diff --git a/src/main/scala/fpspeedrun/Eq.scala b/src/main/scala/fpspeedrun/Eq.scala
index 9dfc567..2960e77 100644
--- a/src/main/scala/fpspeedrun/Eq.scala
+++ b/src/main/scala/fpspeedrun/Eq.scala
@@ -1,33 +1,13 @@
 package fpspeedrun
 import syntax.eq._
 
-import scala.annotation.tailrec
-
 trait Eq[T] {
   def ===(x: T, y: T): Boolean
 }
 
 object Eq {
-  def fromEquals[T]: Eq[T] = _ == _
-
-  implicit val intEq: Eq[Int] = fromEquals
-  implicit val longEq: Eq[Long] = fromEquals
-
-  /** простой вариант */
-  implicit def vectorEq[A: Eq]: Eq[Vector[A]] =
-    (xs, ys) => xs.view.zip(ys).forall { case (x, y) => x === y }
-
-
-  /** я у мамы оптимизатор */
-  implicit def listEq[A: Eq]: Eq[List[A]] = {
-    @tailrec def go(xs: List[A], ys: List[A]): Boolean =
-      xs match {
-        case Nil => ys.isEmpty
-        case x :: xt => ys match {
-          case Nil => false
-          case y :: yt => x === y && go(xt, yt)
-        }
-      }
-    go
+  implicit def compareLists[T](implicit eqq: Eq[T]): Eq[List[T]] = {
+    (x: List[T], y: List[T]) => x.nonEmpty && x.lengthCompare(y.length) == 0 &&
+      x.zip(y).forall { case (f, s) => f === s }
   }
 }
diff --git a/src/main/scala/fpspeedrun/Iso.scala b/src/main/scala/fpspeedrun/Iso.scala
new file mode 100644
index 0000000..c683347
--- /dev/null
+++ b/src/main/scala/fpspeedrun/Iso.scala
@@ -0,0 +1,6 @@
+package fpspeedrun
+
+trait Iso[T, U] {
+  def wrap(x: T): U
+  def unwrap(x: U): T
+}
diff --git a/src/main/scala/fpspeedrun/Monoid.scala b/src/main/scala/fpspeedrun/Monoid.scala
new file mode 100644
index 0000000..76b0a94
--- /dev/null
+++ b/src/main/scala/fpspeedrun/Monoid.scala
@@ -0,0 +1,63 @@
+package fpspeedrun
+
+import scala.language.higherKinds
+import syntax.semigroup._
+
+trait Monoid[T] extends SemiGroup[T] {
+  def empty: T
+}
+
+object Monoid {
+  def apply[T](implicit i: Monoid[T]) = i
+
+  object Laws {
+    def identity[T : Monoid](x: T): Boolean = {
+      (Monoid[T].empty |+| x) == x &&
+        (x |+| Monoid[T].empty) == x
+    }
+
+    def associativity[T : Monoid](x: T, y: T, z: T): Boolean = {
+      ((x |+| y) |+| z) == (x |+| (y |+| z))
+    }
+  }
+
+  /**
+    * Функция, похожая на SemiGroup#combineList, но для Monoid.
+    * В отличие от предыдущей, возвращает не Option[T], а сам T.
+    * Для пустого списка, возвращает "единицу" в понятиях моноида.
+    */
+  def foldList[T : Monoid](list: List[T]): T = {
+    list.foldLeft(Monoid[T].empty) {
+      case (sum, next) => sum |+| next
+    }
+  }
+
+  /**
+    * #foldList, но с крутым синтаксисом и возможностью через параметр типа передавать
+    * желаемое поведение.
+    * Паттерн для синтаксиса называется: partial type application
+    */
+  def foldListVia[U[_]] = new FoldListVia[U]
+  class FoldListVia[U[_]] {
+    def apply[T](list: List[T])(implicit iso: Iso[T, U[T]], monoid: Monoid[U[T]]): T = {
+      val r = list.foldLeft(monoid.empty) {
+        (acc, next) => acc |+| iso.wrap(next)
+      }
+      iso.unwrap(r)
+    }
+  }
+
+  // monoid instances
+  implicit val defaultMonoidInt: Monoid[Int] = new Monoid[Int] {
+    override def empty: Int = 0
+    override def combine(x: Int, y: Int): Int = x+y
+  }
+  implicit val sumMonoidInt: Monoid[Sum[Int]] = new Monoid[Sum[Int]] {
+    override def empty: Sum[Int] = Sum(0)
+    override def combine(x: Sum[Int], y: Sum[Int]): Sum[Int] = Sum(x.x + y.x)
+  }
+  implicit val prodMonoidInt: Monoid[Prod[Int]] = new Monoid[Prod[Int]] {
+    override def empty: Prod[Int] = Prod(1)
+    override def combine(x: Prod[Int], y: Prod[Int]): Prod[Int] = Prod(x.x * y.x)
+  }
+}
\ No newline at end of file
diff --git a/src/main/scala/fpspeedrun/Ord.scala b/src/main/scala/fpspeedrun/Ord.scala
index 231eec3..45ba8be 100644
--- a/src/main/scala/fpspeedrun/Ord.scala
+++ b/src/main/scala/fpspeedrun/Ord.scala
@@ -1,15 +1,30 @@
 package fpspeedrun
+
 import fpspeedrun.Ord.Compare
+import fpspeedrun.Ord.Compare._
 
-trait Ord[T] extends Eq[T]{
+trait Ord[T] extends Eq[T] {
   def compare(x: T, y: T): Compare
 }
 
-object Ord{
+object Ord {
   sealed trait Compare
-  object Compare{
-    case object LT //less than
-    case object EQ //equals to
-    case object GT //greater than
+  object Compare {
+    case object LT extends Compare  // less than
+    case object EQ extends Compare  // equals to
+    case object GT extends Compare  // greater than
   }
-}
+
+  implicit def compareLists[T](implicit ord: Ord[T]): Ord[List[T]] =
+    new Ord[List[T]] {
+      override def compare(x: List[T], y: List[T]): Compare =
+        x.lengthCompare(y.length) match {
+          case neg if neg < 0 => LT
+          case zer if zer == 0 => EQ
+          case _ => GT
+        }
+
+      import syntax.eq._
+      override def ===(x: List[T], y: List[T]): Boolean = x === y
+    }
+}
\ No newline at end of file
diff --git a/src/main/scala/fpspeedrun/Ratio.scala b/src/main/scala/fpspeedrun/Ratio.scala
index 4587510..64763e2 100644
--- a/src/main/scala/fpspeedrun/Ratio.scala
+++ b/src/main/scala/fpspeedrun/Ratio.scala
@@ -1,10 +1,54 @@
 package fpspeedrun
 
-import syntax.eq._
+import fpspeedrun.Ord.Compare._
 
-final case class Ratio(num: Int, den: Int)
+final case class Ratio(numer: Int, denom: Int)
 
 object Ratio {
-  implicit val eq: Eq[Ratio] = (x, y) => x.num.toLong * y.den === x.den.toLong * y.num
-}
 
+  implicit val ordRatio: Ord[Ratio] = new Ord[Ratio] {
+    override def ===(x: Ratio, y: Ratio): Boolean =
+      x.numer * y.denom == y.numer * x.denom
+
+    override def compare(x: Ratio, y: Ratio): Ord.Compare =
+      if (===(x, y)) EQ
+      else if (x.numer * y.denom > y.numer * x.denom) GT
+      else LT
+  }
+
+  // semigroup instances
+  implicit val combineRatio: SemiGroup[Sum[Ratio]] =
+    (x: Sum[Ratio], y: Sum[Ratio]) => Sum(sum(x.x, y.x))
+  implicit val mulCombineRatio: SemiGroup[Prod[Ratio]] =
+    (x: Prod[Ratio], y: Prod[Ratio]) => Prod(mul(x.x, y.x))
+
+  // monoid instances
+  implicit val defaultMonoidRatio: Monoid[Ratio] = new Monoid[Ratio] {
+    override def empty: Ratio = Ratio(0, 1)
+    override def combine(x: Ratio, y: Ratio): Ratio = sum(x, y)
+  }
+  implicit val sumMonoidRatio: Monoid[Sum[Ratio]] = new Monoid[Sum[Ratio]] {
+    override def empty: Sum[Ratio] = Sum(Ratio(0, 1))
+    override def combine(x: Sum[Ratio], y: Sum[Ratio]): Sum[Ratio] = Sum(sum(x.x, y.x))
+  }
+  implicit val mulMonoidRatio: Monoid[Prod[Ratio]] = new Monoid[Prod[Ratio]] {
+    override def empty: Prod[Ratio] = Prod(Ratio(1, 1))
+    override def combine(x: Prod[Ratio], y: Prod[Ratio]): Prod[Ratio] = Prod(mul(x.x, y.x))
+  }
+
+  def sum(x: Ratio, y: Ratio): Ratio = {
+    val num = x.numer * y.denom + x.denom * y.numer
+    val denom = x.denom * y.denom
+    lazy val g = gcd(num, denom)
+    Ratio(num / g, denom / g)
+  }
+
+  def mul(x: Ratio, y: Ratio): Ratio = {
+    val num = x.numer * y.numer
+    val denom = x.denom * y.denom
+    lazy val g = gcd(num, denom)
+    Ratio(num/g, denom/g)
+  }
+
+  def gcd(a: Int, b: Int): Int = if (b==0) a else gcd(b, a%b)
+}
\ No newline at end of file
diff --git a/src/main/scala/fpspeedrun/SemiGroup.scala b/src/main/scala/fpspeedrun/SemiGroup.scala
new file mode 100644
index 0000000..ffddc3b
--- /dev/null
+++ b/src/main/scala/fpspeedrun/SemiGroup.scala
@@ -0,0 +1,51 @@
+package fpspeedrun
+import syntax.semigroup._
+
+trait SemiGroup[T] {
+  def combine(x: T, y: T): T
+}
+
+object SemiGroup {
+  object Laws {
+    def associativity[T : SemiGroup](x: T, y: T, z: T): Boolean = {
+      ((x |+| y) |+| z) == (x |+| (y |+| z))
+    }
+  }
+
+  implicit val combineString: SemiGroup[String] = (x: String, y: String) => x + y
+
+
+  def combineList[T : SemiGroup](list: List[T]): Option[T] = {
+    list.reduceOption(_ |+| _)
+  }
+
+  def combineListVia[U[_]] = new CombineListVia[U]
+
+  // partial type application
+  class CombineListVia[U[_]] {
+    def apply[T](list: List[T])(implicit iso: Iso[T, U[T]], sg: SemiGroup[U[T]]): Option[T] =
+      list.reduceOption((x, y) => iso.unwrap(iso.wrap(x) |+| iso.wrap(y)))
+  }
+}
+
+
+final case class Sum[T](x: T) extends AnyVal
+final case class Prod[T](x: T) extends AnyVal
+
+object Sum {
+  implicit def sumIso[T]: Iso[T, Sum[T]] = new Iso[T, Sum[T]] {
+    override def wrap(x: T): Sum[T] = Sum(x)
+    override def unwrap(x: Sum[T]): T = x.x
+  }
+  implicit val combineInt: SemiGroup[Sum[Int]] =
+    (x: Sum[Int], y: Sum[Int]) => Sum(x.x + y.x)
+}
+
+object Prod {
+  implicit def prodIso[T]: Iso[T, Prod[T]] = new Iso[T, Prod[T]] {
+    override def wrap(x: T): Prod[T] = Prod(x)
+    override def unwrap(x: Prod[T]): T = x.x
+  }
+  implicit val mulCombineInt: SemiGroup[Prod[Int]] =
+    (x: Prod[Int], y: Prod[Int]) => Prod(x.x * y.x)
+}
\ No newline at end of file
diff --git a/src/main/scala/fpspeedrun/syntax/compare.scala b/src/main/scala/fpspeedrun/syntax/compare.scala
new file mode 100644
index 0000000..64b346e
--- /dev/null
+++ b/src/main/scala/fpspeedrun/syntax/compare.scala
@@ -0,0 +1,21 @@
+package fpspeedrun.syntax
+
+import fpspeedrun.Ord
+import fpspeedrun.Ord.Compare.{EQ, GT, LT}
+
+object compare {
+  implicit class CompareOps[T](val x: T) extends AnyVal {
+    def compare(y: T)(implicit ord: Ord[T]): Ord.Compare = ord.compare(x, y)
+
+    def >(y: T)(implicit ord: Ord[T]): Boolean = compare(y) == GT
+    def <(y: T)(implicit ord: Ord[T]): Boolean = compare(y) == LT
+    def >=(y: T)(implicit ord: Ord[T]): Boolean = {
+      val c = compare(y)
+      c == GT || c == EQ
+    }
+    def <=(y: T)(implicit ord: Ord[T]): Boolean = {
+      val c = compare(y)
+      c == LT || c == EQ
+    }
+  }
+}
\ No newline at end of file
diff --git a/src/main/scala/fpspeedrun/syntax/semigroup.scala b/src/main/scala/fpspeedrun/syntax/semigroup.scala
new file mode 100644
index 0000000..b79ff03
--- /dev/null
+++ b/src/main/scala/fpspeedrun/syntax/semigroup.scala
@@ -0,0 +1,10 @@
+package fpspeedrun.syntax
+
+import fpspeedrun.SemiGroup
+
+object semigroup {
+    implicit class SemiGroupOps[T](val x: T) extends AnyVal {
+      def combine(y: T)(implicit sg: SemiGroup[T]): T = sg.combine(x, y)
+      def |+|(y: T)(implicit sg: SemiGroup[T]): T = combine(y)
+    }
+  }
\ No newline at end of file