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<p class="MsoNormal">My latest confusion….<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I’ve got a typeclass (with associated types) monoid sort of thing….<o:p></o:p></p>
<p class="MsoNormal">I can get a Singleton family of Nat to be an instance of the typeclass.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Lists are sort of Natural numbers…with a bit of extra functionality…<o:p></o:p></p>
<p class="MsoNormal">So I should be able to take HList and make that a member of the same typeclass…<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I fail for 2 reasons…1…I have to wrestle with the kinds…in a way I find ununderstandbly irritating.<o:p></o:p></p>
<p class="MsoNormal">And 2…because BOOM.<o:p></o:p></p>
<p class="MsoNormal" style="text-autospace:none">“<span style="font-family:Consolas;color:#AF0000">is a rigid type variable bound by” blab la.<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">My Haskell in many ways is primitive…I seem to be messing with things beyond my ability….but that’s the way to learn I suppose.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> {-# LANGUAGE DataKinds #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE ExplicitForAll #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE FlexibleContexts #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE FlexibleInstances #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE GADTs #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE MultiParamTypeClasses #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE PolyKinds #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE StandaloneDeriving #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE TypeFamilies #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE TypeOperators #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE UndecidableInstances #-}<o:p></o:p></p>
<p class="MsoNormal">> {-# LANGUAGE ScopedTypeVariables #-}<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> import Control.Effect<o:p></o:p></p>
<p class="MsoNormal">> import Control.Effect.Helpers.List<o:p></o:p></p>
<p class="MsoNormal">> import Control.Effect.WriteOnceWriter <o:p></o:p></p>
<p class="MsoNormal">> import Prelude hiding ((>>=),(>>),return,fmap,fail)<o:p></o:p></p>
<p class="MsoNormal">> --import GHC.TypeLits<o:p></o:p></p>
<p class="MsoNormal">> import Data.Type.Equality<o:p></o:p></p>
<p class="MsoNormal">> import Data.Type.Bool<o:p></o:p></p>
<p class="MsoNormal">> --import Data.HList.HList<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data Nat where<o:p></o:p></p>
<p class="MsoNormal">> Z :: Nat<o:p></o:p></p>
<p class="MsoNormal">> S :: Nat -> Nat<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data family Sing (a :: k)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data SNat (a :: Nat) where<o:p></o:p></p>
<p class="MsoNormal">> SZ :: SNat 'Z<o:p></o:p></p>
<p class="MsoNormal">> SS :: SNat a -> SNat ('S a)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> type family (n :: Nat) :+ (m :: Nat) :: Nat<o:p></o:p></p>
<p class="MsoNormal">> type instance 'Z :+ m = m<o:p></o:p></p>
<p class="MsoNormal">> type instance ('S n) :+ m = 'S (n :+ m)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Define something like a monoid over the types…<o:p></o:p></p>
<p class="MsoNormal">(note I have to wrestle with the kind signatures to get the instance of SNat to work, which is fine…but now closes doors to other instances)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> class TMonoid (m :: k -> *) where<o:p></o:p></p>
<p class="MsoNormal">> type O m :: k<o:p></o:p></p>
<p class="MsoNormal">> zero :: m (O m)<o:p></o:p></p>
<p class="MsoNormal">> type TPlus m (d :: k) (e :: k) :: k<o:p></o:p></p>
<p class="MsoNormal">> add :: m a -> m b -> m (TPlus m a b)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">And this works quite nicely<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> instance TMonoid SNat where<o:p></o:p></p>
<p class="MsoNormal">> type O SNat = 'Z<o:p></o:p></p>
<p class="MsoNormal">> zero = SZ<o:p></o:p></p>
<p class="MsoNormal">> type TPlus SNat a b = a :+ b<o:p></o:p></p>
<p class="MsoNormal">> add SZ b = b<o:p></o:p></p>
<p class="MsoNormal">> add (SS a) b = SS (add a b)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Now….<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">(I have to declare different kind?....I can’t get a single simple declaration of TMonoid?)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> class TMonoid' (m :: [*] -> *) where<o:p></o:p></p>
<p class="MsoNormal">> type O' m :: [*]<o:p></o:p></p>
<p class="MsoNormal">> zero' :: m (O' m)<o:p></o:p></p>
<p class="MsoNormal">> type TPlus' m (d :: [*]) (e :: [*]) :: [*]<o:p></o:p></p>
<p class="MsoNormal">> add' :: m a -> m b -> m (TPlus' m a b)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Steal the definition of HList<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data family HList (l::[*]) :: *<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> data instance HList '[] = HNil<o:p></o:p></p>
<p class="MsoNormal">> data instance HList (x ': xs) = x `HCons` HList xs<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">And try to construct an analogous TMonoid of it…<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">> instance TMonoid' HList where<o:p></o:p></p>
<p class="MsoNormal">> type O' HList = '[]<o:p></o:p></p>
<p class="MsoNormal">> zero' = HNil<o:p></o:p></p>
<p class="MsoNormal">> type TPlus' HList a b = a :++ b<o:p></o:p></p>
<p class="MsoNormal">> add' HNil b = b<o:p></o:p></p>
<p class="MsoNormal">> add' (HCons x xs) ys = HCons x (add' xs ys)<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">BOOM<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000">Couldn't match type ‘a’ with ‘'[]’<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> ‘a’ is a rigid type variable bound by<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> the type signature for<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> add' :: HList a -> HList b -> HList (TPlus' HList a b)<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> at broadcast2.lhs:90:5<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> Expected type: HList a<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> Actual type: HList '[]<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> Relevant bindings include<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> add' :: HList a -> HList b -> HList (TPlus' HList a b)<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> (bound at broadcast2.lhs:90:5)<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> In the pattern: HNil<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> In an equation for ‘add'’: add' HNil b = b<o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-family:Consolas;color:#AF0000"> In the instance declaration for ‘TMonoid' HList’<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Hmmm….confused…why does <o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">add SZ b = b<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">work, but the analogous<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">add' HNil b = b<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">fail<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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