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Library

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The library takes inspiration from Haskell's QuickCheck library. The rough idea is that the programer describes invariants that values of a certain type need to satisfy ("properties"), as functions from this type to bool. She also needs to desribe 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:

`'aarbitrary`

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`Gen`

,`Print`

, and`Shrink`

can be used along with`make`

to build one's own arbitrary instances.

`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.

Examples:

- List.rev is involutive:

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

- generate 20 random trees using
`Arbitrary.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.

`b1 ==> b2`

is the logical implication `b1 => b2`

ie `not b1 || b2`

(except that it is strict and will interact better with `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 `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 `assume`

.

`assume cond`

checks the precondition `cond`

, and does nothing if `cond=true`

. If `cond=false`

, it interrupts the current test.

**WARNING** This function, like `(==>)`

, 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)
```

`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`

`module Print : sig ... end`

`module Iter : sig ... end`

`module Shrink : 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 `Test`

)

`type 'a arbitrary = {`

`gen : 'a Gen.t;`

`print : ('a -> string) option;`

(*print values

*)`small : ('a -> int) option;`

(*size of example

*)`shrink : 'a Shrink.t option;`

(*shrink to smaller examples

*)`collect : ('a -> string) option;`

(*map value to tag, and group by tag

*)

`}`

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 counterexamples

**NOTE** the collect field is unstable and might be removed, or moved into `Test`

.

```
val make :
?print:'a Print.t ->
?small:('a -> int) ->
?shrink:'a Shrink.t ->
?collect:('a -> string) ->
'a Gen.t ->
'a arbitrary
```

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

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 `Test.make`

to build a test, and `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`

`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

`val small_int : int arbitrary`

Small signed integers. See `Gen.small_int`

.

`val int32 : int32 arbitrary`

int32 generator. Uniformly distributed

`val int64 : int64 arbitrary`

int 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`

uniformy distributed over `'0'..'9'`

generates strings with a distribution of length of `small_int`

`val string : string arbitrary`

generates strings with a distribution of length of `small_int`

and distribution of characters of `char`

generates strings with distribution of characters if `char`

`val printable_string : string arbitrary`

generates strings with a distribution of length of `small_int`

and distribution of characters of `printable_char`

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_int`

and distribution of characters of `numeral_char`

generates strings with a distribution of characters of `numeral_char`

generates lists with length from the given distribution

generates arrays with length from the given distribution

combines two generators into a generator of pairs

combines three generators into a generator of 3-tuples

```
val quad :
'a arbitrary ->
'b arbitrary ->
'c arbitrary ->
'd arbitrary ->
('a * 'b * 'c * 'd) arbitrary
```

combines four generators into a generator of 4-tuples

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.

generator of functions of arity 2. The remark about `fun1`

also apply here.

Pick an element randomly in the list

Pick an element randomly in the array

```
val frequency :
?print:'a Print.t ->
?small:('a -> int) ->
?shrink:'a Shrink.t ->
?collect:('a -> string) ->
(int * 'a arbitrary) list ->
'a arbitrary
```

Similar to `oneof`

but with frequencies

Same as `oneofl`

, but each element is paired with its frequency in the probability distribution (the higher, the more likely)

Same as `frequencyl`

, but with an array

`map f a`

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

and then transforms them through `f`

.

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

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