On Mon, Mar 24, 2008 at 12:14 AM, Manuel M T Chakravarty
One difference between type families and (value-level) functions is that not all parameters of a type family are treated the same. A type family has a fixed number of type indicies. We call the number of type indicies the type family's arity and by convention, the type indicies come always before other type parameters. In the example
type family F a :: * -> *
F has arity 1, whereas
type family G a b :: *
has arity 2. So, the number of named parameters given is the arity. (The overall kind is still F :: * -> * -> *; ie, the arity is not obvious from the kind, which I am somewhat unhappy about.)
Perhaps type families could use a different kind constructor to
distinguish type indexes from type parameters.
Currently, Haskell kinds are generated by this grammar:
kind ::= "*" | kind "->" kind
We create a new production for "family kinds",
fkind ::= kind | kind "-|>" fkind
Now, we can easily distinguish F and G,
F :: * -|> * -> *
G :: * -|> * -|> *
The grammar allows higher-kinded indexes, like (* -> *) -|> *, but
requires all indexes to precede the regular parameters. (That is, you
can't abstract over a family.)
--
Dave Menendez