Involution implies Noncontradiction and ExcludedMiddle (#1242)

docs/abstraction-diagrams.md

@@ -9,9 +9,10 @@ sidebar_label: "Abstraction Diagrams"
 ```mermaid
 classDiagram
   Absorption~A~ <|-- DistributiveAbsorption~A~
-  Absorption~A~ <|-- Involution~A~
   Absorption~A~ <|-- Noncontradiction~A~
   Absorption~A~ <|-- ExcludedMiddle~A~
+  ExcludedMiddle~A~ <|-- Involution~A~
+  Noncontradiction~A~ <|-- Involution~A~
   class Absorption~A~{
     () or(=> A, => A): A
     () and(=> A, => A): A
@@ -20,20 +21,17 @@ classDiagram
     Boolean
     Set[A]
   }
-  class Involution~A~{
-    Boolean
-    () complement(=> A): A
-  }
   class Noncontradiction~A~{
-    Boolean
     () complement(=> A): A
     () bottom: A
   }
   class ExcludedMiddle~A~{
-    Boolean
     () complement(=> A): A
     () top: A
   }
+  class Involution~A~{
+    Boolean
+  }
 ```
 
 

experimental-laws/shared/src/main/scala/zio/prelude/experimental/laws/InvolutionLaws.scala

@@ -25,6 +25,6 @@ object InvolutionLaws extends Lawful[InvolutionEqual] {
    * The set of all laws that instances of `Involution` must satisfy.
    */
   lazy val laws: Laws[InvolutionEqual] =
-    AbsorptionLaws.laws + involutionLaw
+    ExcludedMiddleLaws.laws + NoncontradictionLaws.laws + involutionLaw
 
 }

experimental/shared/src/main/scala/zio/prelude/experimental/Absorption.scala

@@ -17,14 +17,8 @@ object Absorption {
    */
   def apply[A](implicit absorption: Absorption[A]): Absorption[A] = absorption
 
-  implicit lazy val BoolInstance: DistributiveAbsorption[Boolean]
-    with ExcludedMiddle[Boolean]
-    with Involution[Boolean]
-    with Noncontradiction[Boolean] =
-    new DistributiveAbsorption[Boolean]
-      with ExcludedMiddle[Boolean]
-      with Involution[Boolean]
-      with Noncontradiction[Boolean] {
+  implicit lazy val BoolInstance: DistributiveAbsorption[Boolean] with Involution[Boolean] =
+    new DistributiveAbsorption[Boolean] with Involution[Boolean] {
       override def complement(a: => Boolean): Boolean         = !a
       override val bottom: Boolean                            = false
       override val top: Boolean                               = true

experimental/shared/src/main/scala/zio/prelude/experimental/ExcludedMiddle.scala

@@ -10,7 +10,7 @@ trait ExcludedMiddle[A] extends Complement[A] {
 object ExcludedMiddle {
 
   /**
-   * Summons an implicit `Complement[A]`.
+   * Summons an implicit `ExcludedMiddle[A]`.
    */
   def apply[A](implicit excludedMiddle: ExcludedMiddle[A]): ExcludedMiddle[A] = excludedMiddle
 }

experimental/shared/src/main/scala/zio/prelude/experimental/Involution.scala

@@ -1,7 +1,7 @@
 package zio.prelude
 package experimental
 
-trait Involution[A] extends Complement[A]
+trait Involution[A] extends ExcludedMiddle[A] with Noncontradiction[A]
 
 object Involution {
 

experimental/shared/src/main/scala/zio/prelude/experimental/coherent/coherent.scala

@@ -65,7 +65,7 @@ object ExcludedMiddleEqual {
     }
 }
 
-trait InvolutionEqual[A] extends AbsorptionEqual[A] with Involution[A]
+trait InvolutionEqual[A] extends ExcludedMiddleEqual[A] with NoncontradictionEqual[A] with Involution[A]
 
 object InvolutionEqual {
   implicit def derive[A](implicit involution0: Involution[A], equal0: Equal[A]): InvolutionEqual[A] =
@@ -77,9 +77,9 @@ object InvolutionEqual {
 
       override def and(l: => A, r: => A): A = involution0.and(l, r)
 
-      override def Or: Associative[OrF[A]] = involution0.Or
+      override def Or: Identity[OrF[A]] = involution0.Or
 
-      override def And: Associative[AndF[A]] = involution0.And
+      override def And: Identity[AndF[A]] = involution0.And
 
       protected def checkEqual(l: A, r: A): Boolean = equal0.equal(l, r)
     }