quox/lib/Quox/Decidable.idr

53 lines
1.1 KiB
Idris

module Quox.Decidable
import public Data.Bool.Decidable
import public Decidable.Decidable
import public Decidable.Equality
import public Control.Relation
public export
0 REL : Type -> Type -> Type
REL a b = a -> b -> Type
public export
0 Pred : Type -> Type
Pred a = a -> Type
public export
0 Dec1 : Pred a -> Type
Dec1 p = (x : a) -> Dec (p x)
public export
0 Dec2 : REL a b -> Type
Dec2 p = (x : a) -> (y : b) -> Dec (p x y)
public export
0 Reflects1 : Pred a -> (a -> Bool) -> Type
p `Reflects1` f = (x : a) -> p x `Reflects` f x
public export
0 Reflects2 : REL a b -> (a -> b -> Bool) -> Type
p `Reflects2` f = (x : a) -> (y : b) -> p x y `Reflects` f x y
public export
(||) : Dec p -> Dec q -> Dec (Either p q)
Yes y1 || _ = Yes $ Left y1
No _ || Yes y2 = Yes $ Right y2
No n1 || No n2 = No $ \case Left y1 => n1 y1; Right y2 => n2 y2
public export
(&&) : Dec p -> Dec q -> Dec (p, q)
Yes y1 && Yes y2 = Yes (y1, y2)
Yes _ && No n2 = No $ n2 . snd
No n1 && _ = No $ n1 . fst
public export
reflectToDec : p `Reflects` b -> Dec p
reflectToDec (RTrue y) = Yes y
reflectToDec (RFalse n) = No n