[haskell-llvm] converting functional dependencies to type families
Henning Thielemann
lemming at henning-thielemann.de
Tue Jun 5 23:10:09 BST 2012
Hi all,
when I reported a typechecker performance problem related to functional
dependencies
http://hackage.haskell.org/trac/ghc/ticket/5970
I promised to try to convert from functional dependencies to type
families.
Thus I converted my code and the llvm package to type-families:
http://code.haskell.org/~thielema/llvm-tf/
Here are some of my experiences:
== Advantages of TypeFamilies ==
* Speed
For what I did the type families solution was considerably faster than the
functional dependencies code at least in GHC-7.4.1. Thus the bug in ticket
5970 does no longer hurt me. (In GHC-6.12.3 the conversion to type
families made the compilation even slower.)
* Anonymous type function values
One of the most annoying type classes of the llvm package was the IsSized
class:
class (LLVM.IsType a, IsPositive size) => IsSized a size | a -> size
where size is a type-level decimal natural number.
Many llvm functions require that an LLVM type has a size where the
particular size is not important. However, I always have to name the size
type. I also cannot get rid of it using a subclass, like
class (IsSized a size) => IsAnonymouslySized a where
The 'size' type is somehow sticky.
The conversion of this type class to type families is straightforward:
class (IsType a, PositiveT (SizeOf a)) => IsSized a where
type SizeOf a :: *
Now I have to use SizeOf only if needed. I can also easily define
sub-classes like
class (IsSized a) => C a where
* No TypeSynonymInstances
At the right hand side of a 'type instance' I can use type synonyms like
type instance F T = String
without the TypeSynonymInstance extension. This feels somehow more correct
than refering to a type synonym in a class instance head like in
instance C T String where
The compiler does not need to analyze String in order to find the correct
instance.
* No FlexibleInstances
The same applies to
instance C (T a) (A (B a))
which is a flexible instance that is not required for
type instance F (T a) = A (B a)
* No MultiParamTypeClass, No UndecidableInstances
I have some type classes that convert a type to another type and a tuple
of types to another tuple of types where the element types are converted
accordingly. With functional dependencies:
class MakeValueTuple haskellTuple llvmTuple | haskellTuple -> llvmTuple where
instance (MakeValueTuple ha la, MakeValueTuple hb lb) =>
MakeValueTuple (ha,hb) (la,lb)
The class is a multi-parameter type class and the instance is undecidable.
This is much simpler with type families:
class MakeValueTuple haskellTuple where
type ValueTuple haskellTuple :: *
instance (MakeValueTuple ha, MakeValueTuple hb) =>
MakeValueTuple (ha,hb) where
type ValueTuple (ha,hb) = (ValueTuple ha, ValueTuple hb)
Thus summarized: Type families may replace several other type extensions.
If I ignore the associated type functions then many classes become Haskell
98 with Haskell 98 instances. This is good because those instances prevent
instance conflicts with other non-orphan instances.
== Disadvantage of TypeFamilies ==
* Redundant instance arguments
I have to write the type arguments both in the instance head and in the
function argument. This is especially annoying in the presence of
multi-parameter type classes with bidirectional dependencies. E.g.
class (a ~ Input parameter b, b ~ Output parameter a) => C parameter a b where
type Input parameter b :: *
type Output parameter a :: *
process :: Causal p (parameter, a) b
instance (...) => C (FilterParam a) v (FilterResult v) where
type Input (FilterParam a) (FilterResult v) = v
type Output (FilterParam a) v = FilterResult v
With functional dependencies it was:
class C parameter a b | parameter a -> b, parameter b -> a where
process :: Causal p (parameter, a) b
instance (...) => C (FilterParam a) v (FilterResult v) where
* Bidirectional dependencies
In GHC-6.12.3 it was not possible to write
class (a ~ Back b, b ~ Forth a) => C a b where
Fortunately, this is now allowed in GHC-7. But bidirectional dependencies
are still cumbersome to work with as shown in the example above.
* Equality constraints are not supported for newtype deriving
Not so important, just for completeness:
http://hackage.haskell.org/trac/ghc/ticket/6088
== Confusions ==
* Upper case type function names
Why are type function names upper case, not lower case? They are not
constructors after all. Maybe this is one reason, why I forget from time
to time that type functions are not injective.
Sure, lower-case type variables are implicitly forall quantified in
Haskell 98. In the presence of lower-case type functions we would need
explicit forall quantification.
* Why can associated types not be exported by C(AssocType) syntax?
Why must they be exported independently from the associated class?
* FlexibleContexts
The context (Class (TypeFun a)) requires FlexibleContexts extension,
whereas the equivalent (TypeFun a ~ b, Class b) does not require
FlexibleContexts.
Best,
Henning
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