ChasingBottoms-1.3.0.8: For testing partial and infinite values.

Portability non-portable (GHC-specific) experimental http://www.cse.chalmers.se/~nad/ None

Test.ChasingBottoms.ContinuousFunctions

Description

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 non-strict, 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 non-strict 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 non-strict 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 non-monotone functions in a language like Haskell is that we are using the impure function `isBottom`.

Sometimes using possibly non-monotone 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 <=! y` implies that `f x <=! f y` for all functions `f` (whenever the latter expression returns a total result). This property is not valid in the presence of non-monotone functions.

By avoiding `isBottom` and, unlike the standard `coarbitrary` functions, deferring some pattern matches, we can generate continuous, possibly non-strict functions. There are two steps involved in generating a continuous function using the framework defined here.

1. First the argument to the function is turned into a `PatternMatch`. A `PatternMatch` wraps up the pattern match on the top-level constructor of the argument, plus all further pattern matches on the children of the argument. Just like when `coarbitrary` 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 using `match`.
2. 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 function `transform`.

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) ->
...
```

Synopsis

# 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`
```

`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 top-level 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.

Constructors

 PatternMatch Fieldsapply :: GenTransformerA generator transformer, in the style of `coarbitrary`. more :: Seq PatternMatchFurther pattern matches made possible by this match.

type GenTransformer = forall a. Gen a -> Gen aSource

The type of a generator transformer.

type MakePM a = a -> PatternMatchSource

The type of a `PatternMatch` generator.

data MakeResult a Source

Monad for generating results given previously generated pattern matches.

A `MakeResult a` should be implemented almost as other generators for the type `a`, 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.

Instances

 Monad MakeResult Functor MakeResult Applicative MakeResult

`transform` makes sure that the pattern matches get to influence the generated value. See `MakeResult`.

# Liftings of some QuickCheck functionality

lift' :: Gen a -> MakeResult aSource

Lifting of a `Gen`.

Lifting of `arbitrary`.

choose' :: Random a => (a, a) -> MakeResult aSource

Lifting of `choose`.

elements' :: [a] -> MakeResult aSource

Lifting of `elements`.

oneof' :: [MakeResult a] -> MakeResult aSource

Lifting of `oneof`.

frequency' :: [(Int, MakeResult a)] -> MakeResult aSource

Lifting of `frequency`.

sized' :: (Int -> MakeResult a) -> MakeResult aSource

Lifting of `sized`.

resize' :: Int -> MakeResult a -> MakeResult aSource

Lifting of `resize`.

# Generic `MakePM`

match :: forall a. Data a => MakePM aSource

Generic implementation of `PatternMatch` construction.

# Some `MakeResult`s

An implementation of `MakeResult a` which is suitable when `a` is flat and has an `Arbitrary` instance. Yields bottoms around 10% of the time.

This `MakeResult` yields finite partial lists.

This `MakeResult` yields infinite partial lists.

listOf :: MakeResult a -> MakeResult [a]Source

This `MakeResult` yields finite or infinite partial lists.