On 14 April 2010 03:48, Brent Yorgey <byor...@seas.upenn.edu> wrote:
> Can someone more well-versed in the intricacies of type checking with
> associated types explain this? Or is this a bug in GHC?
Hi Brent
Maybe you can't compose linear maps of the same type, and thus can't
build a valid monoid instance?
If you take the definition of append out out the class - GHCi will
give it a type:
> append (Affine a2 b2) (Affine a1 b1) = Affine (a2 *.* a1) (lapply a2 b1 ^+^
> b2)
*VectorSpace> :t append
append
:: (Scalar v ~ Scalar v1,
Basis v ~ Basis u,
Basis v1 ~ Basis v,
VectorSpace v1,
HasTrie (Basis v),
HasBasis v,
HasBasis u) =>
Affine v1 -> Affine v -> Affine v1
If you add that type back to the file containing append it no longer
type checks...
VectorSpaceTest.hs:44:54:
Couldn't match expected type `Basis u'
against inferred type `Basis u1'
NB: `Basis' is a type function, and may not be injective
Expected type: u :-* v
Inferred type: v :-* v
In the second argument of `(*.*)', namely `a1'
In the first argument of `Affine', namely `(a2 *.* a1)'
Failed, modules loaded: none.
[ It also has the problem that its type isn't compatible with monoidal
mappend anyway ]
You can get empty to type check with this signature:
empty :: (HasTrie u, u ~ Basis v, HasBasis v) => Affine v
But trying to get append to type check with the same class constraints...
append :: (HasTrie u, u ~ Basis v, HasBasis v)
=> Affine v -> Affine v -> Affine v
... gets another error where the inferred type of 'LinearMap' is from
one type to the same type:
VectorSpaceTest.hs:33:54:
Couldn't match expected type `Basis u' against inferred type `u1'
`u1' is a rigid type variable bound by
the type signature for `append' at VectorSpace.hs:31:19
NB: `Basis' is a type function, and may not be injective
Expected type: u :-* v
Inferred type: v :-* v
In the second argument of `(*.*)', namely `a1'
In the first argument of `Affine', namely `(a2 *.* a1)'
Failed, modules loaded: none.
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