--------------------------------------------------------------------------------
-- Unflattening
-{-
+-- The current implementation has problems with literals at level>0;
+-- there are special-purpose hacks for Int and Char, but none for
+-- unit. So I use this instead as a placeholder for <[ () ]>
+
+<[ u ]> = Prelude.error "FIXME"
+
-- This more or less "undoes" the flatten function. People often ask
-- me how you "translate generalized arrows back into multi-level
-- terms".. I'm not sure why you'd want to do that, but this is how:
ga_cancell = Code <[ \(_,x) -> x ]>
ga_cancelr = Code <[ \(x,_) -> x ]>
- ga_uncancell = Code <[ \x -> (%%(),x) ]>
- ga_uncancelr = Code <[ \x -> (x,%%()) ]>
+ ga_uncancell = Code <[ \x -> (u,x) ]>
+ ga_uncancelr = Code <[ \x -> (x,u) ]>
ga_assoc = Code <[ \((x,y),z) -> (x,(y,z)) ]>
ga_unassoc = Code <[ \(x,(y,z)) -> ((x,y),z) ]>
--}
ga_unassoc = GArrowInversePair { forward = ga_unassoc , backward = ga_assoc }
instance GArrowSwap g (**) u => GArrowSwap (GArrowInversePair g (**) u) (**) u where
ga_swap = GArrowInversePair { forward = ga_swap , backward = ga_swap }
-{-
-instance (GArrowDrop g (**) u, GArrowCopy g (**) u) => GArrowCopy (GArrowInversePair g (**) u) (**) u where
- ga_copy = GArrowInversePair { forward = ga_copy , backward = ga_second ga_drop >>> ga_cancelr }
--}
-- but notice that we can't (in general) get
-- instance GArrowDrop g => GArrowDrop (GArrowInversePair g) where ...
-{-
+
-- For that, we need PreLenses, which "log the history" where necessary.
-- I call this a "PreLens" because it consists of the data required
-- for a Lens (as in BCPierce's Lenses) but does not necessarily
id = PreLens { preLens = \x -> (x, (\x -> x)) }
f . g = PreLens { preLens = \x -> let (gx,g') = (preLens g) x in let (fgx,f') = (preLens f) gx in (fgx , \q -> g' (f' q)) }
-instance GArrow PreLens (,) where
+instance GArrow PreLens (,) () where
ga_first f = PreLens { preLens = \(x,z) -> let (y,f') = (preLens f) x in ((y,z),(\(q1,q2) -> (f' q1,q2))) }
ga_second f = PreLens { preLens = \(z,x) -> let (y,f') = (preLens f) x in ((z,y),(\(q1,q2) -> (q1,f' q2))) }
ga_cancell = PreLens { preLens = \(_,x) -> (x, (\x -> ((),x))) }
ga_assoc = PreLens { preLens = \((x,y),z) -> ( (x,(y,z)) , (\(x,(y,z)) -> ((x,y),z)) ) }
ga_unassoc = PreLens { preLens = \(x,(y,z)) -> ( ((x,y),z) , (\((x,y),z) -> (x,(y,z))) ) }
-instance GArrowDrop PreLens (,) where
+instance GArrowDrop PreLens (,) () where
ga_drop = PreLens { preLens = \x -> (() , (\() -> x)) }
-instance GArrowCopy PreLens (,) where
+instance GArrowCopy PreLens (,) () where
ga_copy = PreLens { preLens = \x -> ((x,x) , fst) }
-instance GArrowSwap PreLens (,) where
+instance GArrowSwap PreLens (,) () where
ga_swap = PreLens { preLens = \(x,y) -> ((y,x) , (\(z,q) -> (q,z))) }
data Lens x y where
Lens :: forall x y c1 c2 . ((x,c1)->(y,c2)) -> ((y,c2)->(x,c1)) -> Lens x y
-
+{-
-- can we make lenses out of GArrows other than (->)?
instance Category Lens where
id = Lens (\x -> x) (\x -> x)
(Lens g1 g2) . (Lens f1 f2) = Lens (\(x,(c1,c2)) -> let (y,fc) = f1 (x,c1) in let (z,gc) = g1 (y,c2) in (z,(fc,gc)))
(\(z,(c1,c2)) -> let (y,gc) = g2 (z,c2) in let (x,fc) = f2 (y,c1) in (x,(fc,gc)))
-instance GArrow Lens (,) where
+instance GArrow Lens (,) () where
ga_first (Lens f1 f2) = Lens (\((x1,x2),c) -> let (y,c') = f1 (x1,c) in ((y,x2),c'))
(\((x1,x2),c) -> let (y,c') = f2 (x1,c) in ((y,x2),c'))
ga_second (Lens f1 f2) = Lens (\((x1,x2),c) -> let (y,c') = f1 (x2,c) in ((x1,y),c'))
ga_unassoc = Lens (\((x,(y,z)),()) -> (((x,y),z),()))
(\(((x,y),z),()) -> ((x,(y,z)),()))
-instance GArrowDrop Lens (,) where
+instance GArrowDrop Lens (,) () where
ga_drop = Lens (\(x,()) -> ((),x)) (\((),x) -> (x,()))
-instance GArrowCopy Lens (,) where
+instance GArrowCopy Lens (,) () where
ga_copy = Lens (\(x,()) -> ((x,x),())) (\((x,_),()) -> (x,()))
-instance GArrowSwap Lens (,) where
+instance GArrowSwap Lens (,) () where
ga_swap = Lens (\((x,y),()) -> ((y,x),())) (\((x,y),()) -> ((y,x),()))
-instance BiGArrow Lens (,) where
+instance BiGArrow Lens (,) () where
biga_arr f f' = Lens (\(x,()) -> ((f x),())) (\(x,()) -> ((f' x),()))
biga_inv (Lens f1 f2) = Lens f2 f1
-}
-
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-- An example generalized arrow