# Functional dependencies vs. type families

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:

http://code.haskell.org/~thielema/llvm-tf/

Here are some of my experiences:

## Contents

## 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`

.

## See also

- The llvm package converted to type families: http://code.haskell.org/~thielema/llvm-tf/
- Haskell Cafe post

## Footnotes

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