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July 23, 2020 22:49
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Dependent Types not fully evaluating?
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%default total | |
data Term : Type -> Type where | |
Const : {a : Type} -> a -> Term a | |
Pair : {a : Type} -> {b : Type} -> Term a -> Term b -> Term (a, b) | |
App : {a : Type} -> {b : Type} -> Term (a -> b) -> Term a -> Term b | |
GoLeft : {a : Type} -> Term a -> Maybe Type | |
GoLeft (Const x) = Nothing | |
GoLeft (Pair {a} x y) = Just a | |
GoLeft (App {a} {b} f x) = Just (a -> b) | |
GoRight : {a : Type} -> Term a -> Maybe Type | |
GoRight (Const x) = Nothing | |
GoRight (Pair x {b} y) = Just b | |
GoRight (App {a} f x) = Just a | |
data Context : Maybe Type -> Type where | |
Root : {a : Type} -> Context (Just a) | |
L : {a : Type} -> (x : Term a) -> Context (Just a) -> Context (GoLeft x) | |
R : {a : Type} -> (x : Term a) -> Context (Just a) -> Context (GoRight x) | |
data Zipper : Type -> Type where | |
Zip : {a : Type} -> Term a -> Context (Just a) -> Zipper a | |
Fail : Zipper Void | |
left : (a : Type ** Zipper a) -> (b : Type ** Zipper b) | |
left (ty ** (Zip (Const x) ctx)) = (Void ** Fail) | |
left ((a, b) ** (Zip (Pair x y) ctx)) = (a ** Zip x (L (Pair x y) ctx)) | |
left (b ** (Zip (App {a} f x) ctx)) = (a -> b ** Zip f (L (App f x) ctx)) | |
left (Void ** Fail) = (Void ** Fail) | |
right : (a : Type ** Zipper a) -> (b : Type ** Zipper b) | |
right (ty ** (Zip (Const x) ctx)) = (Void ** Fail) | |
right ((a, b) ** (Zip (Pair x y) ctx)) = (b ** Zip y (R (Pair x y) ctx)) | |
right (_ ** (Zip (App {a} f x) ctx)) = (a ** Zip x (R (App f x) ctx)) | |
right (Void ** Fail) = (Void ** Fail) | |
{- | |
Can't solve constraint between: | |
GoLeft (App f x) | |
and | |
Just (a -> b) | |
at: | |
31 left (b ** (Zip (App {a} f x) ctx)) = (a -> b ** Zip f (R (App f x) ctx)) | |
Can't solve constraint between: | |
GoRight (App f x) | |
and | |
Just a | |
at: | |
37 right (_ ** (Zip (App {a} f x) ctx)) = (a ** Zip x (R (App f x) ctx)) | |
-} |
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