object HigherOrderFunctions extends AnyFlatSpec with ScalaTutorialSection
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Functional languages treat functions as first-class values.
Higher-Order Functions
Functional languages treat functions as first-class values.
This means that, like any other value, a function can be passed as a parameter and returned as a result.
This provides a flexible way to compose programs.
Functions that take other functions as parameters or that return functions as results are called higher order functions.
Motivation
Consider the following programs.
Take the sum of the integers between
a
andb
:def sumInts(a: Int, b: Int): Int = if (a > b) 0 else a + sumInts(a + 1, b)
Take the sum of the cubes of all the integers between
a
andb
:def cube(x: Int): Int = x * x * x def sumCubes(a: Int, b: Int): Int = if (a > b) 0 else cube(a) + sumCubes(a + 1, b)
Take the sum of the factorials of all the integers between
a
andb
:def sumFactorials(a: Int, b: Int): Int = if (a > b) 0 else factorial(a) + sumFactorials(a + 1, b)
Note how similar these methods are. Can we factor out the common pattern?
Summing with Higher-Order Functions
Let's define:
def sum(f: Int => Int, a: Int, b: Int): Int = if (a > b) 0 else f(a) + sum(f, a + 1, b)
We can then write:
def id(x: Int): Int = x def sumInts(a: Int, b: Int) = sum(id, a, b) def sumCubes(a: Int, b: Int) = sum(cube, a, b) def sumFactorials(a: Int, b: Int) = sum(factorial, a, b)
Function Types
The type
A => B
is the type of a function that takes an argument of typeA
and returns a result of typeB
.So,
Int => Int
is the type of functions that map integers to integers.Similarly,
(A1, A2) => B
is the type of functions that take two arguments (of typesA1
andA2
, respectively) and return a result of typeB
.More generally,
(A1, ..., An) => B
is the type of functions that taken
arguments (of typesA1
to An) and return a result of type
B.
Anonymous Functions
Passing functions as parameters leads to the creation of many small functions.
Sometimes it is tedious to have to define (and name) these functions using
def
.Compare to strings: We do not need to define a string using
val
. Instead of:val str = "abc"; println(str)
We can directly write:
println("abc")
because strings exist as literals. Analogously we would like function literals, which let us write a function without giving it a name.
These are called anonymous functions.
Anonymous Function Syntax
Example of a function that raises its argument to a cube:
(x: Int) => x * x * x
Here,
(x: Int)
is the parameter of the function, andx * x * x
is its body.The type of the parameter can be omitted if it can be inferred by the compiler from the context.
If there are several parameters, they are separated by commas:
(x: Int, y: Int) => x + y
Anonymous Functions are Syntactic Sugar
An anonymous function
(x1: T1, …, xn: Tn) => e
can always be expressed usingdef
as follows:{ def f(x1: T1, …, xn: Tn) = e ; f }
where
f
is an arbitrary, fresh name (that's not yet used in the program).One can therefore say that anonymous functions are syntactic sugar.
Summation with Anonymous Functions
Using anonymous functions, we can write sums in a shorter way:
def sumInts(a: Int, b: Int) = sum(x => x, a, b) def sumCubes(a: Int, b: Int) = sum(x => x * x * x, a, b)
Exercise
The
sum
function uses linear recursion. Complete the following tail-recursive version: - def testDataFor(testName: String, theConfigMap: ConfigMap): TestData
- Definition Classes
- AnyFlatSpecLike → Suite
- def testNames: Set[String]
- Definition Classes
- AnyFlatSpecLike → Suite
- def the[T](implicit arg0: ClassTag[T], pos: Position): ResultOfTheTypeInvocation[T]
- Definition Classes
- Matchers
- def theSameElementsAs(xs: GenTraversable[_]): ResultOfTheSameElementsAsApplication
- Definition Classes
- Matchers
- def theSameElementsInOrderAs(xs: GenTraversable[_]): ResultOfTheSameElementsInOrderAsApplication
- Definition Classes
- Matchers
- val theSameInstanceAs: TheSameInstanceAsPhrase
- Definition Classes
- Matchers
- val they: TheyWord
- Attributes
- protected
- Definition Classes
- AnyFlatSpecLike
- def thrownBy(fun: => Any): ResultOfThrownByApplication
- Definition Classes
- Matchers
- def toString(): String
- Definition Classes
- AnyFlatSpec → AnyRef → Any
- val typeCheck: TypeCheckWord
- Definition Classes
- MatcherWords
- def typeCheckedConstraint[A, B](implicit equivalenceOfA: Equivalence[A], ev: <:<[B, A]): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- implicit def unconstrainedEquality[A, B](implicit equalityOfA: Equality[A]): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- val value: ValueWord
- Definition Classes
- Matchers
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
- def withClue[T](clue: Any)(fun: => T): T
- Definition Classes
- Assertions
- def withFixture(test: NoArgTest): Outcome
- Attributes
- protected
- Definition Classes
- TestSuite
- val writable: WritableWord
- Definition Classes
- MatcherWords
Deprecated Value Members
- def conversionCheckedConstraint[A, B](implicit equivalenceOfA: Equivalence[A], cnv: (B) => A): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- Annotations
- @deprecated
- Deprecated
(Since version 3.1.0) The conversionCheckedConstraint method has been deprecated and will be removed in a future version of ScalaTest. It is no longer needed now that the deprecation period of ConversionCheckedTripleEquals has expired. It will not be replaced.
- def convertEquivalenceToAToBConversionConstraint[A, B](equivalenceOfB: Equivalence[B])(implicit ev: (A) => B): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- Annotations
- @deprecated
- Deprecated
(Since version 3.1.0) The convertEquivalenceToAToBConversionConstraint method has been deprecated and will be removed in a future version of ScalaTest. It is no longer needed now that the deprecation period of ConversionCheckedTripleEquals has expired. It will not be replaced.
- def convertEquivalenceToBToAConversionConstraint[A, B](equivalenceOfA: Equivalence[A])(implicit ev: (B) => A): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- Annotations
- @deprecated
- Deprecated
(Since version 3.1.0) The convertEquivalenceToBToAConversionConstraint method has been deprecated and will be removed in a future version of ScalaTest. It is no longer needed now that the deprecation period of ConversionCheckedTripleEquals has expired. It will not be replaced.
- def lowPriorityConversionCheckedConstraint[A, B](implicit equivalenceOfB: Equivalence[B], cnv: (A) => B): CanEqual[A, B]
- Definition Classes
- TripleEquals → TripleEqualsSupport
- Annotations
- @deprecated
- Deprecated
(Since version 3.1.0) The lowPriorityConversionCheckedConstraint method has been deprecated and will be removed in a future version of ScalaTest. It is no longer needed now that the deprecation period of ConversionCheckedTripleEquals has expired. It will not be replaced.
- final val styleName: String
- Definition Classes
- AnyFlatSpecLike → Suite
- Annotations
- @deprecated
- Deprecated
(Since version 3.1.0) The styleName lifecycle method has been deprecated and will be removed in a future version of ScalaTest with no replacement.