Module `QCheck2.Gen`

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:

primitive generators
generator compositions

type 'a t

A random generator for values of type 'a.

type 'a sized = int -> 'a t

Random generator with a size bound.

Primitive generators

val unit : unit t

The unit generator.

Does not shrink.

val bool : bool t

The boolean generator.

Shrinks towards false.

val int : int t

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.

val small_nat : int t

Small positive integers (< 100, 0 included).

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

Shrinks towards 0.

since 0.5.1

val nat : int t

Generates natural numbers (< 10_000).

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

Shrinks towards 0.

val big_nat : int t

Generates natural numbers, possibly large (< 1_000_000).

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

Shrinks towards 0.

since 0.10

val neg_int : int t

Generates non-strictly negative integers (0 included).

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

Shrinks towards 0.

val small_int : int t

Small UNSIGNED integers, for retrocompatibility.

Shrinks towards 0.

deprecated
use small_nat.

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.

since 0.5.2

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.

val int32 : int32 t

Generates uniform int32 values.

Shrinks towards 0l.

val ui32 : int32 t

Generates int32 values.

Shrinks towards 0l.

deprecated
use int32 instead, the name is wrong, values are signed.

val int64 : int64 t

Generates uniform int64 values.

Shrinks towards 0L.

val ui64 : int64 t

Generates int64 values.

Shrinks towards 0L.

deprecated
use int64 instead, the name is wrong, values are signed.

val float : float t

Generates floating point numbers.

Shrinks towards 0..

val pfloat : float t

Generates positive floating point numbers (0. included).

Shrinks towards 0..

val nfloat : float t

Generates negative floating point numbers. (-0. included).

Shrinks towards -0..

val char : char t

Generates characters in the 0..255 range.

Shrinks towards 'a'.

val printable : char t

Generates printable characters.

The exhaustive list of character codes is:

32 to 126, inclusive
'\n'

Shrinks towards 'a' or lower character codes.

val numeral : char t

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.

since 0.20

val bytes : bytes t

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.

since 0.20

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.

since 0.20

val bytes_printable : bytes t

Generator using the printable character generator.

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

since 0.20

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.

since 0.20

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.

since 0.20

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.

val string : string t

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.

since 0.11

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.

since 0.11

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.

since 0.20

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.

since 0.20

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.

val pure : 'a -> 'a t

pure a creates a generator that always returns a.

Does not shrink.

since 0.8

val return : 'a -> 'a t

Synonym for pure

val make_primitive : 
  gen:(Stdlib.Random.State.t -> 'a) ->
  shrink:('a -> 'a Stdlib.Seq.t) ->
  'a t

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

since 0.8

deprecated
is this function still useful? I feel like it is either useless (invariants should already be part of the shrinking logic, not be added later) or a special, incomplete case of Gen.t being an Alternative (not implemented yet). For now we keep it and wait for users feedback (hence deprecation to raise attention).

val set_shrink : ('a -> 'a Stdlib.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.

raises Invalid_argument
if the argument is negative.

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)

raises Invalid_argument
if any of the following holds:
- low > high
- origin < low
- origin > high

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..

since 0.11

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..

raises Invalid_argument
if bound is 0..

since 0.11

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)

raises Invalid_argument
if any of the following holds:
- low > high
- high -. low > max_float
- origin < low
- origin > high

since 0.11

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

a --. b is an alias for float_range ~origin:a a b. See float_range for more information.

since 0.11

val exponential : float -> float t

exponential m generates floating-point numbers following an exponential distribution with a mean of m.

raises Invalid_argument
if m is NaN.

since 0.23

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.

raises Invalid_argument
if low > high.

since 0.13

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.

raises Invalid_argument
or Failure if l is empty

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.

raises Invalid_argument
or Failure if l is empty

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.

raises Invalid_argument
or Failure if l is empty

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".

since 0.11

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.

since 0.6

val int_pos_corners : int list

Non-negative corner cases for int.

since 0.6

val int_corners : int list

All corner cases for int.

since 0.6

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.

since 0.5.3

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.

since 0.10

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.

parameter ratio
a float between 0. and 1. indicating the probability of a sample to be Some _ rather than None (value is 0.85).

since 0.19 (renamed from [opt])

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.

since 0.5.1

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.

since 0.13

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.

since 0.13

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

Generate an option from an optional generator.

Shrinks towards None then shrinks on the value.

since 0.13

val flatten_res : ('a t, 'e) Stdlib.result -> ('a, 'e) Stdlib.result t

Generate a result from Ok gen, an error from Error e.

Shrinks on gen if Ok gen. Does not shrink if Error e.

since 0.13

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

Collapses a generator of generators to a generator.

Shrinks on the generated generators.

since 0.5

Influencing the size of generated values

val sized : 'a sized -> 'a t

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.

since 0.5

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.

since 0.17

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

An infix synonym for map

since 0.13

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

Synonym for ap

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

Synonym for bind

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.

val generate : ?rand:Stdlib.Random.State.t -> n:int -> 'a t -> 'a list

generate ~n gen generates n values using gen (shrinks are discarded).

val generate1 : ?rand:Stdlib.Random.State.t -> 'a t -> 'a

generate1 gen generates one instance of gen (shrinks are discarded).

val generate_tree : ?rand:Stdlib.Random.State.t -> 'a t -> 'a Tree.t

generate_tree ?rand gen generates a random value and its shrinks using gen.