feat: Polish Cats semigroups/monoids for refined types (#277)

Closes #271 
Closes #270 
Closes #268

build.sc

@@ -286,7 +286,8 @@ object cats extends SubModule {
   def artifactName = "iron-cats"
 
   def ivyDeps = Agg(
-    ivy"org.typelevel::cats-core::2.8.0"
+    ivy"org.typelevel::cats-core::2.8.0",
+    ivy"org.typelevel::algebra::2.8.0"
   )
 
   object test extends Tests {

cats/src/io/github/iltotore/iron/Bounds.scala

@@ -0,0 +1,110 @@
+package io.github.iltotore.iron
+
+import io.github.iltotore.iron.constraint.numeric.Greater
+import io.github.iltotore.iron.constraint.numeric.*
+import scala.compiletime.constValue
+import scala.math.Numeric.Implicits.infixNumericOps
+import scala.math.Numeric.IntIsIntegral
+import scala.math.Ordering.Implicits.infixOrderingOps
+
+/**
+  * A way to shift out-of-bounds [[A]] values constrained with [[C]] constraint.
+  * 
+  * @tparam A the base type
+  * @tparam C the constraint type
+  */
+trait Bounds[A, C]:
+
+  /**
+    * Shift value if out of bounds.
+    *
+    * @param value the value to eventually shift
+    * @return the passed value as is or shifted if necessary
+    */
+  def shift(value: A): A :| C
+
+object Bounds:
+
+  /**
+    * Bounds for interval [L, U].
+    *
+    * @return
+    */
+  inline given closedBounds[A, L <: A, U <: A, C](using
+    C ==> Interval.Closed[L, U],
+    Interval.Closed[L, U] ==> C,
+    Numeric[A]
+  ): Bounds[A, C] =
+    new:
+      override def shift(value: A): A :| C =
+        if value > constValue[U] then (value - constValue[U] + constValue[L] - summon[Numeric[A]].one).assume[C]
+        else if value < constValue[L] then ((constValue[U]: A) + value - constValue[L] + summon[Numeric[A]].one).assume[C]
+        else value.assume[C]
+
+  //Positive
+  given posIntBounds[C](using C ==> Positive, Positive ==> C): Bounds[Int, C] = value =>
+    if value <= 0 then (value + Int.MaxValue).assume[C]
+    else value.assume[C]
+
+  given posLongBounds[C](using C ==> Positive, Positive ==> C): Bounds[Long, C] = value =>
+    if value <= 0 then (value + Long.MaxValue).assume[Positive]
+    else value.assume[C]
+
+  given posFloatBounds[C](using C ==> Positive, Positive ==> C): Bounds[Float, C] = value =>
+    if value <= 0 then (value + Float.MaxValue).assume[C]
+    else value.assume[C]
+
+  given posDoubleBounds[C](using C ==> Positive, Positive ==> C): Bounds[Double, C] = value =>
+    if value <= 0 then (value + Double.MaxValue).assume[C]
+    else value.assume[C]
+
+  //Positive0
+  given pos0IntBounds[C](using C ==> Positive0, Positive0 ==> C): Bounds[Int, C] = value =>
+    if value < 0 then (value + Int.MaxValue + 1).assume[C]
+    else value.assume[C]
+
+  given pos0LongBounds[C](using C ==> Positive0, Positive0 ==> C): Bounds[Long, C] = value =>
+    if value < 0 then (value + Long.MaxValue + 1).assume[C]
+    else value.assume[C]
+
+  given pos0FloatBounds[C](using C ==> Positive0, Positive0 ==> C): Bounds[Float, C] = value =>
+    if value < 0 then (value + Float.MaxValue + 1).assume[C]
+    else value.assume[C]
+
+  given pos0DoubleBounds[C](using C ==> Positive0, Positive0 ==> C): Bounds[Double, C] = value =>
+    if value < 0 then (value + Double.MaxValue + 1).assume[C]
+    else value.assume[C]
+
+  //Negative
+  given negIntBounds[C](using C ==> Negative, Negative ==> C): Bounds[Int, C] = value =>
+    if value >= 0 then (value + Int.MinValue).assume[C]
+    else value.assume[C]
+
+  given negLongBounds[C](using C ==> Negative, Negative ==> C): Bounds[Long, C] = value =>
+    if value >= 0 then (value + Long.MinValue).assume[C]
+    else value.assume[C]
+
+  given negFloatBounds[C](using C ==> Negative, Negative ==> C): Bounds[Float, C] = value =>
+    if value >= 0 then (value + Float.MinValue).assume[C]
+    else value.assume[C]
+
+  given negDoubleBounds[C](using C ==> Negative, Negative ==> C): Bounds[Double, C] = value =>
+    if value >= 0 then (value + Double.MinValue).assume[C]
+    else value.assume[C]
+
+  //Negative
+  given neg0IntBounds[C](using C ==> Negative0, Negative0 ==> C): Bounds[Int, C] = value =>
+    if value > 0 then (value + Int.MinValue - 1).assume[C]
+    else value.assume[C]
+
+  given neg0LongBounds[C](using C ==> Negative0, Negative0 ==> C): Bounds[Long, C] = value =>
+    if value > 0 then (value + Long.MinValue - 1).assume[C]
+    else value.assume[C]
+
+  given neg0FloatBounds[C](using C ==> Negative0, Negative0 ==> C): Bounds[Float, C] = value =>
+    if value > 0 then (value + Float.MinValue - 1).assume[C]
+    else value.assume[C]
+
+  given neg0DoubleBounds[C](using C ==> Negative0, Negative0 ==> C): Bounds[Double, C] = value =>
+    if value > 0 then (value + Double.MinValue - 1).assume[C]
+    else value.assume[C]

cats/src/io/github/iltotore/iron/cats.scala

@@ -1,9 +1,7 @@
 package io.github.iltotore.iron
 
-import _root_.cats.data.*
-import _root_.cats.kernel.{CommutativeMonoid, Hash, LowerBounded, PartialOrder, UpperBounded}
+import _root_.cats.data.{EitherNec, EitherNel, Validated, ValidatedNec, ValidatedNel}
 import _root_.cats.syntax.either.*
-import _root_.cats.{Eq, Monoid, Order, Show, Traverse}
 import _root_.cats.data.Validated.{Invalid, Valid}
 import _root_.cats.Functor
 import _root_.cats.implicits.*
@@ -12,6 +10,7 @@ import io.github.iltotore.iron.constraint.numeric.{Greater, Less, Negative, Posi
 import scala.util.NotGiven
 import scala.util.boundary
 import scala.util.boundary.break
+import _root_.cats.Traverse
 
 object cats extends IronCatsInstances:
 
@@ -322,77 +321,3 @@ object cats extends IronCatsInstances:
       traverse.traverse(wrapper): value =>
         Validated.condNel[InvalidValue[A], T](ops.rtc.test(value), ops.assume(value), InvalidValue(value, ops.rtc.message))
 
-  /**
-   * Represent all Cats' typeclass instances for Iron.
-   */
-private trait IronCatsInstances extends IronCatsLowPriority, RefinedTypeOpsCats:
-
-  given [F[_]](using functor: Functor[F]): MapLogic[F] with
-
-    override def map[A, B](wrapper: F[A], f: A => B): F[B] = functor.map(wrapper)(f)
-
-  // The `NotGiven` implicit parameter is mandatory to avoid ambiguous implicit error when both Eq[A] and Hash[A]/PartialOrder[A] exist
-  inline given [A, C](using inline ev: Eq[A], notHashOrOrder: NotGiven[Hash[A] | PartialOrder[A]]): Eq[A :| C] = ev.asInstanceOf[Eq[A :| C]]
-
-  inline given [A, C](using inline ev: PartialOrder[A], notOrder: NotGiven[Order[A]]): PartialOrder[A :| C] = ev.asInstanceOf[PartialOrder[A :| C]]
-
-  inline given [A, C](using inline ev: Order[A]): Order[A :| C] = ev.asInstanceOf[Order[A :| C]]
-
-  inline given [A, C](using inline ev: Show[A]): Show[A :| C] = ev.asInstanceOf[Show[A :| C]]
-
-  inline given [A, C, V](using inline ev: LowerBounded[A], implication: C ==> Greater[V]): LowerBounded[A :| C] =
-    ev.asInstanceOf[LowerBounded[A :| C]]
-
-  inline given [A, C, V](using inline ev: UpperBounded[A], implication: C ==> Greater[V]): UpperBounded[A :| C] =
-    ev.asInstanceOf[UpperBounded[A :| C]]
-
-  private def posMonoid[A, C](using ev: CommutativeMonoid[A], shift: PosShift[A], implication: C ==> Positive): CommutativeMonoid[A :| C] =
-    new CommutativeMonoid[A :| C]:
-
-      override def empty: A :| C = ev.empty.asInstanceOf[A :| C]
-
-      override def combine(a: A :| C, b: A :| C): A :| C = shift.shift(ev.combine(a, b)).asInstanceOf[A :| C]
-
-  inline given posIntCommutativeMonoid[C](using C ==> Positive): CommutativeMonoid[Int :| C] = posMonoid
-
-  inline given posLongCommutativeMonoid[C](using C ==> Positive): CommutativeMonoid[Long :| C] = posMonoid
-
-  inline given posFloatCommutativeMonoid[C](using C ==> Positive): CommutativeMonoid[Float :| C] = posMonoid
-
-  inline given posDoubleCommutativeMonoid[C](using C ==> Positive): CommutativeMonoid[Double :| C] = posMonoid
-
-  private def negMonoid[A, C](using ev: CommutativeMonoid[A], shift: NegShift[A], implication: C ==> Negative): CommutativeMonoid[A :| C] =
-    new CommutativeMonoid[A :| C]:
-
-      override def empty: A :| C = ev.empty.asInstanceOf[A :| C]
-
-      override def combine(a: A :| C, b: A :| C): A :| C = shift.shift(ev.combine(a, b)).asInstanceOf[A :| C]
-
-  inline given negIntCommutativeMonoid[C](using C ==> Negative): CommutativeMonoid[Int :| C] = negMonoid
-
-  inline given negLongCommutativeMonoid[C](using C ==> Negative): CommutativeMonoid[Long :| C] = negMonoid
-
-  inline given negFloatCommutativeMonoid[C](using C ==> Negative): CommutativeMonoid[Float :| C] = negMonoid
-
-  inline given negDoubleCommutativeMonoid[C](using C ==> Negative): CommutativeMonoid[Double :| C] = negMonoid
-
-/**
- * Cats' instances for Iron that need to have a lower priority to avoid ambiguous implicits.
- */
-private trait IronCatsLowPriority:
-
-  inline given [A, C](using inline ev: Hash[A]): Hash[A :| C] = ev.asInstanceOf[Hash[A :| C]]
-
-private trait RefinedTypeOpsCats extends RefinedTypeOpsCatsLowPriority:
-
-  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Eq[mirror.IronType]): Eq[T] = ev.asInstanceOf[Eq[T]]
-
-  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Order[mirror.IronType]): Order[T] = ev.asInstanceOf[Order[T]]
-
-  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Show[mirror.IronType]): Show[T] = ev.asInstanceOf[Show[T]]
-
-  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: PartialOrder[mirror.IronType]): PartialOrder[T] = ev.asInstanceOf[PartialOrder[T]]
-
-private trait RefinedTypeOpsCatsLowPriority:
-
-  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Hash[mirror.IronType]): Hash[T] = ev.asInstanceOf[Hash[T]]

cats/src/io/github/iltotore/iron/instances.scala

@@ -0,0 +1,120 @@
+package io.github.iltotore.iron
+
+import _root_.cats.kernel.{CommutativeMonoid, CommutativeSemigroup, Hash, LowerBounded, PartialOrder, UpperBounded}
+import _root_.cats.{Eq, Monoid, Order, Show, Traverse}
+import io.github.iltotore.iron.constraint.numeric.*
+import scala.util.NotGiven
+import _root_.cats.Functor
+import algebra.instances.all.*
+import algebra.ring.{AdditiveCommutativeMonoid, AdditiveCommutativeSemigroup, MultiplicativeGroup, MultiplicativeMonoid}
+
+/**
+ * Represent all Cats' typeclass instances for Iron.
+ */
+private[iron] trait IronCatsInstances extends IronCatsLowPriority, RefinedTypeOpsCats:
+
+  given [F[_]](using functor: Functor[F]): MapLogic[F] with
+
+    override def map[A, B](wrapper: F[A], f: A => B): F[B] = functor.map(wrapper)(f)
+
+  // The `NotGiven` implicit parameter is mandatory to avoid ambiguous implicit error when both Eq[A] and Hash[A]/PartialOrder[A] exist
+  inline given [A, C](using inline ev: Eq[A], notHashOrOrder: NotGiven[Hash[A] | PartialOrder[A]]): Eq[A :| C] = ev.asInstanceOf[Eq[A :| C]]
+
+  inline given [A, C](using inline ev: PartialOrder[A], notOrder: NotGiven[Order[A]]): PartialOrder[A :| C] = ev.asInstanceOf[PartialOrder[A :| C]]
+
+  inline given [A, C](using inline ev: Order[A]): Order[A :| C] = ev.asInstanceOf[Order[A :| C]]
+
+  inline given [A, C](using inline ev: Show[A]): Show[A :| C] = ev.asInstanceOf[Show[A :| C]]
+
+  inline given [A, C, V](using inline ev: LowerBounded[A], implication: C ==> Greater[V]): LowerBounded[A :| C] =
+    ev.asInstanceOf[LowerBounded[A :| C]]
+
+  inline given [A, C, V](using inline ev: UpperBounded[A], implication: C ==> Greater[V]): UpperBounded[A :| C] =
+    ev.asInstanceOf[UpperBounded[A :| C]]
+
+  private def commutativeSemigroup[A, C](using inner: CommutativeSemigroup[A], bounds: Bounds[A, C]): CommutativeSemigroup[A :| C] =
+    new CommutativeSemigroup[A :| C]:
+
+      override def combine(a: A :| C, b: A :| C): A :| C = bounds.shift(inner.combine(a, b))
+
+  given posIntCommutativeSemigroup: CommutativeSemigroup[Int :| Positive] = commutativeSemigroup[Int, Positive]
+  given posLongCommutativeSemigroup: CommutativeSemigroup[Long :| Positive] = commutativeSemigroup[Long, Positive]
+  given posFloatCommutativeSemigroup: CommutativeSemigroup[Float :| Positive] = commutativeSemigroup[Float, Positive]
+  given posDoubleCommutativeSemigroup: CommutativeSemigroup[Double :| Positive] = commutativeSemigroup[Double, Positive]
+
+  given negIntCommutativeSemigroup: CommutativeSemigroup[Int :| Negative] = commutativeSemigroup[Int, Negative]
+  given negLongCommutativeSemigroup: CommutativeSemigroup[Long :| Negative] = commutativeSemigroup[Long, Negative]
+  given negFloatCommutativeSemigroup: CommutativeSemigroup[Float :| Negative] = commutativeSemigroup[Float, Negative]
+  given negDoubleCommutativeSemigroup: CommutativeSemigroup[Double :| Negative] = commutativeSemigroup[Double, Negative]
+
+  private def commutativeMonoid[A, C](using inner: CommutativeMonoid[A], bounds: Bounds[A, C]): CommutativeMonoid[A :| C] =
+    new CommutativeMonoid[A :| C]:
+
+      override def empty: A :| C = inner.empty.assume[C]
+
+      override def combine(a: A :| C, b: A :| C): A :| C = bounds.shift(inner.combine(a, b))
+
+  given posIntCommutativeMonoid: CommutativeMonoid[Int :| Positive0] = commutativeMonoid[Int, Positive0]
+  given posLongCommutativeMonoid: CommutativeMonoid[Long :| Positive0] = commutativeMonoid[Long, Positive0]
+  given posFloatCommutativeMonoid: CommutativeMonoid[Float :| Positive0] = commutativeMonoid[Float, Positive0]
+  given posDoubleCommutativeMonoid: CommutativeMonoid[Double :| Positive0] = commutativeMonoid[Double, Positive0]
+
+  given negIntCommutativeMonoid: CommutativeMonoid[Int :| Negative0] = commutativeMonoid[Int, Negative0]
+  given negLongCommutativeMonoid: CommutativeMonoid[Long :| Negative0] = commutativeMonoid[Long, Negative0]
+  given negFloatCommutativeMonoid: CommutativeMonoid[Float :| Negative0] = commutativeMonoid[Float, Negative0]
+  given negDoubleCommutativeMonoid: CommutativeMonoid[Double :| Negative0] = commutativeMonoid[Double, Negative0]
+
+/**
+ * Cats' instances for Iron that need to have a lower priority to avoid ambiguous implicits.
+ */
+private trait IronCatsLowPriority:
+
+  inline given [A, C](using inline ev: Hash[A]): Hash[A :| C] = ev.asInstanceOf[Hash[A :| C]]
+
+private trait RefinedTypeOpsCats extends RefinedTypeOpsCatsLowPriority:
+
+  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Eq[mirror.IronType]): Eq[T] = ev.asInstanceOf[Eq[T]]
+
+  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Order[mirror.IronType]): Order[T] = ev.asInstanceOf[Order[T]]
+
+  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Show[mirror.IronType]): Show[T] = ev.asInstanceOf[Show[T]]
+
+  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: PartialOrder[mirror.IronType]): PartialOrder[T] = ev.asInstanceOf[PartialOrder[T]]
+
+private trait RefinedTypeOpsCatsLowPriority:
+
+  inline given [T](using mirror: RefinedTypeOps.Mirror[T], ev: Hash[mirror.IronType]): Hash[T] = ev.asInstanceOf[Hash[T]]
+
+  private def additiveCommutativeSemigroup[A, C](using inner: AdditiveCommutativeSemigroup[A], bounds: Bounds[A, C]): AdditiveCommutativeSemigroup[A :| C] = (x, y) =>
+    bounds.shift(inner.plus(x, y))
+
+  given posIntAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Int :| Positive] = additiveCommutativeSemigroup[Int, Positive]
+  given posLongAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Long :| Positive] = additiveCommutativeSemigroup[Long, Positive]
+  given posFloatAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Float :| Positive] = additiveCommutativeSemigroup[Float, Positive]
+  given posDoubleAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Double :| Positive] = additiveCommutativeSemigroup[Double, Positive]
+
+  given negIntAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Int :| Negative] = additiveCommutativeSemigroup[Int, Negative]
+  given negLongAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Long :| Negative] = additiveCommutativeSemigroup[Long, Negative]
+  given negFloatAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Float :| Negative] = additiveCommutativeSemigroup[Float, Negative]
+  given negDoubleAdditiveCommutativeSemigroup: AdditiveCommutativeSemigroup[Double :| Negative] = additiveCommutativeSemigroup[Double, Negative]
+
+  private def additiveCommutativeMonoid[A, C](using inner: AdditiveCommutativeMonoid[A], bounds: Bounds[A, C]): AdditiveCommutativeMonoid[A :| C] = new:
+
+    override def zero: A :| C = inner.zero.assume[C]
+    override def plus(x: A :| C, y: A :| C): A :| C = bounds.shift(inner.plus(x, y))
+
+  given posIntAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Int :| Positive0] = additiveCommutativeMonoid[Int, Positive0]
+  given posLongAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Long :| Positive0] = additiveCommutativeMonoid[Long, Positive0]
+  given posFloatAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Float :| Positive0] = additiveCommutativeMonoid[Float, Positive0]
+  given posDoubleAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Double :| Positive0] = additiveCommutativeMonoid[Double, Positive0]
+
+  given negIntAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Int :| Negative0] = additiveCommutativeMonoid[Int, Negative0]
+  given negLongAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Long :| Negative0] = additiveCommutativeMonoid[Long, Negative0]
+  given negFloatAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Float :| Negative0] = additiveCommutativeMonoid[Float, Negative0]
+  given negDoubleAdditiveCommutativeMonoid: AdditiveCommutativeMonoid[Double :| Negative0] = additiveCommutativeMonoid[Double, Negative0]
+
+  given multiplicativeMonoid[A, C](using inner: MultiplicativeMonoid[A]): MultiplicativeMonoid[A :| C] =
+    inner.assumeAll[C]
+
+  given multiplicativeGroup[A, C](using inner: MultiplicativeGroup[A]): MultiplicativeGroup[A :| C] =
+    inner.assumeAll[C]