Hi Alex!
2012-07-03 20:18, Alex Rozenshteyn skrev:
I'm trying to implement the lambda calculus (with CBV evaluation) using
the "syntactic" package, in such a way that a simple extension is also
simple to implement.
I am stuck on the fact that it seems that the Value type needs to be
parametrized over the Expr type and I can't seem to figure out how to do it.
The trick is to see that your `Expr` and `Value` can be merged to a
single type:
data Expr group
where
Var :: Ident -> Expr NONVAL
Lam :: Ident -> Expr any -> Expr VAL
App :: Expr any1 -> Expr any2 -> Expr NONVAL
data VAL
data NONVAL
type Value = Expr VAL
eval :: Expr any -> Value
...
(Here I'm using polymorphic constructors to emulate that `Value` is a
sub-type of `Expr`. I could have made a more direct translation with two
lambda constructors. Then all constructors would have been monomorphic.)
Once this is done, the conversion to Syntactic is easy:
data Var :: * -> * where Var :: Ident -> Var (Full NONVAL)
data Lam :: * -> * where Lam :: Ident -> Lam (any :-> Full VAL)
data App :: * -> * where App :: App (any1 :-> any2 :-> Full NONVAL)
type Expr group = ASTF (Lam :+: Var :+: App) group
type Value = ASTF (Lam :+: Var :+: App) VAL
eval :: Expr any -> Value
eval var
| Just (Var _) <- prj var = error "not closed"
eval e@(lam :$ _)
| Just (Lam _) <- prj lam = e
eval (app :$ e1 :$ e2)
| Just App <- prj app = case eval e1 of
(lam :$ e) | Just (Lam i) <- prj lam -> subst e (eval e2) i
_ -> error "illegal application"
subst :: Expr any -> Value -> Ident -> Value
subst = undefined
Of course, you need to generalize the types of `eval` and `subst` in
order to make them extensible. For more details, see this paper:
http://www.cse.chalmers.se/~emax/documents/axelsson2012generic.pdf
(The paper refers to syntactic-1.0 which hasn't been uploaded yet, so
there are some small differences.)
/ Emil
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