FitSpec provides automated assistance in the task of refining test properties
for Haskell functions.

FitSpec tests mutant variations of functions under test against a given
property set, recording any surviving mutants that pass all tests. FitSpec
then reports:

# FitSpec

FitSpec provides automated assistance in the task of refining test properties
for Haskell functions. FitSpec tests mutant variations of functions under test
against a given property set, recording any surviving mutants that pass all
tests. FitSpec then reports:

*surviving mutants:*
indicating incompleteness of properties,
prompting the user to amend a property or to add a new one;
*conjectures:*
indicating redundancy in the property set,
prompting the user to remove properties so to reduce the cost of testing.

## Installing FitSpec

To install the latest FitSpec version from Hackage, just:

```
$ cabal install fitspec
```

Pre-requisites are cmdargs and leancheck.
They should be automatically resolved and installed by Cabal.

## Using FitSpec

As an example, consider the following properties describing a `sort`

function:

```
prop_ordered xs = ordered (sort xs)
prop_length xs = length (sort xs) == length xs
prop_elem x xs = elem x (sort xs) == elem x xs
prop_notElem x xs = notElem x (sort xs) == notElem x xs
prop_min x xs = head (sort (x:xs)) == minimum (x:xs)
```

We provide the above properties to FitSpec in the following program:

```
import FitSpec
import Data.List
properties sort =
[ property $ \xs -> ordered (sort xs)
, property $ \xs -> length (sort xs) == length xs
, property $ \x xs -> elem x (sort xs) == elem x xs
, property $ \x xs -> notElem x (sort xs) == notElem x xs
, property $ \x xs -> head (sort (x:xs)) == minimum (x:xs)
]
where
ordered (x:y:xs) = x <= y && ordered (y:xs)
ordered _ = True
main = mainWith args { names = ["sort xs"]
, nMutants = 4000
, nTests = 4000
, timeout = 0
}
(sort::[Word2]->[Word2])
properties
```

The above program reports, after a few seconds, that our property set is
apparently *neither minimal nor complete*.

```
$ ./fitspec-sort
Apparent incomplete and non-minimal specification based on
4000 test cases for each of properties 1, 2, 3, 4 and 5
for each of 4000 mutant variations.
3 survivors (99% killed), smallest:
\xs -> case xs of
[0,0,1] -> [0,1,1]
_ -> sort xs
apparent minimal property subsets: {1,2,3} {1,2,4}
conjectures: {3} = {4} 96% killed (weak)
{1,3} ==> {5} 98% killed (weak)
```

*Completeness:* Of 4000 mutants, 3 survive testing against our 5 properties.
The surviving mutant is clearly not a valid implementation of `sort`

, but
indeed satisfies those properties. As a specification, the property set is
*incomplete* as it omits to require that sorting preserves the number of
occurrences of each element value: `\x xs -> count x (sort xs) == count x xs`

*Minimality:*
So far as testing has revealed, properties 3 and 4 are equivalent and property
5 follows from 1 and 3 (conjectures). It is *up to the user* to check whether
these conjectures are true. Indeed they are, so in future testing we could
safely omit properties 4 and 5.

*Refinement:* If we omit redundant properties, and add a property to kill the
surviving mutant, our refined properties are:

```
properties sort =
[ \xs -> ordered (sort xs)
, \xs -> length (sort xs) == length xs
, \x xs -> elem x (sort xs) == elem x xs
, \x xs -> count x (sort xs) == count x xs
]
```

(The implementation of `count`

is left as an exercise to the reader.)

FitSpec now reports:

```
Apparent complete but non-minimal specification based on
4000 test cases for each of properties 1, 2, 3 and 4
for each of 4000 mutant variations.
0 survivors (100% killed).
apparent minimal property subsets: {1,4}
conjectures: {4} ==> {2,3} 99% killed (weak)
```

As reported, properties 2 and 3 are implied by property 4, since that is true,
we can safely remove properties 2 and 3 to arrive at a minimal and complete
propety set.

### User-defined datatypes

If you want to use FitSpec to analyse functions over user-defined datatypes,
those datatypes should be made instances of the Listable, Mutable and
ShowMutable typeclasses. Check the Haddock documentation of each class for
how to define instances manually. If datatypes do not follow a data invariant,
instances can be automatically derived using TH by:

```
deriveMutable ''DataType
```

## More documentation

For more examples, see the eg and bench folders.

For further documentation, consult the doc folder and FitSpec API
documentation on Hackage.

(TODO: link to a possible future FitSpec paper goes here)