mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-18 08:42:11 +03:00
182 lines
6.9 KiB
Idris
182 lines
6.9 KiB
Idris
module Decidable.Equality
|
|
|
|
import Data.Maybe
|
|
import Data.Either
|
|
import Data.Nat
|
|
import Data.List
|
|
import Data.List1
|
|
|
|
import public Decidable.Equality.Core as Decidable.Equality
|
|
|
|
%default total
|
|
|
|
--------------------------------------------------------------------------------
|
|
--- Unit
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq () where
|
|
decEq () () = Yes Refl
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Booleans
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq Bool where
|
|
decEq True True = Yes Refl
|
|
decEq False False = Yes Refl
|
|
decEq False True = No absurd
|
|
decEq True False = No absurd
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Nat
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq Nat where
|
|
decEq Z Z = Yes Refl
|
|
decEq Z (S _) = No absurd
|
|
decEq (S _) Z = No absurd
|
|
decEq (S n) (S m) with (decEq n m)
|
|
decEq (S n) (S m) | Yes p = Yes $ cong S p
|
|
decEq (S n) (S m) | No p = No $ \h : (S n = S m) => p $ succInjective n m h
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Maybe
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq t => DecEq (Maybe t) where
|
|
decEq Nothing Nothing = Yes Refl
|
|
decEq Nothing (Just _) = No absurd
|
|
decEq (Just _) Nothing = No absurd
|
|
decEq (Just x') (Just y') with (decEq x' y')
|
|
decEq (Just x') (Just y') | Yes p = Yes $ cong Just p
|
|
decEq (Just x') (Just y') | No p
|
|
= No $ \h : Just x' = Just y' => p $ justInjective h
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Either
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
(DecEq t, DecEq s) => DecEq (Either t s) where
|
|
decEq (Left x) (Left y) with (decEq x y)
|
|
decEq (Left x) (Left x) | Yes Refl = Yes Refl
|
|
decEq (Left x) (Left y) | No contra = No (contra . leftInjective)
|
|
decEq (Left x) (Right y) = No absurd
|
|
decEq (Right x) (Left y) = No absurd
|
|
decEq (Right x) (Right y) with (decEq x y)
|
|
decEq (Right x) (Right x) | Yes Refl = Yes Refl
|
|
decEq (Right x) (Right y) | No contra = No (contra . rightInjective)
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Tuple
|
|
--------------------------------------------------------------------------------
|
|
|
|
pairInjective : (a, b) = (c, d) -> (a = c, b = d)
|
|
pairInjective Refl = (Refl, Refl)
|
|
|
|
public export
|
|
(DecEq a, DecEq b) => DecEq (a, b) where
|
|
decEq (a, b) (a', b') with (decEq a a')
|
|
decEq (a, b) (a', b') | (No contra) =
|
|
No $ contra . fst . pairInjective
|
|
decEq (a, b) (a, b') | (Yes Refl) with (decEq b b')
|
|
decEq (a, b) (a, b) | (Yes Refl) | (Yes Refl) = Yes Refl
|
|
decEq (a, b) (a, b') | (Yes Refl) | (No contra) =
|
|
No $ contra . snd . pairInjective
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- List
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq a => DecEq (List a) where
|
|
decEq [] [] = Yes Refl
|
|
decEq (x :: xs) [] = No absurd
|
|
decEq [] (x :: xs) = No absurd
|
|
decEq (x :: xs) (y :: ys) with (decEq x y)
|
|
decEq (x :: xs) (y :: ys) | No contra =
|
|
No $ contra . fst . consInjective
|
|
decEq (x :: xs) (x :: ys) | Yes Refl with (decEq xs ys)
|
|
decEq (x :: xs) (x :: xs) | (Yes Refl) | (Yes Refl) = Yes Refl
|
|
decEq (x :: xs) (x :: ys) | (Yes Refl) | (No contra) =
|
|
No $ contra . snd . consInjective
|
|
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- List1
|
|
--------------------------------------------------------------------------------
|
|
|
|
public export
|
|
DecEq a => DecEq (List1 a) where
|
|
|
|
decEq (x ::: xs) (y ::: ys) with (decEq x y)
|
|
decEq (x ::: xs) (y ::: ys) | No contra = No (contra . fst . consInjective)
|
|
decEq (x ::: xs) (y ::: ys) | Yes eqxy with (decEq xs ys)
|
|
decEq (x ::: xs) (y ::: ys) | Yes eqxy | No contra = No (contra . snd . consInjective)
|
|
decEq (x ::: xs) (y ::: ys) | Yes eqxy | Yes eqxsys = Yes (cong2 (:::) eqxy eqxsys)
|
|
|
|
-- TODO: Other prelude data types
|
|
|
|
-- For the primitives, we have to cheat because we don't have access to their
|
|
-- internal implementations. We use believe_me for the inequality proofs
|
|
-- because we don't them to reduce (and they should never be needed anyway...)
|
|
-- A postulate would be better, but erasure analysis may think they're needed
|
|
-- for computation in a higher order setting.
|
|
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Int
|
|
--------------------------------------------------------------------------------
|
|
public export
|
|
implementation DecEq Int where
|
|
decEq x y = case x == y of -- Blocks if x or y not concrete
|
|
True => Yes primitiveEq
|
|
False => No primitiveNotEq
|
|
where primitiveEq : forall x, y . x = y
|
|
primitiveEq = believe_me (Refl {x})
|
|
primitiveNotEq : forall x, y . x = y -> Void
|
|
primitiveNotEq prf = believe_me {b = Void} ()
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Char
|
|
--------------------------------------------------------------------------------
|
|
public export
|
|
implementation DecEq Char where
|
|
decEq x y = case x == y of -- Blocks if x or y not concrete
|
|
True => Yes primitiveEq
|
|
False => No primitiveNotEq
|
|
where primitiveEq : forall x, y . x = y
|
|
primitiveEq = believe_me (Refl {x})
|
|
primitiveNotEq : forall x, y . x = y -> Void
|
|
primitiveNotEq prf = believe_me {b = Void} ()
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- Integer
|
|
--------------------------------------------------------------------------------
|
|
public export
|
|
implementation DecEq Integer where
|
|
decEq x y = case x == y of -- Blocks if x or y not concrete
|
|
True => Yes primitiveEq
|
|
False => No primitiveNotEq
|
|
where primitiveEq : forall x, y . x = y
|
|
primitiveEq = believe_me (Refl {x})
|
|
primitiveNotEq : forall x, y . x = y -> Void
|
|
primitiveNotEq prf = believe_me {b = Void} ()
|
|
|
|
--------------------------------------------------------------------------------
|
|
-- String
|
|
--------------------------------------------------------------------------------
|
|
public export
|
|
implementation DecEq String where
|
|
decEq x y = case x == y of -- Blocks if x or y not concrete
|
|
True => Yes primitiveEq
|
|
False => No primitiveNotEq
|
|
where primitiveEq : forall x, y . x = y
|
|
primitiveEq = believe_me (Refl {x})
|
|
primitiveNotEq : forall x, y . x = y -> Void
|
|
primitiveNotEq prf = believe_me {b = Void} ()
|