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# 2016
## 1 Kinds
A: S
B: S -> S
C: a -> S if polymorphic kinds are allowed, otherwise S -> S
D: S -> S -> S
E: S -> (S -> S) -> S
F: ((a -> S) -> S) -> S or a = S in case polymorphic kinds are not allowed
E B A: incorrect, the first type variable should be instantiated with S, not S -> S.
E A: (S -> S) -> S
E A B
F G, with `:: G c = G (c Int)`
## 2 Generic Programming
```clean
generic types a :: a -> [String]
types{|Int|} _ = ["Int"]
types{|Bool|} _ = ["Bool"]
types{|UNIT|} _ = []
types{|PAIR|} fx fy (PAIR x y) = fx x ++ fy y
types{|EITHER|} fl _ (LEFT l) = fl l
types{|EITHER|} _ fr (RIGHT r) = fr r
types{|OBJECT of d|} fx (OBJECT x) = [d.gtd_name:fx x]
types{|CONS|} fx (CONS x) = fx x
derive types [], (,)
typeCount :: a -> Int | types{|*|} a
typeCount x = length (removeDup (types{|*|} x))
```
## 3 Deep Embedding
```clean
// a
instance Functor Res
where
fmap f (Res x) = Res (f x)
fmap _ (Err e) = Err e
instance Applicative Res
where
pure x = Res x
(<*>) (Res f) (Res x) = Res (f x)
(<*>) (Err e) _ = Err e
(<*>) _ (Err e) = Err e
instance Monad Res
where
bind (Res x) f = f x
bind (Err e) _ = Err e
instance fail Res where fail e = Err e
// b
point :: Exp -> Res P
point (Point x y) = pure {x=x, y=y}
point (Add x y) = (+) <$> point x <*> point y
point _ = fail "Point expected"
// c
region :: Exp -> Res Reg
region (Point _ _) = fail "Region expected"
region (Circle r) = pure (CIRCLE r)
region (Add x y) = ADD <$> region x <*> region y
region (Inter x y) = INT <$> region x <*> region y
region (Invert x) = INV <$> region x
region (Move p r) = MOVE <$> point p <*> region r
// d
inside :: Point Region -> Res Bool
inside p r = ins <$> point p <*> region r
```
## 4 iTasks
```clean
insideSim = withShared (Point 1 2, Circle 3) (\shr ->
(updateSharedInformation "Edit" [] shr -&&- viewSharedInformation "Inside" [ViewUsing (uncurry inside)] shr) >>*
[OnAction ActionNew (always insideSim)])
Start w = startEngine insideSim w
```
## 5 Type Safe Deep Embedding
```clean
// a
:: Exp t
= Point_ (BM t P) Int Int
| Circle_ (BM t Reg) Radius
| Add (Exp t) (Exp t)
| Inter_ (BM t Reg) (Exp Reg) (Exp Reg)
| Invert_ (BM t Reg) (Exp Reg)
| Move_ (BM t Reg) (Exp P) (Exp Reg)
Point :== Point_ bm
Circle :== Circle_ bm
Inter :== Inter_ bm
Invert :== Invert_ bm
Move :== Move_ bm
// b
eval :: (Exp a) -> a | + a
eval (Point_ bm x y) = bm.f {x=x,y=y}
eval (Circle_ bm r) = bm.f (CIRCLE r)
eval (Add x y) = eval x + eval y
eval (Inter_ bm x y) = bm.f (INT (eval x) (eval y))
eval (Invert_ bm x) = bm.f (INV (eval x))
eval (Move_ bm p r) = bm.f (MOVE (eval p) (eval r))
// c
inside :: (Exp P) (Exp Reg) -> Bool
inside p r = ins (eval p) (eval r)
Start = inside (Point 1 2) (Circle 3)
```
## 6 Shallow Embedding
```clean
// a
class expr v
where
point :: Int Int -> v P
circle :: Radius -> v Reg
add :: (v a) (v a) -> v a | + a
inter :: (v Reg) (v Reg) -> v Reg
invert :: (v Reg) -> v Reg
move :: (v P) (v Reg) -> v Reg
// b
:: Eval t =: Eval t
instance expr Eval
where
point x y = Eval {x=x, y=y}
circle r = Eval (CIRCLE r)
add (Eval x) (Eval y) = Eval (x + y)
inter (Eval x) (Eval y) = Eval (INT x y)
invert (Eval x) = Eval (INV x)
move (Eval p) (Eval r) = Eval (MOVE p r)
// c
inside :: (Eval P) (Eval Reg) -> Bool
inside (Eval p) (Eval r) = ins p r
Start = inside (point 1 2) (circle 3)
```
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