IsGivenInstance

scala> import cats.implicits._

scala> val someF: Option[Int => Long] = Some(_.toLong + 1L)
scala> val noneF: Option[Int => Long] = None
scala> val someInt: Option[Int] = Some(3)
scala> val noneInt: Option[Int] = None

scala> Apply[Option].ap(someF)(someInt)
res0: Option[Long] = Some(4)

scala> Apply[Option].ap(noneF)(someInt)
res1: Option[Long] = None

scala> Apply[Option].ap(someF)(noneInt)
res2: Option[Long] = None

scala> Apply[Option].ap(noneF)(noneInt)
res3: Option[Long] = None

scala> import cats.implicits._
scala> import cats.CoflatMap
scala> val fa = Some(3)
scala> def f(a: Option[Int]): Int = a match {
    | case Some(x) => 2 * x
    | case None => 0 }
scala> CoflatMap[Option].coflatMap(fa)(f)
res0: Option[Int] = Some(6)

scala> import cats.Id
scala> import cats.Comonad
scala> val id: Id[Int] = 3
scala> Comonad[Id].extract(id)
res0: cats.Id[Int] = 3

scala> import cats.Foldable, cats.implicits._
scala> val fa = Option(1)

Folding by addition to zero:
scala> Foldable[Option].foldLeft(fa, Option(0))((a, n) => a.map(_ + n))
res0: Option[Int] = Some(1)

Folding `Option` with addition from zero:
scala> fa.foldLeft(Option(0))((a, n) => a.map(_ + n))
res1: Option[Int] = Some(1)

There's also an alias `foldl` which is equivalent:
scala> fa.foldl(Option(0))((a, n) => a.map(_ + n))
res2: Option[Int] = Some(1)

scala> import cats.Foldable, cats.Eval, cats.implicits._
scala> val fa = Option(1)

Folding by addition to zero:
scala> val folded1 = Foldable[Option].foldRight(fa, Eval.now(0))((n, a) => a.map(_ + n))
Since `foldRight` yields a lazy computation, we need to force it to inspect the result:
scala> folded1.value
res0: Int = 1

With syntax extensions, we can write the same thing like this:
scala> val folded2 = fa.foldRight(Eval.now(0))((n, a) => a.map(_ + n))
scala> folded2.value
res1: Int = 1

Unfortunately, since `foldRight` is defined on many collections - this
extension clashes with the operation defined in `Foldable`.

To get past this and make sure you're getting the lazy `foldRight` defined
in `Foldable`, there's an alias `foldr`:
scala> val folded3 = fa.foldr(Eval.now(0))((n, a) => a.map(_ + n))
scala> folded3.value
res1: Int = 1

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> def countWords(words: List[String]): Map[String, Int] = words.groupBy(identity).map { case (k, v) => (k, v.length) }
scala> val expectedResult = Map("do" -> NonEmptyList.of(1, 2), "you" -> NonEmptyList.of(1, 1))
scala> val x = List("How", "do", "you", "fly")
scala> val y = List("What", "do", "you", "do")
scala> val result = NonEmptyList.of(x, y).nonEmptyTraverse(countWords)
scala> result === expectedResult
res0: Boolean = true

scala> import cats.implicits._

scala> val noneInt: Option[Int] = None
scala> val some3: Option[Int] = Some(3)
scala> val noneString: Option[String] = None
scala> val someFoo: Option[String] = Some("foo")

scala> Semigroupal[Option].product(noneInt, noneString)
res0: Option[(Int, String)] = None

scala> Semigroupal[Option].product(noneInt, someFoo)
res1: Option[(Int, String)] = None

scala> Semigroupal[Option].product(some3, noneString)
res2: Option[(Int, String)] = None

scala> Semigroupal[Option].product(some3, someFoo)
res3: Option[(Int, String)] = Some((3,foo))

scala> import cats.implicits._

scala> Applicative[Option].pure(10)
res0: Option[Int] = Some(10)

scala> import cats.implicits._

scala> Applicative[Option].unit
res0: Option[Unit] = Some(())

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForList

scala> Functor[List].as(List(1,2,3), "hello")
res0: List[String] = List(hello, hello, hello)

scala> import cats.implicits._
scala> import cats.CoflatMap
scala> val fa = Some(3)
fa: Option[Int] = Some(3)
scala> CoflatMap[Option].coflatten(fa)
res0: Option[Option[Int]] = Some(Some(3))

scala> import cats.implicits._
scala> val keys = List(1, 2, 4, 5)
scala> val map = Map(4 -> "Four", 5 -> "Five")
scala> keys.collectFirstSome(map.get)
res0: Option[String] = Some(Four)
scala> val map2 = Map(6 -> "Six", 7 -> "Seven")
scala> keys.collectFirstSome(map2.get)
res1: Option[String] = None

scala> import cats.implicits._
scala> def parseInt(s: String): Either[String, Int] = Either.catchOnly[NumberFormatException](s.toInt).leftMap(_.getMessage)
scala> val keys1 = List("1", "2", "4", "5")
scala> val map1 = Map(4 -> "Four", 5 -> "Five")
scala> Foldable[List].collectFirstSomeM(keys1)(parseInt(_) map map1.get)
res0: scala.util.Either[String,Option[String]] = Right(Some(Four))

scala> val map2 = Map(6 -> "Six", 7 -> "Seven")
scala> Foldable[List].collectFirstSomeM(keys1)(parseInt(_) map map2.get)
res1: scala.util.Either[String,Option[String]] = Right(None)

scala> val keys2 = List("1", "x", "4", "5")
scala> Foldable[List].collectFirstSomeM(keys2)(parseInt(_) map map1.get)
res2: scala.util.Either[String,Option[String]] = Left(For input string: "x")

scala> val keys3 = List("1", "2", "4", "x")
scala> Foldable[List].collectFirstSomeM(keys3)(parseInt(_) map map1.get)
res3: scala.util.Either[String,Option[String]] = Right(Some(Four))

scala> import cats.implicits._
scala> val xs = List(1, 2, 3, 4)
scala> Foldable[List].collectFold(xs) { case n if n % 2 == 0 => n }
res0: Int = 6

scala> import cats.implicits._
scala> val xs = List(1, 2, 3, 4)
scala> def f(n: Int): Option[Int] = if (n % 2 == 0) Some(n) else None
scala> Foldable[List].collectFoldSome(xs)(f)
res0: Int = 6

scala> import cats.implicits._

scala> val alo = Apply[List].compose[Option]

scala> alo.product(List(None, Some(true), Some(false)), List(Some(2), None))
res1: List[Option[(Boolean, Int)]] = List(None, None, Some((true,2)), None, Some((false,2)), None)

scala> import cats.implicits._
scala> import scala.concurrent.duration._

scala> val durSemigroupList: Semigroup[List[FiniteDuration]] =
    | Invariant[Semigroup].compose[List].imap(Semigroup[List[Long]])(Duration.fromNanos)(_.toNanos)
scala> durSemigroupList.combine(List(2.seconds, 3.seconds), List(4.seconds))
res1: List[FiniteDuration] = List(2 seconds, 3 seconds, 4 seconds)

scala> import cats.implicits._

scala> val alo = Applicative[List].compose[Option]

scala> alo.pure(3)
res0: List[Option[Int]] = List(Some(3))

scala> alo.product(List(None, Some(true), Some(false)), List(Some(2), None))
res1: List[Option[(Boolean, Int)]] = List(None, None, Some((true,2)), None, Some((false,2)), None)

scala> import cats.implicits._
scala> import scala.concurrent.duration._

scala> type ToInt[T] = T => Int
scala> val durSemigroupToInt: Semigroup[ToInt[FiniteDuration]] =
    | Invariant[Semigroup]
    |   .composeContravariant[ToInt]
    |   .imap(Semigroup[ToInt[Long]])(Duration.fromNanos)(_.toNanos)
// semantically equal to (2.seconds.toSeconds.toInt + 1) + (2.seconds.toSeconds.toInt * 2) = 7
scala> durSemigroupToInt.combine(_.toSeconds.toInt + 1, _.toSeconds.toInt * 2)(2.seconds)
res1: Int = 7

scala> import cats.kernel.Comparison
scala> import cats.implicits._

// compares strings by alphabetical order
scala> val alpha: Order[String] = Order[String]

// compares strings by their length
scala> val strLength: Order[String] = Order.by[String, Int](_.length)

scala> val stringOrders: List[Order[String]] = List(alpha, strLength)

// first comparison is with alpha order, second is with string length
scala> stringOrders.map(o => o.comparison("abc", "de"))
res0: List[Comparison] = List(LessThan, GreaterThan)

scala> val le = Applicative[List].composeContravariantMonoidal[Order]

// create Int orders that convert ints to strings and then use the string orders
scala> val intOrders: List[Order[Int]] = le.contramap(stringOrders)(_.toString)

// first comparison is with alpha order, second is with string length
scala> intOrders.map(o => o.comparison(12, 3))
res1: List[Comparison] = List(LessThan, GreaterThan)

// create the `product` of the string order list and the int order list
// `p` contains a list of the following orders:
// 1. (alpha comparison on strings followed by alpha comparison on ints)
// 2. (alpha comparison on strings followed by length comparison on ints)
// 3. (length comparison on strings followed by alpha comparison on ints)
// 4. (length comparison on strings followed by length comparison on ints)
scala> val p: List[Order[(String, Int)]] = le.product(stringOrders, intOrders)

scala> p.map(o => o.comparison(("abc", 12), ("def", 3)))
res2: List[Comparison] = List(LessThan, LessThan, LessThan, GreaterThan)

scala> import cats.implicits._
scala> import scala.concurrent.duration._

scala> val durSemigroupList: Semigroup[List[FiniteDuration]] =
    | Invariant[Semigroup]
    |   .composeFunctor[List]
    |   .imap(Semigroup[List[Long]])(Duration.fromNanos)(_.toNanos)
scala> durSemigroupList.combine(List(2.seconds, 3.seconds), List(4.seconds))
res1: List[FiniteDuration] = List(2 seconds, 3 seconds, 4 seconds)

scala> import cats.implicits._
scala> val map1 = Map[Int, String]()
scala> val p1: String => Boolean = _.length > 0
scala> UnorderedFoldable[Map[Int, *]].count(map1)(p1)
res0: Long = 0

scala> val map2 = Map(1 -> "hello", 2 -> "world", 3 -> "!")
scala> val p2: String => Boolean = _.length > 1
scala> UnorderedFoldable[Map[Int, *]].count(map2)(p2)
res1: Long = 2

scala> import cats.implicits._
scala> val F = Foldable[List]
scala> F.existsM(List(1,2,3,4))(n => Option(n <= 4))
res0: Option[Boolean] = Some(true)

scala> F.existsM(List(1,2,3,4))(n => Option(n > 4))
res1: Option[Boolean] = Some(false)

scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) Option(true) else Option(false))
res2: Option[Boolean] = Some(true)

scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) Option(true) else None)
res3: Option[Boolean] = Some(true)

scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) None else Option(true))
res4: Option[Boolean] = None

scala> import cats.implicits._
scala> val list = List(1,2,3,4)
scala> Foldable[List].findM(list)(n => (n >= 2).asRight[String])
res0: Either[String,Option[Int]] = Right(Some(2))

scala> Foldable[List].findM(list)(n => (n > 4).asRight[String])
res1: Either[String,Option[Int]] = Right(None)

scala> Foldable[List].findM(list)(n => Either.cond(n < 3, n >= 2, "error"))
res2: Either[String,Option[Int]] = Right(Some(2))

scala> Foldable[List].findM(list)(n => Either.cond(n < 3, false, "error"))
res3: Either[String,Option[Int]] = Left(error)

scala> import cats.implicits._
scala> val x: List[Option[List[Int]]] = List(Some(List(1, 2)), Some(List(3)))
scala> val y: List[Option[List[Int]]] = List(None, Some(List(3)))
scala> x.flatSequence
res0: Option[List[Int]] = Some(List(1, 2, 3))
scala> y.flatSequence
res1: Option[List[Int]] = None

scala> import cats._, implicits._
scala> Option(1).flatTap(_ => None)
res0: Option[Int] = None
scala> Option(1).flatTap(_ => Some("123"))
res1: Option[Int] = Some(1)
scala> def nCats(n: Int) = List.fill(n)("cat")
nCats: (n: Int)List[String]
scala> List[Int](0).flatTap(nCats)
res2: List[Int] = List()
scala> List[Int](4).flatTap(nCats)
res3: List[Int] = List(4, 4, 4, 4)

scala> import cats.implicits._
scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
scala> val x = Option(List("1", "two", "3"))
scala> x.flatTraverse(_.map(parseInt))
res0: List[Option[Int]] = List(Some(1), None, Some(3))

scala> import cats.Eval
scala> import cats.implicits._

scala> val nested: Eval[Eval[Int]] = Eval.now(Eval.now(3))
scala> val flattened: Eval[Int] = nested.flatten
scala> flattened.value
res0: Int = 3