[Haskell-cafe] working through "Part I: Dependent Types in Haskell"

Nicholls, Mark nicholls.mark at vimn.com
Mon Apr 27 11:52:53 UTC 2015


working through


but a bit stuck...with an error...

> {-# LANGUAGE DataKinds, TypeFamilies, TypeOperators, UndecidableInstances, GADTs, StandaloneDeriving #-}

> data Nat = Z | S Nat

> data Vector a n where
>   Nil  :: Vector a Z
>   (:-) :: a -> Vector a n -> Vector a (S n)
> infixr 5 :-

I assume init...is a bit like tail but take n - 1 elements from the front....but...

> init' :: Vector a ('S n) -> Vector a n
> init' (x1 :- Nil) = Nil
> init' (x :- xs) = x :- (init' xs)

gives...(I could do with working out what haskell is tryign to tell me).

Could not deduce (n1 ~ 'S n0)
    from the context ('S n ~ 'S n1)
      bound by a pattern with constructor
                 :- :: forall a (n :: Nat). a -> Vector a n -> Vector a ('S n),
               in an equation for 'init''
      at cafe.lhs:13:10-16
      'n1' is a rigid type variable bound by
           a pattern with constructor
             :- :: forall a (n :: Nat). a -> Vector a n -> Vector a ('S n),
           in an equation for 'init''
           at cafe.lhs:13:10
    Expected type: Vector a n
      Actual type: Vector a ('S n0)
    Relevant bindings include
      xs :: Vector a n1 (bound at cafe.lhs:13:15)
    In the expression: x :- (init' xs)
    In an equation for 'init'': init' (x :- xs) = x :- (init' xs)

the ":-" in "init' (x :- xs)"
has type
forall a (n :: Nat). a -> Vector a n -> Vector a ('S n)

yep that makes sense....

if it knew "n ~ n1" then it knows "n1 ~ 'S n0"

so it would know "n ~ 'S n0"

but it only knows "'S n ~ 'S n1"

hmmmm...surely from the def of Nat, thats "obvious"


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