Copyright  (c) Colin Runciman et al. 

License  BSD3 
Maintainer  Roman Cheplyaka <roma@roche.info> 
Safe Haskell  Trustworthy 
Language  Haskell98 
You need this module if you want to generate test values of your own types.
You'll typically need the following extensions:
{# LANGUAGE FlexibleInstances, MultiParamTypeClasses #}
SmallCheck itself defines data generators for all the data types used by the Prelude.
In order to generate values and functions of your own types, you need
to make them instances of Serial
(for values) and CoSerial
(for
functions). There are two main ways to do so: using Generics or writing
the instances by hand.
 cons0 :: a > Series m a
 cons1 :: Serial m a => (a > b) > Series m b
 cons2 :: (Serial m a, Serial m b) => (a > b > c) > Series m c
 cons3 :: (Serial m a, Serial m b, Serial m c) => (a > b > c > d) > Series m d
 cons4 :: (Serial m a, Serial m b, Serial m c, Serial m d) => (a > b > c > d > e) > Series m e
 newtypeCons :: Serial m a => (a > b) > Series m b
 alts0 :: Series m a > Series m a
 alts1 :: CoSerial m a => Series m b > Series m (a > b)
 alts2 :: (CoSerial m a, CoSerial m b) => Series m c > Series m (a > b > c)
 alts3 :: (CoSerial m a, CoSerial m b, CoSerial m c) => Series m d > Series m (a > b > c > d)
 alts4 :: (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d) => Series m e > Series m (a > b > c > d > e)
 newtypeAlts :: CoSerial m a => Series m b > Series m (a > b)
 type Depth = Int
 data Series m a
 class Monad m => Serial m a where
 class Monad m => CoSerial m a where
 newtype Positive a = Positive {
 getPositive :: a
 newtype NonNegative a = NonNegative {
 getNonNegative :: a
 newtype NonEmpty a = NonEmpty {
 getNonEmpty :: [a]
 (\/) :: Monad m => Series m a > Series m a > Series m a
 (><) :: Monad m => Series m a > Series m b > Series m (a, b)
 (<~>) :: Monad m => Series m (a > b) > Series m a > Series m b
 (>>) :: MonadLogic m => forall a b. m a > (a > m b) > m b
 localDepth :: (Depth > Depth) > Series m a > Series m a
 decDepth :: Series m a > Series m a
 getDepth :: Series m Depth
 generate :: (Depth > [a]) > Series m a
 listSeries :: Serial Identity a => Depth > [a]
 list :: Depth > Series Identity a > [a]
 listM :: Monad m => Depth > Series m a > m [a]
 fixDepth :: Series m a > Series m (Series m a)
 decDepthChecked :: Series m a > Series m a > Series m a
 constM :: Monad m => m b > m (a > b)
Generic instances
The easiest way to create the necessary instances is to use GHC generics (available starting with GHC 7.2.1).
Here's a complete example:
{# LANGUAGE FlexibleInstances, MultiParamTypeClasses #} {# LANGUAGE DeriveGeneric #} import Test.SmallCheck.Series import GHC.Generics data Tree a = Null  Fork (Tree a) a (Tree a) deriving Generic instance Serial m a => Serial m (Tree a)
Here we enable the DeriveGeneric
extension which allows to derive Generic
instance for our data type. Then we declare that Tree a
is an instance of
Serial
, but do not provide any definitions. This causes GHC to use the
default definitions that use the Generic
instance.
One minor limitation of generic instances is that there's currently no way to distinguish newtypes and datatypes. Thus, newtype constructors will also count as one level of depth.
Data Generators
Writing Serial
instances for applicationspecific types is
straightforward. You need to define a series
generator, typically using
consN
family of generic combinators where N is constructor arity.
For example:
data Tree a = Null  Fork (Tree a) a (Tree a) instance Serial m a => Serial m (Tree a) where series = cons0 Null \/ cons3 Fork
For newtypes use newtypeCons
instead of cons1
.
The difference is that cons1
is counts as one level of depth, while
newtypeCons
doesn't affect the depth.
newtype Light a = Light a instance Serial m a => Serial m (Light a) where series = newtypeCons Light
For data types with more than 4 fields define consN
as
consN f = decDepth $ f <$> series <~> series <~> series <~> ... { series repeated N times in total }
What does consN do, exactly?
consN
has type
(Serial t_1, ..., Serial t_N) => (t_1 > ... > t_N > t) > Series t
.
consN f
is a series which, for a given depth d > 0
, produces values of the
form
f x_1 ... x_N
where x_i
ranges over all values of type t_i
of depth up to d1
(as defined by the series
functions for t_i
).
consN
functions also ensure that x_i are enumerated in the
breadthfirst order. Thus, combinations of smaller depth come first
(assuming the same is true for t_i
).
If d <= 0
, no values are produced.
cons4 :: (Serial m a, Serial m b, Serial m c, Serial m d) => (a > b > c > d > e) > Series m e #
newtypeCons :: Serial m a => (a > b) > Series m b #
Same as cons1
, but preserves the depth.
Function Generators
To generate functions of an applicationspecific argument type,
make the type an instance of CoSerial
.
Again there is a standard pattern, this time using the altsN
combinators where again N is constructor arity. Here are Tree
and
Light
instances:
instance CoSerial m a => CoSerial m (Tree a) where coseries rs = alts0 rs >> \z > alts3 rs >> \f > return $ \t > case t of Null > z Fork t1 x t2 > f t1 x t2
instance CoSerial m a => CoSerial m (Light a) where coseries rs = newtypeAlts rs >> \f > return $ \l > case l of Light x > f x
For data types with more than 4 fields define altsN
as
altsN rs = do rs < fixDepth rs decDepthChecked (constM $ constM $ ... $ constM rs) (coseries $ coseries $ ... $ coseries rs) { constM and coseries are repeated N times each }
What does altsN do, exactly?
altsN
has type
(Serial t_1, ..., Serial t_N) => Series t > Series (t_1 > ... > t_N > t)
.
altsN s
is a series which, for a given depth d
, produces functions of
type
t_1 > ... > t_N > t
If d <= 0
, these are constant functions, one for each value produced
by s
.
If d > 0
, these functions inspect each of their arguments up to the depth
d1
(as defined by the coseries
functions for the corresponding
types) and return values produced by s
. The depth to which the
values are enumerated does not depend on the depth of inspection.
alts4 :: (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d) => Series m e > Series m (a > b > c > d > e) #
newtypeAlts :: CoSerial m a => Series m b > Series m (a > b) #
Same as alts1
, but preserves the depth.
Basic definitions
Maximum depth of generated test values.
For data values, it is the depth of nested constructor applications.
For functional values, it is both the depth of nested case analysis and the depth of results.
Series
is a MonadLogic
action that enumerates values of a certain
type, up to some depth.
The depth bound is tracked in the SC
monad and can be extracted using
getDepth
and changed using localDepth
.
To manipulate series at the lowest level you can use its Monad
,
MonadPlus
and MonadLogic
instances. This module provides some
higherlevel combinators which simplify creating series.
A proper Series
should be monotonic with respect to the depth — i.e.
localDepth (+1) s
should emit all the values that s
emits (and
possibly some more).
It is also desirable that values of smaller depth come before the values of greater depth.
class Monad m => Serial m a where #
Monad m => Serial m Bool #  
Monad m => Serial m Char #  
Monad m => Serial m Double #  
Monad m => Serial m Float #  
Monad m => Serial m Integer #  
Monad m => Serial m Int #  
Monad m => Serial m () #  
Serial m a => Serial m (NonEmpty a) #  
(Num a, Ord a, Serial m a) => Serial m (NonNegative a) #  
(Num a, Ord a, Serial m a) => Serial m (Positive a) #  
Serial m a => Serial m [a] #  
Serial m a => Serial m (Maybe a) #  
(Integral i, Serial m i) => Serial m (Ratio i) #  
(CoSerial m a, Serial m b) => Serial m (a > b) #  
(Serial m a, Serial m b) => Serial m (Either a b) #  
(Serial m a, Serial m b) => Serial m (a, b) #  
(Serial m a, Serial m b, Serial m c) => Serial m (a, b, c) #  
(Serial m a, Serial m b, Serial m c, Serial m d) => Serial m (a, b, c, d) #  
class Monad m => CoSerial m a where #
coseries :: Series m b > Series m (a > b) #
A proper coseries
implementation should pass the depth unchanged to
its first argument. Doing otherwise will make enumeration of curried
functions nonuniform in their arguments.
coseries :: (Generic a, GCoSerial m (Rep a)) => Series m b > Series m (a > b) #
A proper coseries
implementation should pass the depth unchanged to
its first argument. Doing otherwise will make enumeration of curried
functions nonuniform in their arguments.
Monad m => CoSerial m Bool #  
Monad m => CoSerial m Char #  
Monad m => CoSerial m Double #  
Monad m => CoSerial m Float #  
Monad m => CoSerial m Integer #  
Monad m => CoSerial m Int #  
Monad m => CoSerial m () #  
CoSerial m a => CoSerial m [a] #  
CoSerial m a => CoSerial m (Maybe a) #  
(Integral i, CoSerial m i) => CoSerial m (Ratio i) #  
(Serial m a, CoSerial m a, Serial m b, CoSerial m b) => CoSerial m (a > b) #  
(CoSerial m a, CoSerial m b) => CoSerial m (Either a b) #  
(CoSerial m a, CoSerial m b) => CoSerial m (a, b) #  
(CoSerial m a, CoSerial m b, CoSerial m c) => CoSerial m (a, b, c) #  
(CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d) => CoSerial m (a, b, c, d) #  
Convenient wrappers
Positive x
: guarantees that x > 0
.
Positive  

newtype NonNegative a #
NonNegative x
: guarantees that x >= 0
.
(Num a, Ord a, Serial m a) => Serial m (NonNegative a) #  
Enum a => Enum (NonNegative a) #  
Eq a => Eq (NonNegative a) #  
Integral a => Integral (NonNegative a) #  
Num a => Num (NonNegative a) #  
Ord a => Ord (NonNegative a) #  
Real a => Real (NonNegative a) #  
Show a => Show (NonNegative a) #  
NonEmpty xs
: guarantees that xs
is not null
NonEmpty  

Other useful definitions
(>>) :: MonadLogic m => forall a b. m a > (a > m b) > m b #
Fair conjunction. Similarly to the previous function, consider the distributivity law for MonadPlus:
(mplus a b) >>= k = (a >>= k) `mplus` (b >>= k)
If 'a >>= k' can backtrack arbitrarily many tmes, (b >>= k) may never be considered. (>>) takes similar care to consider both branches of a disjunctive computation.
generate :: (Depth > [a]) > Series m a #
A simple series specified by a function from depth to the list of values up to that depth.
listSeries :: Serial Identity a => Depth > [a] #
Given a depth, return the list of values generated by a Serial instance.
Example, list all integers up to depth 1:
listSeries 1 :: [Int]  returns [0,1,1]
list :: Depth > Series Identity a > [a] #
Return the list of values generated by a Series
. Useful for
debugging Serial
instances.
Examples:
list 3
series
:: [Int]  returns [0,1,1,2,2,3,3]list 3 (
series
::Series
Identity
Int)  returns [0,1,1,2,2,3,3]list 2
series
:: [[Bool]]  returns [[],[True],[False]]
The first two are equivalent. The second has a more explicit type binding.
fixDepth :: Series m a > Series m (Series m a) #
Fix the depth of a series at the current level. The resulting series will no longer depend on the "ambient" depth.
decDepthChecked :: Series m a > Series m a > Series m a #
If the current depth is 0, evaluate the first argument. Otherwise, evaluate the second argument with decremented depth.