# Testing Polysemy With polysemy-check

Last week we covered how to port an existing codebase to polysemy. The “why you might want to do this” was left implicit, but to be more explicit about things, it’s because littering your codebase with IO makes things highly-coupled and hard to test. By forcing yourself to think about effects, you are forced to pull concerns apart, and use the type-system to document what’s going on. But more importantly for today, it gives us a layer of indirection inside of which we can insert testing machinery.

To take an extreme example from the codebase I’m currently working on, compare a function with its original (non-polysemized) type:

api :: Opts -> ServerT API App

which looks very simple, and gives the false impression that api is fairly uninteresting. However, there is an amazing amount of IO hiding inside of App, which becomes significantly more evident when we give this type explicit dependency constraints:

api ::
Members
'[ AReqIDStore,
AssIDStore,
BrigAccess,
DefaultSsoCode,
Error SparError,
GalleyAccess,
IdP,
Input Opts,
Logger (Msg -> Msg)
Logger String,
Now,
Random,
Reporter,
SAML2,
SAMLUserStore,
SamlProtocolSettings,
ScimExternalIdStore,
ScimTokenStore,
ScimUserTimesStore,
]
r =>
Opts ->
ServerT API (Sem r)

Wow! Not so innocent-looking now, is it? Each Member constraint here is a unit of functionality that was previously smuggled in via IO. Not only have we made them more visible, but we’ve now exposed a big chunk of testable surface-area. You see, each one of these members provides an abstract interface, which we can implement in any way we’d like.

Because IO is so hard to test, the idea of polysemy is that we can give several interpretaions for our program — one that is pure, lovely, functional, and, importantly, very easy to test. Another interpretation is one that runs fast in IO. The trick then is to decompose the problem of testing into two steps:

1. show that the program is correct under the model interpreter
2. show that the model interpreter is equivalent to the real interpreter

This sounds great in principle, but as far as I know, it’s never been actually done in practice. My suspicion is that people using polysemy in the wild don’t get further than step 1 (which is OK — a good chunk of the value in effect systems is in the decomposition itself.) Doing all of the work to show equivalence of your interpreters is a significant amount of work, and until now, there have been no tools to help.

Introducing polysemy-check: a new library for proving all the things you’d want to prove about a polysemy codebase. polysemy-check comes with a few tools for synthesizing QuickCheck properties, plus machinery for getting Arbitrary instances for effects for free.

## Using polysemy-check🔗

To get started, you’re going to need to give two instances for every effect in your system-under-test. Let’s assume we have a stack effect:

data Stack s m a where
Push :: s -> Stack s m ()
Pop :: Stack s m (Maybe s)
RemoveAll :: Stack s m ()
Size :: Stack s m Int

makeSem ''Stack

The instances we need are given by:

deriving instance (Show s, Show a) => Show (Stack s m a)
deriveGenericK ''Stack

where deriveGenericK is TemplateHaskell that from kind-generics (but is re-exported by polysemy-check.) kind-generics is GHC.Generics on steroids: it’s capable of deriving generic code for GADTs.

The first thing that probably comes to mind when you consider QuickCheck is “checking for laws.” For example, we should expect that push s followed by pop should be equal to pure (Just s). Laws of this sort give meaning to effects, and act as sanity checks on their interpreters.

Properties for laws can be created via prepropLaw:

prepropLaw
:: forall effs r a f
. ( (forall z. Eq z => Eq (f z))
, (forall z. Show z => Show (f z))
)
=> ( Eq a
, Show a
, ArbitraryEff effs r
)
=> Gen (Sem r a, Sem r a)
-> (forall z. Sem r (a, z) -> IO (f (a, z)))
-> Property

Sorry for the atrocious type. If you’re looking for Boring Haskell, you’d best look elsewhere.

The first argument here is a QuickCheck generator which produces two programs that should be equivalent. The second argument is the interpreter for Sem under which the programs must be equivalent, or will fail the resulting Property. Thus, we can write the push/pop law above as:

law_pushPop
:: forall s r f effs res
. (
-- The type that our generator returns
res ~ (Maybe s)

-- The effects we want to be able to synthesize for contextualized
-- testing
, effs ~ '[Stack s]

-- Misc constraints you don't need to care about
, Arbitrary s
, Eq s
, Show s
, ArbitraryEff effs r
, Members effs r
, (forall z. Eq z => Eq (f z))
, (forall z. Show z => Show (f z))
)
=> (forall a. Sem r (res, a) -> IO (f (res, a)))
-> Property
law_pushPop = prepropLaw @effs \$ do
s <- arbitrary
pure ( push s >> pop
, pure (Just s)
)

Sorry. Writing gnarly constraints is the cost not needing to write gnarly code. If you know how to make this better, please open a PR!

There’s something worth paying attention to in law_pushPop — namely the type of the interpreter (forall a. Sem r (Maybe s, a) -> IO (f (Maybe s, a))). What is this forall a thing doing, and where does it come from? As written, our generator would merely checks the equivalence of the exact two given programs, but this is an insufficient test. We’d instead like to prove the equivalence of the push/pop law under all circumstances.

Behind the scenes, prepropLaw is synthesizing a monadic action to run before our given law, as well as some actions to run after it. These actions are randomly pulled from the effects inside the effs ~ '[Stack s] row (and so here, they will only be random Stack actions.) The a here is actually the result of these “contextual” actions. Complicated, but you really only need to get it right once, and can copy-paste it forevermore.

Now we can specialize law_pushPop (plus any other laws we might have written) for a would-be interpreter of Stack s. Any interpreter that passes all the properties is therefore proven to respect the desired semantics of Stack s.

## Wrapping Up🔗

polysemy-check can do lots more, but this post is overwhelming already. So next week we’ll discuss how to prove the equivalence of interpreters, and how to ensure your effects are sane with respect to one another.