Idris2/libs/base/Decidable/Decidable.idr

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769 B
Idris

module Decidable.Decidable
import Data.Rel
import Data.Fun
||| An n-ary relation is decidable if we can make a `Dec`
||| of its result type for each combination of inputs
public export
IsDecidable : (k : Nat) -> (ts : Vect k Type) -> Rel ts -> Type
IsDecidable k ts p = liftRel (the (Vect k Type) ts) (the (Rel ts) p) Dec
||| Interface for decidable n-ary Relations
public export
interface Decidable k ts p where
total decide : IsDecidable k ts p
||| Given a `Decidable` n-ary relation, provides a decision procedure for
||| this relation.
decision : (ts : Vect k Type) -> (p : Rel ts) -> (Decidable k ts p) => liftRel ts p Dec
decision ts p = decide {ts} {p}
using (a : Type, x : a)
public export
data Given : Dec a -> Type where
Always : Given (Yes x)