Yes, you can do this. Enable ConstraintKinds, import Data.Type.Bool and something exporting Constraint, and change your Add constructor to Add :: (r ~ Or t t', If (Not r) (t ~ 'False, t' ~ 'False) (() :: Constraint) => Expr t -> Expr t' -> Expr r Then both eval and eval' are accepted. There may be some cleaner way; I'm no expert. On Dec 7, 2016 2:43 AM, "Guillaume Bouchard" < guillaum.bouchard+haskell@gmail.com> wrote: Hi. I have the following GADT : ----------------------------- type family Or a b where Or 'False 'False = 'False Or _ _ = 'True data Expr t where Add :: Expr t -> Expr t' -> Expr (Or t t') Lit :: Int -> Expr 'False Var :: Expr 'True ---------------------- The idea is that if the `Expr` contains a sub `Var`, its type is `Expr 'True`, else it is `Expr 'False`. I now want to evaluate my expression, something like that : -------------- eval :: Expr t -> Int eval (Lit i) = i eval (Add a b) = eval a + eval b eval Var = error "Cannot evaluate expression with variable" ---------------- Using the GADT I previously defined, I'm tempted to remove the impossible "Var" case with : --------------- eval' :: Expr 'False -> Int eval' (Lit i) = i eval' (Add a b) = eval' a + eval' b ---------------- However this does not typecheck because GHC cannot deduce that `a` and `b` are `~ Expr 'False`. Because the type family `Or` is not injective. The wiki https://ghc.haskell.org/trac/ghc/wiki/InjectiveTypeFamilies classifies injectives types families in three categories, but I don't think my `Or` appears in any of them. Actually `Or` is injective only if `Or t t' ~ 'False` and in this case, we can deduce that `t ~ 'False` and `t' ~ 'False`. I qualify it as a "partialy injective type family". The type checker does not know that, hence my code does not compile. Is there a solution, other than writing a custom type checker plugin? Is there a way to provide the inverse type family function, something such as: type family InverseOr a where InverseOr 'False = ('False, 'False) Thank you. -- G. _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.