Values of custom types usually have invariants imposed upon them. In this post I motivate and announce the `validity`

, `genvalidity`

and `genvalidity-hspec`

libraries that have just come out.

Contrary to what we might like to think, an absence of compilation errors does not imply correctly functioning code. In some cases we expect some invariants to hold about our data, but we don't necessarily check them rigorously.

This is a situation in which the typesystem may be expensive to use to guarantee correctness. That's why we will use testing instead.

## A running example

I will take a contrived example to keep the blogpost short. Assume we have the following context:

```
-- | [...]
-- INVARIANT >= 2
newtype GreaterThanOne
= GreaterThanOne Int
-- | [...]
-- INVARIANT >= 2
-- INVARIANT must be a prime
newtype Prime
= Prime Int
```

For now, we just assume that invariants hold. If we now want to write a safe `primeFactorisation`

function, it might have the following type.

`primeFactorisation :: GreaterThanOne -> Maybe [Prime]`

Now we will go on to how we can actually make this safe and test the validity assumptions.

## Validity

To be able to express the invariants that we would like to enforce on our data, we can write the following function:

`myDataIsValid :: MyData -> Bool`

We express, in code, exactly what it means for a `MyData`

to be valid. That way we can later check whether our `MyData`

is valid.

This is the validity package comes in. It is really simple and contains not much more than the following type class, but it opens up some possibilities which I will talk about in the rest of this post.

```
class Validity a where
isValid :: a -> Bool
```

In the case of the running example, the `Validity`

instances could look as follows.

```
instance Validity GreaterThanOne where
GreaterThanOne n) = n >= 2
isValid (
isPrime :: Int -> Bool
instance Validity Prime where
Prime n) = n >= 2 && isPrime n isValid (
```

## Genvalidity

Now that we have this concept of `Validity`

, we can start writing tests using it. We will ignore the tests which assert that the output is a valid prime factorisation for now. We can then write the following tests with respect to validity:

```
"primeFactorisation" $ do
describe "fails for invalid GreaterThanOne's" $
it GreaterThanOne <$> arbitrary) `suchThat` (not . isValid)) $ \i ->
forAll ((`shouldBe` Nothing
primeFactorisation i
"produces valid primes if it succeeds" $
it GreaterThanOne <$> arbitrary) $ \i ->
forAll (case primeFactorisation i of
Nothing -> return () -- Can happen
Just ps -> ps `shouldSatisfy` all isValid
```

This is quite a mouthful, isn't it? There are also some non-stylistic problems:

`someGenerator `suchThat` (not . isValid)`

runs`someGenerator`

and retries as long as`isValid`

is satisfied. For types that are mostly valid, this can take a long time and will slow down testing significantly.Generators like

`GreaterThanOne <$> arbitrary`

become quite large (in code) for larger structures. Ideally we would only write them once.

Enter genvalidity. `genvalidity`

provides a typeclass called `GenValidity`

:

```
class Validity a => GenValidity a where
genUnchecked :: Gen a
genValid :: Gen a
= genUnchecked `suchThat` isValid
genValid
genInvalid :: Gen a
= genUnchecked `suchThat` (not . isValid) genInvalid
```

When you instantiatie `GenValidity`

for your custom data type, tests involving `isValid`

become much easier to write:

```
"primeFactorisation" $ do
describe "fails for invalid GreaterThanOne's" $
it $ \i ->
forAll genInvalid `shouldBe` Nothing
primeFactorisation i
"produces valid primes if it succeeds" $
it $ \i ->
forAll genUnchecked case primeFactorisation i of
Nothing -> return () -- Can happen
Just ps -> ps `shouldSatisfy` isValid
```

`genInvalid`

Has a default implementation, but when generating `GreaterThanOne`

s, on average 50% of all generations have to be retried at least once. We can specialize this implementation to run faster by using an absolute value function:

```
class GenValidity GreaterThanOne where
= GreaterThanOne <$> arbitrary
genUnchecked = (GreaterThanOne . abs) <$> arbitrary genValid
```

## Standard tests

We can use these new toys to write tests as described above, but we can also use some of the standard tests that are available via `genvalidity-hspec`

. For example, the above tests can be rewritten as follows:

```
"primeFactorisation" $ do
describe "fails for invalid GreaterThanOne's" $
it
failsOnInvalidInput primeFactorisation
"produces valid primes if it succeeds" $
it validIfSucceeds primeFactorisation
```

Because we have now written a custom implementation of `genValid`

for `GreaterThanOne`

, we should also add the `validitySpec`

:

`Proxy :: Proxy GreaterThanOne) validitySpec (`

This will ensure that `genValid`

and `genInvalid`

keep working as intended. However, it cannot check that all possible valid(/invalid) values can still be generated by `genValid`

(/`genInvalid`

), so be careful and check that yourself.