A generator is responsible for generating pseudo-random values and provide shrinks (smaller values) when a test fails.

This module provides some of the most important features of QCheck:

A random generator for values of type `'a`

.

`type 'a sized = int -> 'a t`

Random generator with a size bound.

#### Primitive generators

The unit generator.

Does not shrink.

The boolean generator.

Shrinks towards `false`

.

Generates integers uniformly.

Shrinks towards `0`

.

`val pint : ?origin:int -> int t`

Generates non-strictly positive integers uniformly (`0`

included).

Shrinks towards `origin`

if specified, otherwise towards `0`

.

Small positive integers (< `100`

, `0`

included).

Non-uniform: smaller numbers are more likely than bigger numbers.

Shrinks towards `0`

.

Generates natural numbers (< `10_000`

).

Non-uniform: smaller numbers are more likely than bigger numbers.

Shrinks towards `0`

.

Generates natural numbers, possibly large (< `1_000_000`

).

Non-uniform: smaller numbers are more likely than bigger numbers.

Shrinks towards `0`

.

Generates non-strictly negative integers (`0`

included).

Non-uniform: smaller numbers (in absolute value) are more likely than bigger numbers.

Shrinks towards `0`

.

Small UNSIGNED integers, for retrocompatibility.

Shrinks towards `0`

.

`val small_signed_int : int t`

Small SIGNED integers, based on `small_nat`

.

Non-uniform: smaller numbers (in absolute value) are more likely than bigger numbers.

Shrinks towards `0`

.

`val small_int_corners : unit -> int t`

As `small_int`

, but each newly created generator starts with a list of corner cases before falling back on random generation.

Generates uniform `int32`

values.

Shrinks towards `0l`

.

Generates `int32`

values.

Shrinks towards `0l`

.

Generates uniform `int64`

values.

Shrinks towards `0L`

.

Generates `int64`

values.

Shrinks towards `0L`

.

Generates floating point numbers.

Shrinks towards `0.`

.

Generates positive floating point numbers (`0.`

included).

Shrinks towards `0.`

.

Generates negative floating point numbers. (`-0.`

included).

Shrinks towards `-0.`

.

Generates characters in the `0..255`

range.

Shrinks towards `'a'`

.

Generates printable characters.

The exhaustive list of character codes is:

Shrinks towards `'a'`

or lower character codes.

Generates numeral characters `'0'..'9'`

.

Shrinks towards `'0'`

.

`val bytes_size : ?gen:char t -> int t -> bytes t`

Builds a bytes generator from a (non-negative) size generator. Accepts an optional character generator (the default is `char`

).

Shrinks on the number of characters first, then on the characters.

Bytes generator using the `char`

character generator. Bytes size is generated by `nat`

. See also `bytes_of`

and `bytes_printable`

for versions with custom char generator.

Shrinks on the number of characters first, then on the characters.

`val bytes_of : char t -> bytes t`

Builds a bytes generator using the given character generator.

Shrinks on the number of characters first, then on the characters.

`val bytes_printable : bytes t`

Generator using the `printable`

character generator.

Shrinks on the number of characters first, then on the characters.

`val bytes_small : bytes t`

Builds a bytes generator using the `char`

character generator, length is `small_nat`

.

Shrinks on the number of characters first, then on the characters.

`val bytes_small_of : char t -> bytes t`

Builds a bytes generator using the given character generator, length is `small_nat`

.

Shrinks on the number of characters first, then on the characters.

`val string_size : ?gen:char t -> int t -> string t`

Builds a string generator from a (non-negative) size generator. Accepts an optional character generator (the default is `char`

).

Shrinks on the number of characters first, then on the characters.

Builds a string generator. String size is generated by `nat`

. The default character generator is `char`

. See also `string_of`

and `string_printable`

for versions with custom char generator.

Shrinks on the number of characters first, then on the characters.

`val string_of : char t -> string t`

Builds a string generator using the given character generator.

Shrinks on the number of characters first, then on the characters.

`val string_printable : string t`

Builds a string generator using the `printable`

character generator.

Shrinks on the number of characters first, then on the characters.

`val string_small : string t`

Builds a string generator using the `char`

characher generator, length is `small_nat`

.

Shrinks on the number of characters first, then on the characters.

`val string_small_of : char t -> string t`

Builds a string generator using the given characher generator, length is `small_nat`

.

Shrinks on the number of characters first, then on the characters.

`val small_string : ?gen:char t -> string t`

Builds a string generator, length is `small_nat`

. Accepts an optional character generator (the default is `char`

). Shrinks on the number of characters first, then on the characters. This function is kept for backward compatibility: The optional argument is in fact a mandatory `option`

, see c-cube/qcheck#162. Use `string_small`

instead.

`pure a`

creates a generator that always returns `a`

.

Does not shrink.

`make_primitive ~gen ~shrink`

creates a generator from a function `gen`

that creates a random value (this function must only use the given `Random.State.t`

for randomness) and a function `shrink`

that, given a value `a`

, returns a lazy list of "smaller" values (used when a test fails).

This lower-level function is meant to build generators for "primitive" types that can neither be built with other primitive generators nor through composition, or to have more control on the shrinking steps.

`shrink`

must obey the following rules (for your own definition of "small"):

`shrink a = Seq.empty`

when `a`

is the smallest possible value`shrink a`

must return values strictly smaller than `a`

, ideally from smallest to largest (for faster shrinking)`let rec loop a = match shrink a () with | Nil -> () | Cons (smaller_a, _) -> loop smaller_a`

must end for all values `a`

of type `'a`

(i.e. there must not be an infinite number of shrinking steps).

⚠️ This is an unstable API as it partially exposes the implementation. In particular, the type of `Random.State.t`

may very well change in a future version, e.g. if QCheck switches to another randomness library.

`val add_shrink_invariant : ('a -> bool) -> 'a t -> 'a t`

`add_shrink_invariant f gen`

returns a generator similar to `gen`

except all shrinks satisfy `f`

. This way it's easy to preserve invariants that are enforced by generators, when shrinking values

`val set_shrink : ('a -> 'a Seq.t) -> 'a t -> 'a t`

`set_shrink shrink gen`

sets the shrinker to `shrink`

for `gen`

.

`val no_shrink : 'a t -> 'a t`

`no_shrink gen`

returns a generator using `gen`

but with shrinking disabled

#### Ranges

`val int_bound : int -> int t`

Uniform integer generator producing integers within `0..bound`

.

Shrinks towards `0`

.

`val int_range : ?origin:int -> int -> int -> int t`

`int_range ?origin low high`

is an uniform integer generator producing integers within `low..high`

(inclusive).

Shrinks towards `origin`

if specified, otherwise towards `0`

(but always stays within the range).

Examples:

`int_range ~origin:6 (-5) 15`

will shrink towards `6`

`int_range (-5) 15`

will shrink towards `0`

`int_range 8 20`

will shrink towards `8`

(closest to `0`

within range)`int_range (-20) (-8)`

will shrink towards `-8`

(closest to `0`

within range)

`val (--) : int -> int -> int t`

`a -- b`

is an alias for `int_range a b`

. See `int_range`

for more information.

`val float_bound_inclusive : ?origin:float -> float -> float t`

`float_bound_inclusive ?origin bound`

returns a random floating-point number between `0.`

and `bound`

(inclusive). If `bound`

is negative, the result is negative or zero. If `bound`

is `0.`

, the result is `0.`

.

Shrinks towards `origin`

if given, otherwise towards `0.`

.

`val float_bound_exclusive : ?origin:float -> float -> float t`

`float_bound_exclusive origin bound`

returns a random floating-point number between `0.`

and `bound`

(exclusive). If `bound`

is negative, the result is negative or zero.

Shrinks towards `origin`

if given, otherwise towards `0.`

.

`val float_range : ?origin:float -> float -> float -> float t`

`float_range ?origin low high`

generates floating-point numbers within `low`

and `high`

(inclusive).

Shrinks towards `origin`

if specified, otherwise towards `0.`

(but always stays within the range).

Examples:

`float_range ~origin:6.2 (-5.8) 15.1`

will shrink towards `6.2`

`float_range (-5.8) 15.1`

will shrink towards `0.`

`float_range 8.5 20.1`

will shrink towards `8.5`

(closest to `0.`

within range)`float_range (-20.1) (-8.5)`

will shrink towards `-8.5`

(closest to `0.`

within range)

`val (--.) : float -> float -> float t`

`a --. b`

is an alias for `float_range ~origin:a a b`

. See `float_range`

for more information.

`val char_range : ?origin:char -> char -> char -> char t`

`char_range ?origin low high`

generates chars between `low`

and `high`

, inclusive. Example: `char_range 'a' 'z'`

for all lower case ASCII letters.

Shrinks towards `origin`

if specified, otherwise towards `low`

.

#### Choosing elements

`val oneof : 'a t list -> 'a t`

`oneof l`

constructs a generator that selects among the given list of generators `l`

.

Shrinks towards the first generator of the list.

`val oneofl : 'a list -> 'a t`

`oneofl l`

constructs a generator that selects among the given list of values `l`

.

Shrinks towards the first element of the list.

`val oneofa : 'a array -> 'a t`

`oneofa a`

constructs a generator that selects among the given array of values `a`

.

Shrinks towards the first element of the array.

`val frequency : (int * 'a t) list -> 'a t`

Constructs a generator that selects among a given list of generators. Each of the given generators are chosen based on a positive integer weight.

Shrinks towards the first element of the list.

`val frequencyl : (int * 'a) list -> 'a t`

Constructs a generator that selects among a given list of values. Each of the given values are chosen based on a positive integer weight.

Shrinks towards the first element of the list.

`val frequencya : (int * 'a) array -> 'a t`

Constructs a generator that selects among a given array of values. Each of the array entries are chosen based on a positive integer weight.

Shrinks towards the first element of the array.

#### Shuffling elements

`val shuffle_a : 'a array -> 'a array t`

Returns a copy of the array with its elements shuffled.

`val shuffle_l : 'a list -> 'a list t`

Creates a generator of shuffled lists.

`val shuffle_w_l : (int * 'a) list -> 'a list t`

Creates a generator of weighted shuffled lists. A given list is shuffled on each generation according to the weights of its elements. An element with a larger weight is more likely to be at the front of the list than an element with a smaller weight. If we want to pick random elements from the (head of) list but need to prioritize some elements over others, this generator can be useful.

Example: given a weighted list `[1, "one"; 5, "five"; 10, "ten"]`

, the generator is more likely to generate `["ten"; "five"; "one"]`

or `["five"; "ten"; "one"]`

than `["one"; "ten"; "five"]`

because "ten" and "five" have larger weights than "one".

#### Corner cases

`val graft_corners : 'a t -> 'a list -> unit -> 'a t`

`graft_corners gen l ()`

makes a new generator that enumerates the corner cases in `l`

and then behaves like `g`

.

Does not shrink if the test fails on a grafted value. Shrinks towards `gen`

otherwise.

`val int_pos_corners : int list`

Non-negative corner cases for int.

`val int_corners : int list`

All corner cases for int.

#### Lists, arrays and options

`val list : 'a t -> 'a list t`

Builds a list generator from an element generator. List size is generated by `nat`

.

Shrinks on the number of elements first, then on elements.

`val small_list : 'a t -> 'a list t`

Generates lists of small size (see `small_nat`

).

Shrinks on the number of elements first, then on elements.

`val list_size : int t -> 'a t -> 'a list t`

Builds a list generator from a (non-negative) size generator and an element generator.

Shrinks on the number of elements first, then on elements.

`val list_repeat : int -> 'a t -> 'a list t`

`list_repeat i g`

builds a list generator from exactly `i`

elements generated by `g`

.

Shrinks on elements only.

`val array : 'a t -> 'a array t`

Builds an array generator from an element generator. Array size is generated by `nat`

.

Shrinks on the number of elements first, then on elements.

`val array_size : int t -> 'a t -> 'a array t`

Builds an array generator from a (non-negative) size generator and an element generator.

Shrinks on the number of elements first, then on elements.

`val small_array : 'a t -> 'a array t`

Generates arrays of small size (see `small_nat`

).

Shrinks on the number of elements first, then on elements.

`val array_repeat : int -> 'a t -> 'a array t`

`array_repeat i g`

builds an array generator from exactly `i`

elements generated by `g`

.

Shrinks on elements only.

`val option : ?ratio:float -> 'a t -> 'a option t`

`option gen`

is an `option`

generator that uses `gen`

when generating `Some`

values.

Shrinks towards `None`

then towards shrinks of `gen`

.

`val opt : ?ratio:float -> 'a t -> 'a option t`

`opt`

is an alias of `option`

for backward compatibility.

#### Combining generators

`val pair : 'a t -> 'b t -> ('a * 'b) t`

`pair gen1 gen2`

generates pairs.

Shrinks on `gen1`

and then `gen2`

.

`val triple : 'a t -> 'b t -> 'c t -> ('a * 'b * 'c) t`

`triple gen1 gen2 gen3`

generates triples.

Shrinks on `gen1`

, then `gen2`

and then `gen3`

.

`val quad : 'a t -> 'b t -> 'c t -> 'd t -> ('a * 'b * 'c * 'd) t`

`quad gen1 gen2 gen3 gen4`

generates quadruples.

Shrinks on `gen1`

, then `gen2`

, then `gen3`

and then `gen4`

.

#### Tuple of generators

##### Shrinks on `gen1`

, then `gen2`

, then ...

`val tup2 : 'a t -> 'b t -> ('a * 'b) t`

`val tup3 : 'a t -> 'b t -> 'c t -> ('a * 'b * 'c) t`

`val tup4 : 'a t -> 'b t -> 'c t -> 'd t -> ('a * 'b * 'c * 'd) t`

`val tup5 : 'a t -> 'b t -> 'c t -> 'd t -> 'e t -> ('a * 'b * 'c * 'd * 'e) t`

```
val tup6 :
'a t ->
'b t ->
'c t ->
'd t ->
'e t ->
'f t ->
('a * 'b * 'c * 'd * 'e * 'f) t
```

```
val tup7 :
'a t ->
'b t ->
'c t ->
'd t ->
'e t ->
'f t ->
'g t ->
('a * 'b * 'c * 'd * 'e * 'f * 'g) t
```

```
val tup8 :
'a t ->
'b t ->
'c t ->
'd t ->
'e t ->
'f t ->
'g t ->
'h t ->
('a * 'b * 'c * 'd * 'e * 'f * 'g * 'h) t
```

```
val tup9 :
'a t ->
'b t ->
'c t ->
'd t ->
'e t ->
'f t ->
'g t ->
'h t ->
'i t ->
('a * 'b * 'c * 'd * 'e * 'f * 'g * 'h * 'i) t
```

#### Convert a structure of generator to a generator of structure

`val flatten_l : 'a t list -> 'a list t`

Generate a list of elements from individual generators.

Shrinks on the elements of the list, in the list order.

`val flatten_a : 'a t array -> 'a array t`

Generate an array of elements from individual generators.

Shrinks on the elements of the array, in the array order.

`val flatten_opt : 'a t option -> 'a option t`

Generate an option from an optional generator.

Shrinks towards `None`

then shrinks on the value.

Generate a result from `Ok gen`

, an error from `Error e`

.

Shrinks on `gen`

if `Ok gen`

. Does not shrink if `Error e`

.

`val join : 'a t t -> 'a t`

Collapses a generator of generators to a generator.

Shrinks on the generated generators.

#### Influencing the size of generated values

Creates a generator from a size-bounded generator by first generating a size using `nat`

and passing the result to the size-bounded generator.

Shrinks on the size first, then on the generator.

`val sized_size : int t -> 'a sized -> 'a t`

Creates a generator from a size-bounded generator by first generating a size using the integer generator and passing the result to the size-bounded generator.

Shrinks on the size first, then on the generator.

#### Recursive data structures

`val fix : (('a -> 'b t) -> 'a -> 'b t) -> 'a -> 'b t`

Parametrized fixpoint combinator for generating recursive values.

The fixpoint is parametrized over an generator state `'a`

, and the fixpoint computation may change the value of this state in the recursive calls.

In particular, this can be used for size-bounded generators (with `'a`

as `int`

). The passed size-parameter should decrease to ensure termination.

Example:

```
type tree = Leaf of int | Node of tree * tree
let leaf x = Leaf x
let node x y = Node (x,y)
let g = QCheck.Gen.(sized @@ fix
(fun self n -> match n with
| 0 -> map leaf nat
| n ->
frequency
[1, map leaf nat;
2, map2 node (self (n/2)) (self (n/2))]
))
```

`fix f`

shrinks on the generators returned by `f`

.

`val delay : (unit -> 'a t) -> 'a t`

Delay execution of some code until the generator is actually called. This can be used to manually implement recursion or control flow in a generator.

### Composing generators

QCheck generators compose well: it means one can easily craft generators for new values or types from existing generators.

Part of the following documentation is greatly inspired by Gabriel Scherer's excellent Generator module documentation.

#### Functor

`Gen.t`

is a functor (in the Haskell sense of "mappable"): it has a `map`

function to transform a generator of `'a`

into a generator of `'b`

, given a simple function `'a -> 'b`

.

```
let even_gen : int Gen.t = Gen.map (fun n -> n * 2) Gen.int
let odd_gen : int Gen.t = Gen.map (fun n -> n * 2 + 1) Gen.int
let lower_case_string_gen : string Gen.t = Gen.map String.lowercase Gen.string_printable
type foo = Foo of string * int
let foo_gen : foo Gen.t =
Gen.map (fun (s, n) -> Foo (s, n)) Gen.(pair string_printable int)
```

#### Applicative

`Gen.t`

is applicative: it has a `map2`

function to apply a function of 2 (or more) arguments to 2 (or more) generators.

Another equivalent way to look at it is that it has an `ap`

function to apply a generator of functions to a generator of values. While at first sight this may look almost useless, it actually permits a nice syntax (using the operator alias `<*>`

) for functions of any number of arguments.

```
(* Notice that this looks suspiciously like the [foo] example above:
this is no coincidence! [pair] is a special case of [map2] where
the function wraps arguments in a tuple. *)
type foo = Foo of string * int
let foo_gen : foo Gen.t =
Gen.map2 (fun s n -> Foo (s, n)) Gen.string_printable Gen.int
let string_prefixed_with_keyword_gen : string Gen.t =
Gen.map2 (fun prefix s -> prefix ^ s)
(Gen.oneofl ["foo"; "bar"; "baz"])
Gen.string_printable
```

Applicatives are useful when you need several random values to build a new generator, **and the values are unrelated**. A good rule of thumb is: if the values could be generated in parallel, then you can use an applicative function to combine those generators.

Note that while `map2`

and `map3`

are provided, you can use functions with more than 3 arguments (and that is where the `<*>`

operator alias really shines):

```
val complex_function : bool -> string -> int -> string -> int64 -> some_big_type
(* Verbose version, using map3 and ap *)
let big_type_gen : some_big_type Gen.t = Gen.(
ap (
ap (
map3 complex_function
bool
string_printable
int)
string_printable)
int64)
(* Sleeker syntax, using operators aliases for map and ap *)
let big_type_gen : some_big_type Gen.t = Gen.(
complex_function
<$> bool
<*> string_printable
<*> int
<*> string_printable
<*> int64)
```

#### Monad

`Gen.t`

is a monad: it has a `bind`

function to return a **generator** (not a value) based on **another generated value**.

As an example, imagine you want to create a generator of `(int, string) result`

that is an `Ok`

90% of the time and an `Error`

10% of the time. You can generate a number between 0 and 9 and return a generator of `int`

(wrapped in an `Ok`

using `map`

) if the generated number is lower than 9, otherwise return a generator of `string`

(wrapped in an `Error`

using `map`

):

```
let int_string_result : (int, string) result Gen.t = Gen.(
bind (int_range 0 9) (fun n ->
if n < 9
then map Result.ok int
else map Result.error string_printable))
(* Alternative syntax with operators *)
let int_string_result : (int, string) result Gen.t = Gen.(
int_range 0 9 >>= fun n ->
if n < 9
then int >|= Result.ok
else string_printable >|= Result.error)
(* Another allternative syntax with OCaml 4.08+ binding operators *)
let int_string_result : (int, string) result Gen.t = Gen.(
let* n = int_range 0 9 in
if n < 9
then int >|= Result.ok
else string_printable >|= Result.error)
```

Note that this particular use case can be simplified by using `frequency`

:

```
let int_string_result : (int, string) result Gen.t = Gen.(
frequency [
(9, int >|= Result.ok);
(1, string_printable >|= Result.error)
])
```

`val map : ('a -> 'b) -> 'a t -> 'b t`

`map f gen`

transforms a generator `gen`

by applying `f`

to each generated element.

Shrinks towards the shrinks of `gen`

with `f`

applied to them.

`val (>|=) : 'a t -> ('a -> 'b) -> 'b t`

An infix synonym for `map`

. Note the order of arguments is reversed (usually more convenient for composing).

`val (<$>) : ('a -> 'b) -> 'a t -> 'b t`

`val map2 : ('a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t`

`map2 f gen1 gen2`

transforms two generators `gen1`

and `gen2`

by applying `f`

to each pair of generated elements.

Shrinks on `gen1`

and then `gen2`

.

`val map3 : ('a -> 'b -> 'c -> 'd) -> 'a t -> 'b t -> 'c t -> 'd t`

`map3 f gen1 gen2 gen3`

transforms three generators `gen1`

, `gen2`

, and `gen3`

by applying `f`

to each triple of generated elements.

Shrinks on `gen1`

, then `gen2`

, and then `gen3`

.

`val ap : ('a -> 'b) t -> 'a t -> 'b t`

`ap fgen gen`

composes a function generator and an argument generator into a result generator.

Shrinks on `fgen`

and then `gen`

.

`val (<*>) : ('a -> 'b) t -> 'a t -> 'b t`

`val bind : 'a t -> ('a -> 'b t) -> 'b t`

`bind gen f`

first generates a value of type `'a`

with `gen`

and then passes it to `f`

to generate a value of type `'b`

. This is typically useful when a generator depends on the value generated by another generator.

Shrinks on `gen`

and then on the resulting generator.

`val (>>=) : 'a t -> ('a -> 'b t) -> 'b t`

`val let+ : 'a t -> ('a -> 'b) -> 'b t`

Binding operator alias for `map`

.

Example:

```
let+ n = int_range 0 10 in
string_of_int n
(* is equivalent to *)
map (fun n -> string_of_int n) (int_range 0 10)
```

`val and+ : 'a t -> 'b t -> ('a * 'b) t`

Binding operator alias for `pair`

.

Example:

```
let+ n = int_range 0 10
and+ b = bool in
if b then string_of_int n else "Not a number"
(* is equivalent to *)
map
(fun (n, b) -> if b then string_of_int n else "Not a number")
(pair (int_range 0 10) bool)
```

`val let* : 'a t -> ('a -> 'b t) -> 'b t`

Binding operator alias for `bind`

.

Example:

```
let* n = int_range 0 9 in
if n < 9
then int >|= Result.ok
else string_printable >|= Result.error
(* is equivalent to *)
bind (int_range 0 9) (fun n ->
if n < 9
then map Result.ok int
else map Result.error string_printable)
```

`val and* : 'a t -> 'b t -> ('a * 'b) t`

Binding operator alias for `pair`

.

Example:

```
let* n = int_range 0 9
and* b = bool in
if n < 9 then int >|= Result.ok
else if b then pure (Error "Some specific error")
else string_printable >|= Result.error
(* is equivalent to *)
bind (pair (int_range 0 9) bool) (fun (n, b) ->
if n < 9 then map Result.ok int
else if b then pure (Error "Some specific error")
else map Result.error string_printable)
```

### Debug generators

These functions should not be used in tests: they are provided for convenience to debug/investigate what values and shrinks a generator produces.

`generate ~n gen`

generates `n`

values using `gen`

(shrinks are discarded).

`generate1 gen`

generates one instance of `gen`

(shrinks are discarded).

`generate_tree ?rand gen`

generates a random value and its shrinks using `gen`

.