Type-indexed type fingerprints

I have the feeling that it might well be possible to reduce the size of the trusted codebase somewhat by introducing type-indexed fingerprints. Imagine

data TypeRep (a :: k) where
    TrTyCon :: {-# UNPACK #-} !FingerprintIx a -> !TyCon -> [SomeTypeRep]
            -> TypeRep (a :: k)
    TrApp   :: forall k1 k2 (a :: k1 -> k2) (b :: k1).
               {-# UNPACK #-} !FingerprintIx (a b)
            -> TypeRep (a :: k1 -> k2)
            -> TypeRep (b :: k1)
            -> TypeRep (a b)
    TrFun   :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
                      (a :: TYPE r1) (b :: TYPE r2).
               {-# UNPACK #-} !FingerprintIx (a -> b)
            -> TypeRep a
            -> TypeRep b
            -> TypeRep (a -> b)

We could have some primitive operations like

mkFunFP :: FingerPrintIx a -> FingerPrintIx b -> FingerPrintIx (a -> b)
mkAppFP :: FingerPrintIx (a -> b) -> FingerPrintIx a -> FingerPrintIx b

eq :: FingerPrintIx a -> FingerPrintIx b -> Maybe (a :~~: b)
eqE :: FingerPrintIx a -> FingerPrintIx b -> Either (a :~~: b -> c) (a :~~: b)

Trac metadata

Trac field	Value
Version	8.2.1
Type	FeatureRequest
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Core Libraries
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