to. As per above, you can index into it and the stream will be evaluated up to that index and no further.

You can iterate over it too (warning: iter on a stream given to you by Hypothesis in this way will never terminate):

```
>>>> it = iter(x)
>>>> next(it)
32
>>>> next(it)
132
>>>> next(it)
209
>>>> next(it)
843
```

Slicing will also work, and will give you back Streams. If you set an upper
bound then iter on those streams *will* terminate:

```
>>>> list(x[:5])
[32, 132, 209, 843, -19]
>>>> y = x[1::2]
>>>> y
Stream(...)
>>>> y[0]
132
>>>> y[1]
843
>>>> y
Stream(132, 843, ...)
```

You can also apply a function to transform a stream:

```
>>>> t = strategy(streaming(int)).example()
>>>> tm = t.map(lambda n: n * 2)
>>>> tm[0]
26
>>>> t[0]
13
>>>> tm
Stream(26, ...)
>>>> t
Stream(13, ...)
```

map creates a new stream where each element of the stream is the function applied to the corresponding element of the original stream. Evaluating the new stream will force evaluating the original stream up to that index.

(Warning: This isn’t the map builtin. In Python 3 the builtin map should do more or less the right thing, but in Python 2 it will never terminate and will just eat up all your memory as it tries to build an infinitely long list)

These are the only operations a Stream supports. There are a few more internal ones, but you shouldn’t rely on them.

## 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.:

```
>>> strategy([int]).map(sorted).example()
[1, 5, 17, 21, 24, 30, 45, 82, 88, 88, 90, 96, 105]
```

### Filtering¶

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

```
>>> strategy(int).filter(lambda x: x > 11).example()
1873
>>> strategy(int).filter(lambda x: x > 11).example()
73
```

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

```
>>> strategy(int).filter(lambda x: False).example()
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "/home/david/projects/hypothesis/src/hypothesis/searchstrategy/strategies.py", line 175, in example
'Could not find any valid examples in 20 tries'
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:

```
>>> strategy((int, int)).map(
... lambda x: tuple(sorted(x))).filter(lambda x: x[0] != x[1]).example()
(42, 1281698)
```

### 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 tuples all of the same length:

```
>>> strategy(
... integers_in_range(0, 10)).flatmap(lambda n: [(int,) * n]).example()
[(170, -747, 564), (-534, 7226, 4), (83, 11647, 170)]
```

In this example we first choose a length for our tuples, then we build a description of a list of tuples of those lengths.

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).

## Defining entirely new strategies¶

The full SearchStrategy API is only “semi-public”, in that it may (but usually won’t) break between minor versions but won’t break between patch releases.

However Hypothesis exposes a simplified version of the interface that you can use to build pretty good strategies. In general it’s pretty strongly recommended that you don’t use this if you can build your strategy out of existing ones, but it works perfectly well.

Here is an example of using the simplified interface:

```
from hypothesis.searchstrategy import BasicStrategy
class Bitfields(BasicStrategy):
"""A BasicStrategy for generating 128 bit integers to be treated as if they
were bitfields."""
def generate_parameter(self, random):
# This controls the shape of the data that can be generated by
# randomly screening off some bits.
return random.getrandbits(128)
def generate(self, random, parameter_value):
# This generates a random value subject to a parameter we have
# previously generated
return parameter_value & random.getrandbits(128)
def simplify(self, random, value):
# Simplify by settings bits to zero.
for i in range(128):
k = 1 << i
# It's important to test this because otherwise it would create a
# cycle where value simplifies to value. This would cause
# Hypothesis to get stuck on that value and not be able to simplify
# it further.
if value & k:
yield value & (~k)
def copy(self, value):
# integers are immutable so there's no need to copy them
return value
```

Only generate is strictly necessary to implement. copy will default to using deepcopy, generate_parameter will default to returning None, and simplify will default to not simplifying.

The reason why the parameters are important is that they let you “shape” the data so that it works with adaptive assumptions, which work by being more likely to reuse parameter values that don’t cause assumptions to be violated.

Simplify is of course what Hypothesis uses to produce simpler examples. It will greedily apply it to your data to produce the simplest example it possible can. You should avoid having cycles or unbounded paths in the graph, as this will tend to hurt example quality and performance.

You don’t need to register subclasses of BasicStrategy. They work out of the box, either as classes or instances:

```
>>> strategy(Bitfields).example()
70449389301502165026254673882738917538
>>> strategy(Bitfields()).example()
180947746395888412520415493036267606532
```

Caveats:

- BasicStrategy is not a subclass of SearchStrategy, only convertible to it.
- The values produced by BasicStrategy are opaque to Hypothesis in a way that ones it is more intimately familiar with are not, because it’s impossible to safely and sensibly deduplicate arbitrary Python objects. This is mostly fine but it blocks certain heuristics and optimisations Hypothesis uses for improving the simplification process. As such implementations using BasicStrategy might get slightly worse examples than the equivalent native ones.
- You should not use BasicData for anything which you need control over the life cycle of, e.g. ORM objects. Hypothesis will keep instances of these values around for a potentially arbitrarily long time and will not do any clean up for disposing of them other than letting them be GCed as normal.

However if it’s genuinely the best way for you to do it, you should feel free to use BasicStrategy. These caveats should be read in the light of the fact that the full Hypothesis SearchStrategy interface is really very powerful, and the ones using BasicStrategy are merely a bit better than the normal quickcheck interface.

## Using the SearchStrategy API directly¶

If you’re really super enthused about this search strategies thing and you want to learn all the gory details of how it works under the hood, you can use the full blown raw SearchStrategy interface to experience the full power of Hypothesis.

As mentioned, this is not a public API. If you use this API your code may break between minor version updates and I won’t feel bad about it.

The API is defined and relatively well commented in strategies.py and there is a worked example available here.