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 anS
instance in a "standard" way (using..g..
), but  there are other types which have
S
instances defined differently and noC
instance at all.
Again, that is a familiar situation: every Monad
has is Applicative
with (<*>) = ap
, but nonmonadic 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 FunctorApplicativeMonad hierarchy being a case in point. If we were gifted with foresight, we might prefer an "optin" 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 optin 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. userwritten)
Functor
instances will not have a defaultfmap
implementation,  explicit
Applicative
instances will be offered the defaultfmap
from theApplicative
class declaration,  explicit
Monad
instances should be offered theMonad
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.
 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.
 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 classCrelated 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.
 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 commaseparated)
Each class declaration head should designate left of =>
the declared class's ordinary (i.e., nonintrinsic) 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 reflexivetransitive 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=>
)? rootwhere
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 ofApplicative
, but it is a defaulted member ofMonad
;fmap
is a defaulted member of bothApplicative
andMonad
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 "preempted" 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 preempted on an individual basis. For the above, we should have written
class ({# PREEMPT #}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 {# PREEMPT #}
will not contribute to an intrinsic superclass closure if the corresponding instance is explicitly in scope. A warning will be issued when this preemption 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 preemption, 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 preempt 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 preemption. 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 preemption would happen within a single instance declaration. Such preemption 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
givesOrd a => Ord (Square a)
as usual andOrd a => Eq (Square a)
with default implementation;deriving (Ord, Eq) gives
Ord a => Ord (Square a)and
Eq a => Eq (Square a)`, with no preemption warning;deriving (Ord  Eq)
gives justOrd a => Ord (Square a)
requiring a separate handrolledEq (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 complainonambiguity 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
then clients need to know whether their WhizzBanger
instances need to bring an Eq
instance or will get one. This liberalization cuts the instance
notation in class declarations but not the necessity to be aware of what it makes explicit.