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<p class="MsoNormal">Hello,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">working through <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">https://www.fpcomplete.com/user/konn/prove-your-haskell-for-great-safety/dependent-types-in-haskell<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">but a bit stuck...with an error...<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> {-# LANGUAGE DataKinds, TypeFamilies, TypeOperators, UndecidableInstances, GADTs, StandaloneDeriving #-}<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data Nat = Z | S Nat<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data Vector a n where<o:p></o:p></p>
<p class="MsoNormal">> Nil :: Vector a Z<o:p></o:p></p>
<p class="MsoNormal">> (:-) :: a -> Vector a n -> Vector a (S n)<o:p></o:p></p>
<p class="MsoNormal">> infixr 5 :-<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I assume init...is a bit like tail but take n - 1 elements from the front....but...<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> init' :: Vector a ('S n) -> Vector a n<o:p></o:p></p>
<p class="MsoNormal">> init' (x1 :- Nil) = Nil<o:p></o:p></p>
<p class="MsoNormal">> init' (x :- xs) = x :- (init' xs) <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">gives...(I could do with working out what haskell is tryign to tell me).<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Could not deduce (n1 ~ 'S n0)<o:p></o:p></p>
<p class="MsoNormal"> from the context ('S n ~ 'S n1)<o:p></o:p></p>
<p class="MsoNormal"> bound by a pattern with constructor<o:p></o:p></p>
<p class="MsoNormal"> :- :: forall a (n :: Nat). a -> Vector a n -> Vector a ('S n),<o:p></o:p></p>
<p class="MsoNormal"> in an equation for ‘init'’<o:p></o:p></p>
<p class="MsoNormal"> at cafe.lhs:13:10-16<o:p></o:p></p>
<p class="MsoNormal"> ‘n1’ is a rigid type variable bound by<o:p></o:p></p>
<p class="MsoNormal"> a pattern with constructor<o:p></o:p></p>
<p class="MsoNormal"> :- :: forall a (n :: Nat). a -> Vector a n -> Vector a ('S n),<o:p></o:p></p>
<p class="MsoNormal"> in an equation for ‘init'’<o:p></o:p></p>
<p class="MsoNormal"> at cafe.lhs:13:10<o:p></o:p></p>
<p class="MsoNormal"> Expected type: Vector a n<o:p></o:p></p>
<p class="MsoNormal"> Actual type: Vector a ('S n0)<o:p></o:p></p>
<p class="MsoNormal"> Relevant bindings include<o:p></o:p></p>
<p class="MsoNormal"> xs :: Vector a n1 (bound at cafe.lhs:13:15)<o:p></o:p></p>
<p class="MsoNormal"> In the expression: x :- (init' xs)<o:p></o:p></p>
<p class="MsoNormal"> In an equation for ‘init'’: init' (x :- xs) = x :- (init' xs)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"> <o:p></o:p></p>
<p class="MsoNormal"> so...<o:p></o:p></p>
<p class="MsoNormal"><o:p></o:p></p>
<p class="MsoNormal">the ":-" in "init' (x :- xs)"<o:p></o:p></p>
<p class="MsoNormal">has type <o:p></o:p></p>
<p class="MsoNormal">forall a (n :: Nat). a -> Vector a n -> Vector a ('S n)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">yep that makes sense....<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">if it knew "n ~ n1" then it knows "n1 ~ 'S n0"<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">so it would know "n ~ 'S n0"<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">but it only knows "'S n ~ 'S n1"<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">hmmmm...surely from the def of Nat, thats "obvious"<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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