CouldBeGivenInstance

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.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> 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._

// integer-rounded division
scala> def divide[F[_]](dividend: Int, divisor: Int)(implicit F: ApplicativeError[F, String]): F[Int] =
    | if (divisor === 0) F.raiseError("division by zero")
    | else F.pure(dividend / divisor)

scala> type ErrorOr[A] = Either[String, A]

scala> divide[ErrorOr](6, 3)
res0: ErrorOr[Int] = Right(2)

scala> divide[ErrorOr](6, 0)
res1: ErrorOr[Int] = Left(division by zero)

scala> import cats.implicits._
scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
scala> List("1", "2", "3").traverse(parseInt)
res0: Option[List[Int]] = Some(List(1, 2, 3))
scala> List("1", "two", "3").traverse(parseInt)
res1: Option[List[Int]] = None

scala> import cats.implicits._

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

scala> import cats._, implicits._

scala> def pf: PartialFunction[String, String] = { case "error" => "ERROR" }

scala> ApplicativeError[Either[String, *], String].adaptError("error".asLeft[Int])(pf)
res0: Either[String,Int] = Left(ERROR)

scala> ApplicativeError[Either[String, *], String].adaptError("err".asLeft[Int])(pf)
res1: Either[String,Int] = Left(err)

scala> ApplicativeError[Either[String, *], String].adaptError(1.asRight[String])(pf)
res2: Either[String,Int] = Right(1)

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 scala.util.{Try, Success, Failure}

scala> def checkError(result: Either[Throwable, Int]): Try[String] = result.fold(_ => Failure(new java.lang.Exception), _ => Success("success"))

scala> val a: Try[Int] = Failure(new Throwable("failed"))
scala> a.attemptTap(checkError)
res0: scala.util.Try[Int] = Failure(java.lang.Exception)

scala> val b: Try[Int] = Success(1)
scala> b.attemptTap(checkError)
res1: scala.util.Try[Int] = Success(1)

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 = 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> 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 = 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> 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)