HasMembership: fix dec instances

Author: omelkonian

Class/HasMembership/Instances.agda

@@ -4,49 +4,18 @@ module Class.HasMembership.Instances where
 open import Class.Prelude
 open import Class.HasMembership.Core
 
-open import Class.DecEq.Core
-
-open import Class.Decidable.Core
--- open import Class.Decidable.Instances
-
 instance
-
   M-List : HasMembership {ℓ} List
   M-List = record {LMem}
     where import Data.List.Membership.Propositional as LMem
 
-  Dec∈-List : ⦃ _ : DecEq A ⦄ → _∈_ {F = List}{A} ⁇²
-  Dec∈-List = ⁇² DL._∈?_
-    where import Data.List.Membership.DecPropositional _≟_ as DL
+  M-List⁺ : HasMembership {ℓ} List⁺
+  M-List⁺ ._∈_ x xs = x ∈  L⁺.toList xs
 
   M-Vec : HasMembership {ℓ} (flip Vec n)
   M-Vec ._∈_ = λ x → VMem._∈_ x
     where import Data.Vec.Membership.Propositional as VMem
 
-  Dec∈-Vec : ⦃ _ : DecEq A ⦄ → _∈_ {F = flip Vec n}{A} ⁇²
-  Dec∈-Vec = ⁇² λ x → DV._∈?_ x
-    where import Data.Vec.Membership.DecPropositional _≟_ as DV
-
-  M-List⁺ : HasMembership {ℓ} List⁺
-  M-List⁺ ._∈_ x xs = x ∈  L⁺.toList xs
-
-  Dec∈-List⁺ : ⦃ _ : DecEq A ⦄ → _∈_ {F = List⁺}{A} ⁇²
-  Dec∈-List⁺ .dec = _ ∈? L⁺.toList _
-
-  import Data.Maybe.Relation.Unary.Any as Mb
-
   M-Maybe : HasMembership {ℓ} Maybe
   M-Maybe ._∈_ x mx = Mb.Any (_≡ x) mx
-
-  Dec∈-Maybe : ⦃ _ : DecEq A ⦄ → _∈_ {F = Maybe}{A} ⁇²
-  Dec∈-Maybe .dec = Mb.dec (_≟ _) _
-
-module _ {A B : Type} (f : A → B) where
-
-  import Data.List.Membership.Propositional.Properties as LMem
-
-  ∈⁺-map⁺ : ∀ {x xs} → x ∈ xs → f x ∈ L⁺.map f xs
-  ∈⁺-map⁺ = LMem.∈-map⁺ f
-
-  ∈⁺-map⁻ : ∀ {y xs} → y ∈ L⁺.map f xs → ∃ λ x → x ∈ xs × y ≡ f x
-  ∈⁺-map⁻ = LMem.∈-map⁻ f
+    where import Data.Maybe.Relation.Unary.Any as Mb

Test/HasMembership.agda

@@ -1,4 +1,4 @@
-{-# OPTIONS --cubical-compatible #-}
+{-# OPTIONS --without-K #-}
 module Test.HasMembership where
 
 open import Class.Prelude
@@ -8,6 +8,24 @@ open import Class.ToN
 _ = mapWith∈ (List ℕ ∋ 10 ∷ 20 ∷ 30 ∷ []) toℕ
   ≡ (0 ∷ 1 ∷ 2 ∷ [])
   ∋ refl
+_ = mapWith∈ (List⁺ ℕ ∋ 10 ∷ 20 ∷ 30 ∷ []) toℕ
+  ≡ (0 ∷ 1 ∷ 2 ∷ [])
+  ∋ refl
 _ = mapWith∈ (Vec ℕ 3 ∋ 10 ∷ 20 ∷ 30 ∷ []) toℕ
   ≡ (0 ∷ 1 ∷ 2 ∷ [])
   ∋ refl
+_ = mapWith∈ (Maybe ℕ ∋ just 10) (const 1)
+  ≡ just 1
+  ∋ refl
+
+open import Class.DecEq
+open import Class.Decidable
+
+_ = 20 ∈ (List ℕ ∋ 10 ∷ 20 ∷ 30 ∷ [])
+  ∋ auto
+_ = 20 ∈ (List⁺ ℕ ∋ 10 ∷ 20 ∷ 30 ∷ [])
+  ∋ auto
+_ = 20 ∈ (Vec ℕ 3 ∋ 10 ∷ 20 ∷ 30 ∷ [])
+  ∋ auto
+_ = 10 ∈ just 10
+  ∋ auto