CSC 347 - Concepts of Programming Languages

Methods and Functions: Currying

Instructor: Stefan Mitsch

Example

• In Scala 3, implement a function to add two integer numbers.

• def add(a: Int, b: Int): Int = {
    a + b
  }
  

• Is this really a function or rather a method?

Learning Objectives

How are methods in object-oriented programming and functions in functional programming related?

• Understand the difference between methods and functions in Scala
• Understand the difference between tupled and curried definitions
• Understand partial application

Functional Programming

• We say that functions are first-class if they can be
  • declared within any scope,
  • passed as arguments to other functions, and
  • returned as results of functions.

• Functions foreach, map, filter are higher-order functions
  • they take a function as argument
  • Also common: return a function as the result

Paired Methods

def add1(x:Int, y:Int) = x+y
add1(11, 21)

add1: (x: Int, y: Int)Int
res1: Int = 32

• This is the usual style of methods that take multiple arguments
• It is a method that
  • Takes a pair of Ints
  • Returns an Int

Curried Methods

def add2(x:Int)(y:Int) = x+y
add2(11)(21)

add2: (x: Int)(y: Int)Int
res2: Int = 32

• This is a curried definition
• It is a method that
  • Takes an Int
  • Returns a method of type (y:Int)Int Not to be confused with the function Int=>Int
  • So together the type of the method is add2: (x:Int)(y:Int)Int Not to be confused with the function Int=>Int=>Int

Functions

• Scala has first-class support for both functions and methods

def plus (x:Int, y:Int) = x+y
plus(1,2)

val plus = (x:Int, y:Int) => x+y
plus(1,2)

Functions

val add3 = (x:Int, y:Int) => x+y
add3(11, 21)

add3: (Int, Int) => Int = $$Lambda$4576/0x00000008018d1840@6ae4d2ad
res3: Int = 32

• This is a function that
  • Takes a pair of Ints
  • Returns an Int

Curried Functions

val add4 = (x:Int) => (y:Int) => x+y
add4(11)(21)

add4: Int => (Int => Int) = $$Lambda$...
res4: Int = 32

• This is a curried definition
• It is a function that
  • Takes an Int
  • Returns a function of type Int=>Int

Curried Methods

def add5(x:Int) = (y:Int) => x+y
add5(11)(21)

add5: (x: Int)Int => Int
res5: Int = 32

• You can mix the notations
• This is a method that
  • Takes an Int
  • Returns a function of type Int=>Int

Functions vs. Methods

def add1(x:Int, y:Int) = x+y
def add2(x:Int)(y:Int) = x+y
val add1f = add1 _
val add2f = add2 _

add1: (x: Int, y: Int)Int
add2: (x: Int)(y: Int)Int
add1f: (Int, Int) => Int = $$Lambda$...
add2f: Int => (Int => Int) = $$Lambda$...

• Another use of wildcard operator _
  • don't care pattern
  • anonymous function expression

Partial Application

val add4 = (x:Int) => (y:Int) => x+y
def add5(x:Int) = (y:Int) => x+y
val add4p = add4(11)
val add5p = add5(11)
val r4 = add4p(21)
val r5 = add5p(21)

add4: Int => (Int => Int) = $$Lambda$
add5: (x: Int)Int => Int
add4p: Int => Int = $$Lambda$
add5p: Int => Int = $$Lambda$
r4: Int = 32
r5: Int = 32

Partial Application

def add1(x:Int, y:Int) = x+y
def add2(x:Int)(y:Int) = x+y
val add3 = (x:Int, y:Int) => x+y
val add4 = (x:Int) => (y:Int) => x+y
def add5(x:Int) = (y:Int) => x+y
val add1p = add1(11, _)  /* x=>add1(11, x) */
val add2p = add2(11)(_)  /* x=>add2(11)(x) */
val add3p = add3(11, _)  /* x=>add3(11, x) */
val add4p = add4(11)
val add5p = add5(11)
val fs = List(add1p, add2p, add3p, add4p, add5p)
for f <- fs yield f(21)

fs: List[Int => Int] = List($$Lambda$,$$Lambda$,$$Lambda$,$$Lambda$,$$Lambda$)
res1: List[Int] = List(32, 32, 32, 32, 32)

Functions and Methods

def a (x:Int) = x + 1;
val b = (x:Int) => x + 1;
val c = new Function[Int,Int] { 
  def apply(x:Int) = x + 1 
}
val d : PartialFunction[Any, Int]  = { 
  case i: Int => i + 1 
}
val fs = List(a,b,c,d)
for f <- fs yield f(4)

fs: List[Int => Int] = List($$Lambda$, $$Lambda$, <function1>, <function1>)
res1: List[Int] = List(5, 5, 5, 5)

• What's going on here?

• Functions vs Methods

Functions and Methods

• def defines a method with explicit parameter types

• => defines a function with inferable parameter types
• Functions are objects with method apply
  • Function e:X=>Y gets compiled to an object

    object e:
      def apply(x:X) : Y = ...
    

  • Function application e(args) is method invocation e.apply(args)

Summary

• Tupled definitions: functions with multiple arguments
• Curried definitions: a family of single-argument functions
• In Scala, functions are objects with an apply method
• Partial application creates new functions