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Functional dependencies vs. type families

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Latest revision as of 20:35, 27 January 2014

When I reported a typechecker performance problem related to functional dependencies I promised to try to convert from functional dependencies to type families.

Thus I converted my code and the llvm package to type-families:

Here are some of my experiences:


[edit] 1 Advantages of TypeFamilies

[edit] 1.1 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.)

[edit] 1.2 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
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
only if needed.

I can also easily define sub-classes like

class (IsSized a) => C a where

[edit] 1.3 Type functions in foreign declarations

A foreign import or export must not have type constraints but it can contain type functions. That is, you must not declare

foreign import ccall unsafe "llvm_convert"
   convert :: (MakeValueTuple a b) => StablePtr a -> IO (Ptr b)
for a type class
with a functional dependency from

but you can declare

foreign import ccall unsafe "llvm_convert"
   convert :: StablePtr a -> IO (Ptr (ValueTuple b))
for a type function

[edit] 1.4 No TypeSynonymInstances

At the right hand side of a
type instance
I can use type synonyms like
type instance F T = String
without the

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
in order to find the correct instance.

[edit] 1.5 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)

[edit] 1.6 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.

[edit] 2 Disadvantage of TypeFamilies

[edit] 2.1 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

[edit] 2.2 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.

[edit] 2.3 Equality constraints are not supported for newtype deriving

Not so important, just for completeness:

[edit] 3 Confusions

[edit] 3.1 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.

[edit] 3.2 Why can associated types not be exported by C(AssocType) syntax?

Why must they be exported independently from the associated class?

[edit] 3.3 FlexibleContexts

The context
(Class (TypeFun a))
extension, whereas the equivalent
(TypeFun a ~ b, Class b)
does not require

[edit] 4 See also

[edit] 5 Footnotes

This article was written in June 2012 when GHC-7.4.1 was the current version of GHC.