# Superclass Cycle via Associated Type

Simon Peyton-Jones simonpj at microsoft.com
Fri Jul 22 17:49:54 CEST 2011

```I talked to Dimitrios.  Fundamentally we think we should be able to handle recursive superclasses, albeit we have a bit more work to do on the type inference engine first.

The situation we think we can handle ok is stuff like Edward wants (I've removed all the methods):

class LeftModule Whole m => Additive m
class Additive m => Abelian m
class (Semiring r, Additive m) => LeftModule r m
class Multiplicative m where (*) :: m -> m -> m
class LeftModule Natural m => Monoidal m
class (Abelian m, Multiplicative m, LeftModule m m) => Semiring m
class (LeftModule Integer m, Monoidal m) => Group m
class Multiplicative m => Unital m
class (Monoidal r, Unital r, Semiring r) => Rig
class (Rig r, Group r) => Ring r

The superclasses are recursive but
a) They constrain only type variables
b) The variables in the superclass context are all
mentioned in the head.  In class Q => C a b c
fv(Q) is subset of {a,b,c}

Question to all: is that enough?

======= The main difficulty with going further ==============

Here's an extreme case
class A [a] => A a where
op :: a -> Int

f :: A a => a -> Int
f x = [[[[[x]]]]] + 1

The RHS of f needs A [[[[[a]]]]]
The type sig provides (A a), and hence (A [a]),
and hence (A [[a]]) and so on.

BUT it's hard for the solver to spot all the now-infinite number of things that are provided by the type signature.

Gabor's example is less drastic
class Immutable (Frozen a) => Mutable a where
type Frozen a
class Mutable (Thawed a) => Immutable a where
type Thawed a

but not much less drastic.  (Mutable a) in a signature has a potentially infinite number of superclasses
Immutable (Frozen a)
Mutable (Thawed (Frozen a))
...etc...

It's not obvious how to deal with this.

However Gabor's example can perhaps be rendered with a MPTC:

class (Frozen t ~ f, Thawed f ~ t) => Mutable f t where
type Frozen a
type Thawed a
unsafeFreeze :: t -> Frozen t
unsafeThaw :: f -> Thawed f

And you can do *that* today.

Simon

```

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