Intrinsic Superclasses

Note This page is a new version of the DefaultSuperclassInstances proposal, and may ultimately supplant it. For now, I'm keeping the two separate as the delta is large, superficially at least. See also on Reddit. Another proposal in this space, worthy of comparison to the one below, is here: InstanceTemplates.

The Problem

Sometimes we want to refactor the type class hierarchy, and it always hurts.

(More broadly, we have the recurrent problem of how to program defensively against progress. We may wish for benevolent evolution in the library, but we have to program against the library as it stands, and then the granting of our wishes breaks our code!)

Moreover, whether refactoring a legacy hierarchy or not, some subclasses give rise to default definitions for some of their superclasses. E.g., Ord can induce a standard definition of Eq , Monad induces Applicative , Applicative and Traversable both induce Functor . In these cases, we commonly just want the obvious default implementations and it is a nuisance to spell them out longhand.

Requirement 1: Some instance definitions in source code should generate multiple internal instances.

The typical scenario is that we have a library class

class C x where f :: ... g :: ...

but then realise that C is the "has g " special case of a useful general notion S . ( Monad and Applicative are useful real life models for C and S , respectively). We would really prefer to have had the library supply

class S x where f :: ... class S x => C x where g :: ...

The cost of putting this generalization into the library is that all the client code will break. Where the client previously wrote

instance C a => C (T a) where f = ...impl of f at type T... g = ...impl of g at type T...

she must instead write

instance C a => S (T a) where f = ...impl of f at type T... instance C a => C (T a) where g = ...impl of g at type T...

Busy people will complain bitterly that they haven't the time to add S instances everywhere, so the success of C will get in the way of insight about S . This is not a bad reason to resist making Functor and Applicative superclasses of Monad . It would have been pleasant to introduce Applicative as a generalization of Monad and somehow have all our old Monad instances generate Applicative instances too.

We want to fix things so that S can be introduced in such a way that C instances in client code yield, by default, both C and S instances internally, each with the constraints given in the client code. We do not imagine that all superclasses should have this relationship with their subclasses, but that some intrinsic superclasses might. The various definitions in client instances will need to be distributed to the appropriate internal instances of the class itself and its intrinsic superclasses.

Requirement 2: Some subclasses should give default definitions for things declared in their superclasses.

Our refactoring problem deepens when classes define default methods. What if our library defined class C with a default method for f that uses g , thus:

class C x where f :: ... f = ...g... g :: ...

Now our split hits trouble. We cannot have

class S x where f :: ... f = ...g... class S x => C x where g :: ...

because (technically) g is no longer in scope for the default f definition, and (morally) because only the S s which are also C should have that default definition anyway.

The default method for S 's method f rightly belongs in the declaration of C , not S , because

types with a C instance can be given an S instance in a "standard" way (using ..g.. ), but

instance can be given an instance in a "standard" way (using ), but there are other types which have S instances defined differently and no C instance at all.

Again, that is a familiar situation: every Monad has is Applicative with (<*>) = ap , but non-monadic Applicative instances have (<*>) defined in other ways.

Imagined solution. If only we could write something like

class S x where f :: ... class (instance S x) => C x where g :: ... f = ...g...

where the extra instance marking the superclass constraint makes S an intrinsic superclass of C . Accordingly, f can be treated as if it were a method of C , both for purposes of C 's instances, and for default definition in the C class declaration.

If this machinery had been in place when Applicative was invented, we could just have given

class (instance Functor f) => Applicative f where return :: x -> f x (<*>) :: f (a -> b) -> f a -> f b fmap = (<*>) . return class (instance Applicative m) => Monad m where (>>=) :: m a -> (a -> m b) -> m b mf <*> ma = mf >>= \ f -> ma >>= \ a -> return (f a)

Note that explicit Functor instances do not have a default implementation of fmap (that being rather the point of such instances), but that explicit Applicative and Monad would, under this proposal.

The imagined solution delivers the instance of the intrinsic superclass by default, largely motivated by the refactoring issue, which has had nontrivial negative consequences for the evolution of the library, the Functor-Applicative-Monad hierarchy being a case in point. If we were gifted with foresight, we might prefer an "opt-in" approach, where default instances can be generated cheaply but not in total silence.

Many default superclass instances are likely to define some but not all of the superclass members. E.g., we can make return a member of Applicative : we would then expect a Monad instance to define return but to acquire a default definition of <*> . An opt-in notation would need to (and could) say more than deriving Applicative .

Requirement 3: A member's most local definition is its definition.

Requirement 2 implies that the default implementation of a method might come from somewhere other than the class declaration in which the method is declared. Indeed, there might be multiple defaults. We could choose to give Monad its own specialized fmap :

class (instance Applicative m) => Monad m where fmap f ma = ma >>= \ a -> return (f a)

So now where is a default defintion for fmap both in Monad and in its superclass Applicative . We need to choose between these candidate definitions, and the obvious way to do so is to apply the existing principle that the more local overrides the more generic.

If we gave Monad a default fmap , we should then expect that

explicit (i.e. user-written) Functor instances will not have a default fmap implementation,

instances will not have a default implementation, explicit Applicative instances will be offered the default fmap from the Applicative class declaration,

instances will be offered the default from the class declaration, explicit Monad instances should be offered the Monad -specific default instead.

Requirement 4: Transitionally, we must minimize damage to client code with explicit instances now duplicated by intrinsic superclass instances.

Even if we can build a technology which supports such a treatment, we face further problems rolling it out across the legacy codebase. We hit some trouble if we take an existing subclass and make it intrinsic, e.g.,

class (instance Eq x) => Ord x where compare :: x -> x -> Ordering x == y = case compare x y of {EQ -> True; _ -> False}

because every old Ord instance will now generate an Eq instance for which a duplicate must already exist.

Worse is the situation with Monad and Applicative where we make an existing class into a new superclass and make it intrinsic: the prior constraints no longer make the whereabouts of duplicated Applicative instances particularly predictable.

Note that we might need to keep explicit instances, especially when they have weaker constraints than the defaults. E.g., if we leave it to the intrinsic machinery, we will find that

instance Monad m => Monad (StateT s m) where ...

generates

instance Monad m => Applicative (StateT s m) where ...

which would have been enough to keep alive client code just involving Monad , but misses the opportunity to weaken the constraint to

instance Applicative m => Applicative (StateT s m) where ...

The problem becomes worse when we make newly intrinsic an established superclass. We should very much dislike to have

instance Ord a => Eq [a] where ... -- overconstrained

thrust upon us.

It is far from obvious how to automate the recipe for weakening constraints in generated instances, so we shall have to be content with manual override for the time being.

As a matter of routine, client code contains "missing instances": we resent their absence from the library so we write them ourselves, and then we resent them when they are added to the library because our workaround breaks. It is not at all obvious how to mitigate this problem.

Requirement 5: Whatever mechanism we employ for generating instances, we need an explicit means to disable it.

We face not only conflicts between explicit and intrinsic instances, but also between multiple intrinsic instances. We should expect

class (instance Functor t, instance Foldable t) => Traversable t where traverse :: Applicative f => (a -> f b) -> t a -> f (t b) fmap f = runIdentity . traverse (Identity . f) foldMap f = runConst . traverse (Const . f)

but now if we define

data Square x = x :& x instance Monad Square where return x = x :& x (a :& a') >>= f = case (f a, f a') of (b :& _, _ :& b') -> b :& b' instance Traversable Square where traverse f (a :& a') = return (:&) <*> f a <*> f a'

then we have silently generated duplicate instances for Functor Square and no particular reason to choose one over the other.

Imagined solution. We might perhaps write

data Square x = x :& x instance Monad Square - Functor where ... instance Traversable Square where ...

to inhibit the Functor instance arising from Monad but retain that from Traversable . It is probably a good thing in any case to be clear about which instances should be generated and which not.

We face the same problem when we want to declare multiple intrinsic superclasses. Imagine

class (instance Monad f, instance Traversable f) => Transposable f where... instance Transposable Square where ... -- which Functor Square do I get?

because we could then derive that Functor is an intrinsic superclass of Transposable (perhaps with different default fmap definitions) in two ways. We should adopt the same solution and allow exclusions when declaring intrinsic superclasses, e.g.,

class (instance Monad f - Functor, instance Traversable f) => Transposable f where...

That is, we need a suitable language for describing which set of internal instances we mean, for use both in the heads of instance definitions and in the intrinsic superclasses of class declarations. In both cases, we need to perform a closure computation, tracing back from a given atomic constraint to find all the intrinsic superclasses which have not been explicitly excluded.

Desirable 6: The internal instances generated by an instance definition should be clear from its head and those of relevant class declarations.

When you declare an instance, you should already be aware of which superclass instances must also exist, as documented in the head of the corresponding class declaration. This proposal changes the nature of the obligation (because some superclasses will be instantiated automatically unless you choose otherwise) but the specification is in the same place.

The earlier DefaultSuperclassInstances proposal did not have this property: default superclass instances were declared and given default implementations in the bodies of class declarations, duplicating some information from the head even though they had similar impact on the instances generated.

Note that this property is in conflict with Requirement 4: to maintain legacy code, we must restrict the generation of internal instances for intrinsic superclasses with attention to the instances which otherwise exist already, so that the meaning of one instance definition vary with the presence or absence of another. We should recognize this anomaly as a necessary evil and minimize its impact.

Terminology

To nail down the technicalities of the proposal, we shall need names for things, and notation to present the things thus named.

Members, Defaults, Superclasses

Firstly, let us talk about the stuff which gets declared in classes, defined by default in classes, and defined in instances:

The members of a class C are the methods and associated type and data families which may be defined in instance definitions for C.

of a class C are the methods and associated type and data families which may be defined in instance definitions for C. A defaulted member of a class C is a member with a default definition: C instances may either omit them or override the default with an explicit definition.

of a class C is a member with a default definition: C instances may either omit them or override the default with an explicit definition. A superclass S of a class C is a class which must be given a corresponding instance for each instance of C.

We say "member" rather than "method" to include things like associated type families (which may be defaulted) and associated data families (which may not, because data constructors cannot be duplicated).

E.g., in

class Monoid c => Agglomeration c where type Element c glomOne :: Element c -> c glomList :: [Element c] -> c glomList = foldr mempty (mappend . glomOne)

Monoid is a superclass of Agglomeration , and the members are Element , glomOne and glomList , with glomList being defaulted.

These definitions make sense in Haskell as at present and are not altered by this proposal. They are phrased carefully in terms of which instances one can or must write, and which things can or must be defined in those instances. The proposal does extend how classes acquire members and how members are defaulted, as a consequence of declaring some superclasses to be intrinsic.

Immediate members, defaults and superclasses

We use the adjective "immediate" of class-C-related things to imply that the relationship is made explicit in the declaration of class C.

The immediate members of a class C are the methods and associated type and data families which are declared in the class declaration for C.

In current Haskell, all members are immediate, but this proposal introduces a distinction. When we write

class (instance Functor f) => Applicative f where return :: x -> f x (<*>) :: f (a -> b) -> f a -> f b fmap = (<*>) . return

we make fmap a member of Applicative by virtue of fmap being an immediate member of the intrinsic superclass Functor . However, fmap is not an immediate member of Applicative : the immediate members of Applicative are return and (<*>) .

Fact The name of a class member uniquely determines the class of which it is an immediate member and thus the internal instances in which its definitions belong.

An immediately defaulted member of a class C is a member of class C which is given a default definition in the declaration of C.

In current Haskell, the only defaulted members are immediately defaulted members (indeed, immediately defaulted immediate members). However, the above makes fmap an immediately defaulted member of Applicative , even though it is not an immediate member of Applicative : it is the defaulting which is immediate to the class declaration, not the membership. If we then add

class (instance Applicative m) => Monad m where (>>=) :: m a -> (a -> m b) -> m b mf <*> ma = mf >>= \ f -> ma >>= \ a -> return (f a)

without giving a further definition of fmap , then we make (<*>) an immediately defaulted member of Monad and fmap a (not immediately) defaulted member of Monad .

An immediate superclass S of a class C is any class which heads a constraint in the declaration of C.

S of a class C is any class which heads a constraint in the declaration of C. A superclass of C is either an immediate superclass of C or a superclass of an immediate superclass of C.

The above declarations make Applicative an immediate superclass of Monad and Functor an immediate superclass of Applicative . Functor is then a superclass of Monad , but not an immediate superclass.

Intrinsic superclasses, roots and closures

A class's declaration determines its immediate superclasses, thence transitively all of its superclasses. Some of those superclasses are now to be designated "intrinsic".

An intrinsic superclass of a class C is a superclass of C whose immediate members may be defined in an instance for C.

In current Haskell, this classification is well defined, even though the set it classifies is empty. But there's still time to change all that!

In the heads of class declarations, we shall need to say which superclasses are intrinsic. In the heads of instance declarations, we shall need to say which intrinsic superclasses are also being instantiated. We can do both by computing an intrinsic superclass closure from a given atomic class constraint with given explicit exclusions (e.g., Monad Square - Functor ).

An intrinsic superclass root is the pair of an atomic class constraint with a list of excluded class names.

The proposed syntax for an intrinsic superclass root is just

root ::= atom ( - Name+)?

atom ::= Name type+

(Grammar grammar: postfix ? for 0 or 1, postfix + for 1 or more, postfix ,* for 0 or more comma-separated)

Each class declaration head should designate left of => the declared class's ordinary (i.e., non-intrinsic) superclasses and its intrinsic superclass roots. The proposal is to label the latter with keyword instance , as in

class (instance Monad f - Functor, instance Traversable f) => Transposable f where...

The intrinsic superclass closure of a given intrinsic superclass root, ISC(C ts - Xs), is the set of atomic class constraints given by the reflexive-transitive closure induced by the intrinsic superclass roots given in class declarations of C and its superclasses, excluding the named classes, Xs, and their intrinsic superclasses. Hence ISC(Monad f) = {Monad f, Applicative f, Functor f} ISC(Monad f - Functor) = {Monad f, Applicative f} ISC(Monad f - Applicative) = {Monad f} ISC(Transposable f) = {Monad f, Applicative f, Traversable f, Foldable f, Functor f}

The algorithm for computing intrinsic superclass closures is made precise in the technical presentation of the proposal.

The Proposal

The following proposal satisfies Requirements 1,2,3 and 5, and Desirable 6. We shall address Requirement 4 later on this page.

New Syntax

We propose to change only the syntax of class and instance heads, allowing intrinsic superclasses declarations, instance root, in classes, and instance ... root where definitions.

toplevel ::= ...

| class (sups => )? Name name+ where declarations

| instance (constrs => )? root where definitions

sups ::= sup | ( sup,* )

sup ::= atom | instance root

constrs ::= atom | ( atom,* )

Static semantics

An intrinsic superclass root, instance S ss - Xs => C xs in a class declaration, makes S ss a superclass constraint of C xs, with at least the same static checks (e.g. cycle avoidance) which are currently enforced.

The heads of class declarations determine the intrinsic superclass closure ISC(R) of a given root R, as follows.

ISC(R) = ISC'(R, {})

ISC'(C ts - Ys, Xs) = {} if C in X; otherwise

ISC'(C ts - Ys, Xs) = {C ts} + ISC'(R1[ts/xs], Ys union Xs) +..+ ISC'(Rn[ts/xs], Ys union Xs) where class ( instance R1,.., instance Rn,A1,..,Am) => C xs

As + Bs is undefined if for some C, C ts in A and C ts' in B; otherwise, As + Bs = As union Bs

So

ISC(Monad f - Functor) = ISC'(Monad f - Functor, {}) = {Monad f} + ISC'(Applicative f, {Functor}) = {Monad f} + {Applicative f} + ISC'(Functor f, {Functor}) = {Monad f} + {Applicative f} + {} = {Monad f, Applicative f}

An additional check is required: if the declaration of class C xs results in ISC(C xs) being undefined, then class C is rejected, which is the situation exactly when you try to make something an intrinsic superclass in more than one way, as in

class (instance Monad f, instance Traversable f) => Transposable f where -- Functor twice

We also forbid

class (instance Tweedle dum, instance Tweedle dee) => Diddly dum dee where ...

because we have no uniform way to send Tweedle members to the appropriate immediate instance, but we would permit any of

class (instance Tweedle dum, Tweedle dee) => Diddly dum dee where ... class (Tweedle dum, instance Tweedle dee) => Diddly dum dee where ... class (Tweedle dum, Tweedle dee) => Diddly dum dee where ...

The members of a class C are taken to include not only the immediate members declared in C's declaration, but also the members of C's intrinsic superclasses. C's declaration may give default definitions for those of C's members (methods, type families) which admit defaulting, as in current Haskell but not restricted to immediate members.

An instance definition, instance As => R ..., is permitted exactly if the corresponding internal instances instance As => A for each A in ISC(R) would be permitted in current Haskell. Each member defined in the body must be an immediate member for some A in ISC(R), allowing us to distribute the body of a source instance to its internal instances, which are then checked by the current rules. We may now write

instance Applicative Square where pure a = a :& a (f :& g) <*> (a :& b) = f a :& g b fmap f (a :& b) = f a :& f b

or

instance Applicative Square - Functor where pure a = a :& a (f :& g) <*> (a :& b) = f a :& g b instance Functor Square fmap f (a :& b) = f a :& f b

but not

instance Applicative Square - Functor where pure a = a :& a (f :& g) <*> (a :& b) = f a :& g b fmap f (a :& b) = f a :& f b -- excluded

Instance inference is unaffected by this proposal. It applies, just as before, to the internal instances generated as indicated above, with intrinsic superclasses treated just as ordinary superclasses when deducing superclass constraints from subclass assumptions.

Dynamic Semantics

Dictionary construction is unaffected by this proposal, following the derivation of internal instances just as before. The only issue we must resolve is the selection of default definitions from what might now be a stack of intrinsic superclasses.

The defaulted members of a class C shall be the immediately defaulted members of C or the defaulted members of C's immediate intrinsic superclasses, with the immediate default definitions prioritized over the superclass defaults.

We may thus write

class (instance Functor f) => Applicative f where return, pure :: x -> f x pure = return (<*>) :: f (a -> b) -> f a -> f b fmap = (<*>) . return class (instance Applicative m) => Monad m where (>>=) :: m a -> (a -> m b) -> m b pure = return mf <*> ma = mf >>= \ f -> ma >>= \ a -> return (f a) fmap f ma = ma >>= \ a -> return (f a)

and note that

<*> is not a defaulted member of Applicative , but it is a defaulted member of Monad ;

is not a defaulted member of , but it is a defaulted member of ; fmap is a defaulted member of both Applicative and Monad but with different default definitions.

(By the way, the above negotiation with return and pure should allow existing Applicative instances to work as intended, but generate a warning that return has not been defined.)

Transitional Relief for Legacy Code

In the discussion of the static semantics, an example conspicuous by its absence is the status quo:

instance Applicative Square where pure a = a :& a (f :& g) <*> (a :& b) = f a :& g b instance Functor Square fmap f (a :& b) = f a :& f b

The proposal as it stands implies that the Applicative Square instance would generate an instance for Functor , duplicating the explicit instance. Indeed, whenever we make an existing superclass intrinsic, every instance of the subclass duplicates an instance which must exist in the legacy codebase. Think of all those deriving (Eq,Ord) s! Requirement 4 is distinctly unsatisfied.

To do better at Requirement 4, we can choose to dilute Desirable 6 by throwing out the parts of an intrinsic closure which are already "pre-empted" by explicit instances. To do so would recover the above legacy declaration, but still exclude

instance Applicative Square where pure a = a :& a (f :& g) <*> (a :& b) = f a :& g b fmap = (<*>) . pure instance Functor Square fmap f (a :& b) = f a :& f b

We should not encourage such definitions, but we surely must be able to live with them until people update to the new technology. One suitably nuanced approach might be to support a pragma in class declarations which allows intrinsic superclasses to be pre-empted on an individual basis. For the above, we should have written

class ({-# PRE-EMPT #-}instance Functor f) => Applicative f where ...

to signal that an intrinsic closure computation can be cut short at that point by an explicit instance.

Proposal An immediate intrinsic superclass marked {-# PRE-EMPT #-} will not contribute to an intrinsic superclass closure if the corresponding instance is explicitly in scope. A warning will be issued when this pre-emption happens.

This proposal requires no more checking than is already required to rule out duplicate instances: it just prioritizes the explicit instance over its implicitly generated counterpart instead of complaining.

When we make an existing superclass intrinsic, we can thus ensure no code breakage for the transitional period where we allow pre-emption, whilst issuing warnings to fix code soon.

We still face legacy problems when we make an old class into a new intrinsic superclass, as we will with Applicative for Monad . Modules which make new things Applicative and Monad ic will be fine, but if a module imports a Monad and makes it Applicative , we will have an unavoidable duplicate. It seems dangerous to allow silently generate code to pre-empt explicit code, and even if we did, we could not be sure that the generated instance would have constraints as generous as the later explicit instance, so code compiled with the latter might break against the former.

We might hope that, in future, people might become sufficiently good at deciding to make immediate superclasses intrinsic from the start that we can do away with the need for pre-emption. It seems a necessary evil now.

Multiple Instances

We might consider allowing a single instance declaration to define multiple instances explicitly, provided we retain the property that it is clear how to split their members into immediate instances and how to find default members. E.g. we might write

data Fred = Fred instance (Read Fred, Show Fred) where read _ = Fred show _ = "Fred"

Just as before, we should have to exclude

instance (Monad Square, Traversable Square) where return a = a :& a (a :& a') >>= f = case (f a, f a') of (b :& _, _ :& b') -> b :& b' traverse f (a :& a') = return (:&) <*> f a <*> f a'

because it is not clear which default Functor instance is intended. But we would allow

instance (Monad Square - Functor, Traversable Square) where return a = a :& a (a :& a') >>= f = case (f a, f a') of (b :& _, _ :& b') -> b :& b' traverse f (a :& a') = return (:&) <*> f a <*> f a'

It would seem churlish to require such definitions to exclude explicitly instances which are present explicitly in the very same header. Nor would it be in violation of Requirement 6, as the pre-emption would happen within a single instance declaration. Such pre-emption needs no warning.

Note that one could then write

instance (Monad Square, Traversable Square, Functor Square) where return a = a :& a (a :& a') >>= f = case (f a, f a') of (b :& _, _ :& b') -> b :& b' traverse f (a :& a') = return (:&) <*> f a <*> f a'

and compile to get a warning that the promised explicit Functor instance is missing its implementation of fmap .

The same logic should clearly apply to deriving clauses, so that (e.g. for Square )

deriving Ord gives Ord a => Ord (Square a) as usual and Ord a => Eq (Square a) with default implementation;

gives as usual and with default implementation; deriving (Ord, Eq) gives Ord a => Ord (Square a) and Eq a => Eq (Square a)`, with no pre-emption warning;

Ord a => Ord (Square a) Eq a => Eq (Square a)`, with no pre-emption warning; deriving (Ord - Eq) gives just Ord a => Ord (Square a) requiring a separate hand-rolled Eq (Square a) instance.

Counterfactuals

Arising from discussion, further modifications are worth considering, if only to step back from them.

Liberalization 7 Use type inference to disambiguate member distribution.

We could imagine permitting

class Foo x where foo :: x -> x class (instance Foo x, instance Foo y) => Goo x y where goo :: x -> y

and if we saw

instance Goo Int Bool where foo x = 3 foo x = True goo = (0 <)

it would be obvious that we meant

instance Foo Int where foo x = 3 instance Foo Bool where foo x = True instance Goo Int Bool where goo = (0 <)

because type information tells us which foo belongs where.

That is, we could adopt a policy of complaining only if type inference fails to disambiguate the distribution of members to internal instances.

We might need enough notation to opt out of Foo x but not Foo y . More explicit notation will be necessary whenever the given definitions. E.g.,

instance Goo Int Bool where foo 0 = 3 foo x = x foo x = True goo = (0 <)

does not establish in which instance the foo x = x line belongs.

Of course, one could reject such programs as ambiguous, but certainly, the static semantics of such a system is far more subtle than the present proposal.

Liberalization 8 Make superclasses intrinsic by default.

We could drop the use of instance to mark which superclasses are intended as intrinsic. Again adopting a complain-on-ambiguity semantics, we could generate a superclass instance automatically from a subclass instance whenever there is at least one candidate member definition: either a default in the subclass, or an explicit definition in the subclass instance. So

class Bing x where bing :: x class Bing x => Bong x where bong :: x instance Bong Int where bing = 1 bong = 0

generates a Bing Int instance too, as does

class Bing x where bing :: x class Bing x => Bong x where bong :: x bing = bong instance Bong Int where bong = 0

but

class Bing x where bing :: x class Bing x => Bong x where bong :: x instance Bong Int where bong = 0

generates only a Bong Int instance (rather than an empty Bing Int instance).

Such a proposal would require a little more subtlety to determine which instances are generated, but might be sustainable.

Certainly, it would still require authors of client code to be aware of whether a given class is likely to generate superclass instances. If I define some rather special purpose library with

class Eq x => WhizzBanger x where whizz :: x -> x -> x bang :: x -> Bool