gistfile1.txt

--  Vec2,  Vec3, Vec4  for x/y, x/y/z, x/y/z/w 

instance Functor Vec3 where
    fmap f (Vec3 x y z) = Vec3 (f x) (f y) (f z)

-- Docs tell me...
--class (Functor f)=> Applicative f   where  
--    pure :: a -> f a  
--    (<*>) :: f (a -> b) -> f a -> f b

instance Applicative Vec3  where  
    pure a = Vec3 a a a     -- ??? 'lifts the function' into fields of Vec3 ??
    (Vec3 f0 f1 f2) <*> (Vec3 a0 a1 a2) = Vec3 (f0 a0)(f1 a1)(f2 a2)


class VectorOps x where
--    vbinop::(a->b->c) ->  x a  ->  x b  -> x c      -- ???  liftA2 , .. but what to instacne to get it?
    vreduce::(a->a->a) ->  x a  ->  a              -- in the process of replacig this with 'foldl1'
--    vscalarop::(a->b->c) ->  x a  -> b ->  x c  -- replaced with 'fmap'


instance VectorOps Vec3 where
    vbinop f (Vec3 x0 y0 z0) (Vec3 x1 y1 z1)= Vec3 (f x0 x1)(f y0 y1)(f z0 z1) 
    

vscalarop:: Functor v=>(a->b->c) -> v a -> b -> v c
vscalarop f v0 scalar= fmap (\x->f x scalar) v0


-
vbinop::Applicative v=>(a->b->c)->v a->v b->v c
vbinop = liftA2

-- ???
vbinop::Applicative v=>(a->b->c)->v a->v b->v c
vbinop = liftA2


-- 

vmul v0 v1 =vbinop (*) v0 v1
vadd v0 v1 =vbinop (+) v0 v1
vsub v0 v1 =vbinop (-) v0 v1
vdiv v0 v1 =vbinop (/) v0 v1
vdot va vb = vreduce (+) (vmul va vb)