module QCheck:`sig`

..`end`

The library takes inspiration from Haskell's QuickCheck library. The rough idea is that the programmer describes invariants that values of a certain type need to satisfy ("properties"), as functions from this type to bool. She also needs to describe how to generate random values of the type, so that the property is tried and checked on a number of random instances.

This explains the organization of this module:

`'a arbitrary`

is used to describe how to generate random values, shrink them (make counter-examples as small as possible), print them, etc. Auxiliary modules such as`QCheck.Gen`

,`QCheck.Print`

, and`QCheck.Shrink`

can be used along with`QCheck.make`

to build one's own arbitrary instances.

`QCheck.Test`

is used to describe a single test, that is, a property of type`'a -> bool`

combined with an`'a arbitrary`

that is used to generate the test cases for this property. Optional parameters allow to specify the random generator state, number of instances to generate and test, etc.

- List.rev is involutive:

```
let test =
QCheck.(Test.make ~count:1000
(list int) (fun l -> List.rev (List.rev l) = l));;
QCheck.Test.check_exn test;;
```

- Not all lists are sorted (false property that will fail. The 15 smallest counter-example lists will be printed):

```
let test = QCheck.(
Test.make
~count:10_000 ~max_fail:3
(list small_nat)
(fun l -> l = List.sort compare l));;
QCheck.Test.check_exn test;;
```

- generate 20 random trees using
`QCheck.Gen.fix`

:

```
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))]
))
Gen.generate ~n:20 g;;
```

More complex and powerful combinators can be found in Gabriel Scherer's
`Generator`

module. Its documentation can be found
here.

`val (==>) : ``bool -> bool -> bool`

`b1 ==> b2`

is the logical implication `b1 => b2`

ie `not b1 || b2`

(except that it is strict and will interact
better with `QCheck.Test.check_exn`

and the likes, because they will know
the precondition was not satisfied.).
**WARNING**: this function should only be used in a property
(see `QCheck.Test.make`

), because it raises a special exception in case of
failure of the first argument, to distinguish between failed test
and failed precondition. Because of OCaml's evaluation order,
both `b1`

and `b2`

are always evaluated; if `b2`

should only be
evaluated when `b1`

holds, see `QCheck.assume`

.

`val assume : ``bool -> unit`

`assume cond`

checks the precondition `cond`

, and does nothing
if `cond=true`

. If `cond=false`

, it interrupts the current test.
**WARNING** This function, like `QCheck.(==>)`

, should only be used in
a test, not outside.
Example:

```
Test.make (list int) (fun l ->
assume (l <> []);
List.hd l :: List.tl l = l)
```

`val assume_fail : ``unit -> 'a`

`assume_fail ()`

is like `assume false`

, but can take any type
since we know it always fails (like `assert false`

).
This is useful to ignore some branches in `if`

or `match`

.
Example:

```
Test.make (list int) (function
| [] -> assume_fail ()
| _::_ as l -> List.hd l :: List.tl l = l)
```

module Gen:`sig`

..`end`

Generate Random Values

module Print:`sig`

..`end`

Show Values

module Iter:`sig`

..`end`

Iterators

module Shrink:`sig`

..`end`

Shrink Values

Observables are usable as arguments for random functions. The random function will observe its arguments in a way that is determined from the observable instance.

Inspired from https://blogs.janestreet.com/quickcheck-for-core/
and Koen Claessen's "Shrinking and Showing functions".

module Observable:`sig`

..`end`

A value of type `'a arbitrary`

glues together a random generator,
and optional functions for shrinking, printing, computing the size,
etc. It is the "normal" way of describing how to generate
values of a given type, to be then used in tests (see `QCheck.Test`

).

type`'a`

stat =`string * ('a -> int)`

A statistic on a distribution of values of type **MUST** return a positive integer.

`'a`

.
The function `type ``'a`

arbitrary = {

` ` |
`gen : ` |
|||

` ` |
`print : ` |
`(*` |
print values
| `*)` |

` ` |
`small : ` |
`(*` |
size of example
| `*)` |

` ` |
`shrink : ` |
`(*` |
shrink to smaller examples
| `*)` |

` ` |
`collect : ` |
`(*` |
map value to tag, and group by tag
| `*)` |

` ` |
`stats : ` |
`(*` |
statistics to collect and print
| `*)` |

A value of type

`'a arbitrary`

is an object with a method for generating random
values of type `'a`

, and additional methods to compute the size of values,
print them, and possibly shrink them into smaller counter-examples.
**NOTE** the collect field is unstable and might be removed, or
moved into `QCheck.Test`

.

`val make : ``?print:'a Print.t ->`

?small:('a -> int) ->

?shrink:'a Shrink.t ->

?collect:('a -> string) ->

?stats:'a stat list -> 'a Gen.t -> 'a arbitrary

Builder for arbitrary. Default is to only have a generator, but other
arguments can be added.

`val set_print : ``'a Print.t -> 'a arbitrary -> 'a arbitrary`

`val set_small : ``('a -> int) -> 'a arbitrary -> 'a arbitrary`

`val set_shrink : ``'a Shrink.t -> 'a arbitrary -> 'a arbitrary`

`val set_collect : ``('a -> string) -> 'a arbitrary -> 'a arbitrary`

`val set_stats : ``'a stat list -> 'a arbitrary -> 'a arbitrary`

`val add_stat : ``'a stat -> 'a arbitrary -> 'a arbitrary`

Add a statistic to the arbitrary instance.

**Since** 0.6

`val gen : ``'a arbitrary -> 'a Gen.t`

Access the underlying random generator of this arbitrary object.

**Since** 0.6

A test is a universal property of type `foo -> bool`

for some type `foo`

,
with an object of type `foo arbitrary`

used to generate, print, etc. values
of type `foo`

.

See `QCheck.Test.make`

to build a test, and `QCheck.Test.check_exn`

to
run one test simply.
For more serious testing, it is better to create a testsuite
and use `QCheck_runner`

.

module TestResult:`sig`

..`end`

Result of running a test

module Test:`sig`

..`end`

The infrastructure used to find counter-examples to properties can also be used to find data satisfying a predicate,

See https://github.com/c-cube/qcheck/issues/31

`exception No_example_found of ``string`

`val find_example : ``?name:string ->`

?count:int -> f:('a -> bool) -> 'a Gen.t -> 'a Gen.t

`find_example ~f gen`

uses `gen`

to generate some values of type `'a`

,
and checks them against `f`

. If such a value is found, it is returned.
Otherwise an exception is raised.
`QCheck.Test.make`

.`No_example_found`

if no example is found within `count`

tries.`name`

: description of the example to find (used in the exception).`count`

: number of attempts.`f`

: the property that the example must satisfy.`val find_example_gen : ``?rand:Random.State.t ->`

?name:string -> ?count:int -> f:('a -> bool) -> 'a Gen.t -> 'a

Toplevel version of

**Since** 0.6

**Raises**

`QCheck.find_example`

.
`find_example_gen ~f arb ~n`

is roughly the same as
`Gen.generate1 (find_example ~f arb |> gen)`

.`No_example_found`

if no example was found within `count`

tries.`rand`

: the random state to use to generate inputs.`QCheck.arbitrary`

`val choose : ``'a arbitrary list -> 'a arbitrary`

Choose among the given list of generators. The list must not
be empty; if it is Invalid_argument is raised.

`val unit : ``unit arbitrary`

Always generates

`()`

, obviously.`val bool : ``bool arbitrary`

Uniform boolean generator.

`val float : ``float arbitrary`

Generates regular floats (no nan and no infinities).

`val pos_float : ``float arbitrary`

Positive float generator (no nan and no infinities).

`val neg_float : ``float arbitrary`

Negative float generator (no nan and no infinities).

`val int : ``int arbitrary`

Int generator. Uniformly distributed.

`val int_bound : ``int -> int arbitrary`

`int_bound n`

is uniform between `0`

and `n`

included.`val int_range : ``int -> int -> int arbitrary`

`int_range a b`

is uniform between `a`

and `b`

included. `b`

must be
larger than `a`

.`val small_nat : ``int arbitrary`

Small unsigned integers.

**Since** 0.5.1

`val small_int : ``int arbitrary`

`val small_signed_int : ``int arbitrary`

Small signed integers.

**Since** 0.5.2

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

Synonym to

`QCheck.int_range`

.`val int32 : ``int32 arbitrary`

Int32 generator. Uniformly distributed.

`val int64 : ``int64 arbitrary`

Int64 generator. Uniformly distributed.

`val pos_int : ``int arbitrary`

Positive int generator. Uniformly distributed.

`val small_int_corners : ``unit -> int arbitrary`

As

`small_int`

, but each newly created generator starts with
a list of corner cases before falling back on random generation.`val neg_int : ``int arbitrary`

Negative int generator. The distribution is similar to that of

`small_int`

, not of `pos_int`

.`val char : ``char arbitrary`

Uniformly distributed on all the chars (not just ascii or
valid latin-1).

`val printable_char : ``char arbitrary`

Uniformly distributed over a subset of chars.

`val numeral_char : ``char arbitrary`

Uniformly distributed over

`'0'..'9'`

.`val string_gen_of_size : ``int Gen.t -> char Gen.t -> string arbitrary`

`val string_gen : ``char Gen.t -> string arbitrary`

Generates strings with a distribution of length of

`small_nat`

.`val string : ``string arbitrary`

Generates strings with a distribution of length of

`small_nat`

and distribution of characters of `char`

.`val small_string : ``string arbitrary`

`val small_list : ``'a arbitrary -> 'a list arbitrary`

Generates lists of small size (range

**Since** 0.5.3

`0 -- 10`

).`val string_of_size : ``int Gen.t -> string arbitrary`

Generates strings with distribution of characters if

`char`

.`val printable_string : ``string arbitrary`

Generates strings with a distribution of length of

`small_nat`

and distribution of characters of `printable_char`

.`val printable_string_of_size : ``int Gen.t -> string arbitrary`

Generates strings with distribution of characters of

`printable_char`

.`val small_printable_string : ``string arbitrary`

`val numeral_string : ``string arbitrary`

Generates strings with a distribution of length of

`small_nat`

and distribution of characters of `numeral_char`

.`val numeral_string_of_size : ``int Gen.t -> string arbitrary`

Generates strings with a distribution of characters of

`numeral_char`

.`val list : ``'a arbitrary -> 'a list arbitrary`

Generates lists with length generated by

`small_nat`

.`val list_of_size : ``int Gen.t -> 'a arbitrary -> 'a list arbitrary`

Generates lists with length from the given distribution.

`val array : ``'a arbitrary -> 'a array arbitrary`

Generates arrays with length generated by

`small_nat`

.`val array_of_size : ``int Gen.t -> 'a arbitrary -> 'a array arbitrary`

Generates arrays with length from the given distribution.

`val pair : ``'a arbitrary -> 'b arbitrary -> ('a * 'b) arbitrary`

Combines two generators into a generator of pairs.
Order of elements can matter (w.r.t shrinking, see

`QCheck.Shrink.pair`

)`val triple : ``'a arbitrary ->`

'b arbitrary -> 'c arbitrary -> ('a * 'b * 'c) arbitrary

Combines three generators into a generator of 3-tuples.
Order matters for shrinking, see

`QCheck.Shrink.pair`

and the likes`val quad : ``'a arbitrary ->`

'b arbitrary ->

'c arbitrary ->

'd arbitrary -> ('a * 'b * 'c * 'd) arbitrary

Combines four generators into a generator of 4-tuples.
Order matters for shrinking, see

`QCheck.Shrink.pair`

and the likes`val option : ``'a arbitrary -> 'a option arbitrary`

Choose between returning Some random value, or None.

`val fun1_unsafe : ``'a arbitrary -> 'b arbitrary -> ('a -> 'b) arbitrary`

Deprecated.use

Generator of functions of arity 1. The functions are always pure and total functions:

**Since** 0.6

`QCheck.fun_`

instead.Generator of functions of arity 1. The functions are always pure and total functions:

- when given the same argument (as decided by Pervasives.(=)), it returns the same value
- it never does side effects, like printing or never raise exceptions etc.
The functions generated are really printable.
renamed from
`QCheck.fun1`

.

`val fun2_unsafe : ``'a arbitrary ->`

'b arbitrary ->

'c arbitrary -> ('a -> 'b -> 'c) arbitrary

Deprecated.use

Generator of functions of arity 2. The remark about

**Since** 0.6

`QCheck.fun_`

instead.Generator of functions of arity 2. The remark about

`fun1`

also apply
here.
renamed from `QCheck.fun2`

.`type ``'_`

fun_repr

Internal data for functions. A

`'f fun_`

is a function
of type `'f`

, fundamentally.`type ``'_`

fun_ =

`|` |
`Fun : ` |

A function packed with the data required to print/shrink it. See

`QCheck.Fn`

to see how to apply, print, etc. such a function.
One can also directly pattern match on it to obtain the executable function.

For example:

```
QCheck.Test.make
QCheck.(pair (fun1 Observable.int bool) (small_list int))
(fun (Fun (_,f), l) -> l=(List.rev_map f l |> List.rev l))
```

module Fn:`sig`

..`end`

Utils on functions

`val fun1 : ``'a Observable.t ->`

'b arbitrary -> ('a -> 'b) fun_ arbitrary

`fun1 o ret`

makes random functions that take an argument observable
via `o`

and map to random values generated from `ret`

.
To write functions with multiple arguments, it's better to use `QCheck.Tuple`

or `QCheck.Observable.pair`

rather than applying `QCheck.fun_`

several times
(shrinking will be faster).module Tuple:`sig`

..`end`

`val fun_nary : ``'a Tuple.obs ->`

'b arbitrary -> ('a Tuple.t -> 'b) fun_ arbitrary

`fun_nary`

makes random n-ary functions.
Example:
```
let module O = Observable in
fun_nary Tuple.(O.int @-> O.float @-> O.string @-> o_nil) bool)
```

`val fun2 : ``'a Observable.t ->`

'b Observable.t ->

'c arbitrary -> ('a -> 'b -> 'c) fun_ arbitrary

`val fun3 : ``'a Observable.t ->`

'b Observable.t ->

'c Observable.t ->

'd arbitrary -> ('a -> 'b -> 'c -> 'd) fun_ arbitrary

`val fun4 : ``'a Observable.t ->`

'b Observable.t ->

'c Observable.t ->

'd Observable.t ->

'e arbitrary ->

('a -> 'b -> 'c -> 'd -> 'e) fun_ arbitrary

`val oneofl : ``?print:'a Print.t ->`

?collect:('a -> string) -> 'a list -> 'a arbitrary

Pick an element randomly in the list.

`val oneofa : ``?print:'a Print.t ->`

?collect:('a -> string) -> 'a array -> 'a arbitrary

Pick an element randomly in the array.

`val oneof : ``'a arbitrary list -> 'a arbitrary`

Pick a generator among the list, randomly.

`val always : ``?print:'a Print.t -> 'a -> 'a arbitrary`

Always return the same element.

`val frequency : ``?print:'a Print.t ->`

?small:('a -> int) ->

?shrink:'a Shrink.t ->

?collect:('a -> string) ->

(int * 'a arbitrary) list -> 'a arbitrary

Similar to

`QCheck.oneof`

but with frequencies.`val frequencyl : ``?print:'a Print.t ->`

?small:('a -> int) -> (int * 'a) list -> 'a arbitrary

Same as

`QCheck.oneofl`

, but each element is paired with its frequency in
the probability distribution (the higher, the more likely).`val frequencya : ``?print:'a Print.t ->`

?small:('a -> int) -> (int * 'a) array -> 'a arbitrary

Same as

`QCheck.frequencyl`

, but with an array.`val map : ``?rev:('b -> 'a) -> ('a -> 'b) -> 'a arbitrary -> 'b arbitrary`

`map f a`

returns a new arbitrary instance that generates values using
`a#gen`

and then transforms them through `f`

.`rev`

: if provided, maps values back to type `'a`

so that the printer,
shrinker, etc. of `a`

can be used. We assume `f`

is monotonic in
this case (that is, smaller inputs are transformed into smaller outputs).`val map_same_type : ``('a -> 'a) -> 'a arbitrary -> 'a arbitrary`

Specialization of

`map`

when the transformation preserves the type, which
makes shrinker, printer, etc. still relevant.`val map_keep_input : ``?print:'b Print.t ->`

?small:('b -> int) ->

('a -> 'b) -> 'a arbitrary -> ('a * 'b) arbitrary

`map_keep_input f a`

generates random values from `a`

, and maps them into
values of type `'b`

using the function `f`

, but it also keeps the
original value.
For shrinking, it is assumed that `f`

is monotonic and that smaller input
values will map into smaller values.`print`

: optional printer for the `f`

's output.