Copyright  (c) Nils Anders Danielsson 20052015 

License  See the file LICENCE. 
Maintainer  http://www.cse.chalmers.se/~nad/ 
Stability  experimental 
Portability  nonportable (GHCspecific) 
Safe Haskell  None 
Language  Haskell98 
Note: This module is unfinished and experimental. However, I do not think that I will ever finish it, so I have released it in its current state. The documentation below may not be completely correct. The source code lists some things which should be addressed.
A framework for generating possibly nonstrict, partial, continuous functions.
The functions generated using the standard QuickCheck Arbitrary
instances are all strict. In the presence of partial and infinite
values testing using only strict functions leads to worse coverage
than if more general functions are used, though.
Using isBottom
it is relatively easy to generate possibly
nonstrict functions that are, in general, not monotone. For
instance, using
type Cogen a = forall b. a > Gen b > Gen b integer :: Gen Integer integer = frequency [ (1, return bottom), (10, arbitrary) ] coBool :: CoGen Bool coBool b  isBottom b = variant 0 coBool False = variant 1 coBool True = variant 2 function :: Cogen a > Gen b > Gen (a > b) function coGen gen = promote (\a > coGen a gen)
we can generate possibly nonstrict functions from Bool
to
Integer
using function coBool integer
. There is a high
likelihood that the functions generated are not monotone, though.
The reason that we can get nonmonotone functions in a language
like Haskell is that we are using the impure function isBottom
.
Sometimes using possibly nonmonotone functions is good enough,
since that set of functions is a superset of the continuous
functions. However, say that we want to test that x
implies that <=!
yf x
for all functions <=!
f yf
(whenever the
latter expression returns a total result). This property is not
valid in the presence of nonmonotone functions.
By avoiding isBottom
and, unlike the standard coarbitrary
functions, deferring some pattern matches, we can generate
continuous, possibly nonstrict functions. There are two steps
involved in generating a continuous function using the framework
defined here.
 First the argument to the function is turned into a
PatternMatch
. APatternMatch
wraps up the pattern match on the toplevel constructor of the argument, plus all further pattern matches on the children of the argument. Just like whencoarbitrary
is used a pattern match is represented as a generator transformer. The difference here is that there is not just one transformation per input, but one transformation per constructor in the input.PatternMatch
es can be constructed generically usingmatch
.  Then the result is generated, almost like for a normal
Arbitrary
instance. However, for each constructor generated a subset of the transformations from step 1 are applied. This transformation application is wrapped up in the functiontransform
.
The net result of this is that some pattern matches are performed later, or not at all, so functions can be lazy.
Here is an example illustrating typical use of this framework:
data Tree a = Branch (Tree a) (Tree a)  Leaf a deriving (Show, Typeable, Data) finiteTreeOf :: MakeResult a > MakeResult (Tree a) finiteTreeOf makeResult = sized' tree where tree size = transform $ if size == 0 then baseCase else frequency' [ (1, baseCase) , (1, liftM2 Branch tree' tree') ] where tree' = tree (size `div` 2) baseCase = frequency' [ (1, return bottom) , (2, liftM Leaf makeResult) ]
Note the use of transform
. To use this function to generate
functions of type Bool > Tree Integer
we can use
forAll (functionTo (finiteTreeOf flat)) $ \(f :: Bool > Tree Integer) > ...
 function :: MakePM a > MakeResult b > Gen (a > b)
 functionTo :: Data a => MakeResult b > Gen (a > b)
 data PatternMatch = PatternMatch {}
 type GenTransformer = forall a. Gen a > Gen a
 type MakePM a = a > PatternMatch
 data MakeResult a
 transform :: MakeResult a > MakeResult a
 lift' :: Gen a > MakeResult a
 arbitrary' :: Arbitrary a => MakeResult a
 choose' :: Random a => (a, a) > MakeResult a
 elements' :: [a] > MakeResult a
 oneof' :: [MakeResult a] > MakeResult a
 frequency' :: [(Int, MakeResult a)] > MakeResult a
 sized' :: (Int > MakeResult a) > MakeResult a
 resize' :: Int > MakeResult a > MakeResult a
 match :: forall a. Data a => MakePM a
 flat :: Arbitrary a => MakeResult a
 finiteListOf :: MakeResult a > MakeResult [a]
 infiniteListOf :: MakeResult a > MakeResult [a]
 listOf :: MakeResult a > MakeResult [a]
Basic framework
function :: MakePM a > MakeResult b > Gen (a > b) Source
Generator for continuous, not necessarily strict functions. Functions are generated by first generating pattern matches, and then generating a result.
functionTo :: Data a => MakeResult b > Gen (a > b) Source
functionTo
specialises function
:
functionTo
=function
match
data PatternMatch Source
PatternMatch
packages up the possible outcomes of a pattern
match in a style suitable for generating functions. A pattern match
is a generator (Gen
) transformer based on the toplevel
constructor, and a sequence (see
http://www.soi.city.ac.uk/~ross/software/html/Data.Sequence.html) of
PatternMatch
es based on the children of that constructor.
PatternMatch  

type GenTransformer = forall a. Gen a > Gen a Source
The type of a generator transformer.
type MakePM a = a > PatternMatch Source
The type of a PatternMatch
generator.
data MakeResult a Source
Monad for generating results given previously generated pattern matches.
A
should be implemented almost as other generators for
the type MakeResult
aa
, with the difference that transform
should be
used wherever the resulting function should be allowed to pattern
match (typically for each constructor emitted). See example above.
transform :: MakeResult a > MakeResult a Source
transform
makes sure that the pattern matches get to influence
the generated value. See MakeResult
.
Liftings of some QuickCheck functionality
lift' :: Gen a > MakeResult a Source
Lifting of a Gen
.
arbitrary' :: Arbitrary a => MakeResult a Source
Lifting of arbitrary
.
choose' :: Random a => (a, a) > MakeResult a Source
Lifting of choose
.
elements' :: [a] > MakeResult a Source
Lifting of elements
.
oneof' :: [MakeResult a] > MakeResult a Source
Lifting of oneof
.
frequency' :: [(Int, MakeResult a)] > MakeResult a Source
Lifting of frequency
.
sized' :: (Int > MakeResult a) > MakeResult a Source
Lifting of sized
.
resize' :: Int > MakeResult a > MakeResult a Source
Lifting of resize
.
Generic MakePM
match :: forall a. Data a => MakePM a Source
Generic implementation of PatternMatch
construction.
Some MakeResult
s
flat :: Arbitrary a => MakeResult a Source
An implementation of
which is suitable when MakeResult
aa
is flat and has an Arbitrary
instance. Yields bottoms around 10%
of the time.
finiteListOf :: MakeResult a > MakeResult [a] Source
This MakeResult
yields finite partial lists.
infiniteListOf :: MakeResult a > MakeResult [a] Source
This MakeResult
yields infinite partial lists.
listOf :: MakeResult a > MakeResult [a] Source
This MakeResult
yields finite or infinite partial lists.