Question

In my Scala course an example has given. It was about finding a more generalized function, which can be used to define an arithmetic summation function and an arithmetic production function. Here are the functions that should be generalized.

def sum(f:Int=>Int)(a:Int,b:Int):Int ={
 if(a>b) 0
 else f(a) + sum(f)(a+1,b)
}

def product(f:Int=>Int)(a:Int,b:Int):Int={
 if(a>b)1
 else f(a)*product(f)(a+1,b)
}

To generalize these functions the teacher gave such a function :

def mapReduce(f:Int=>Int,combine: (Int,Int)=>Int, zero:Int)(a:Int,b:Int):Int ={
    if(a>b) zero
    else combine(f(a),mapReduce(f, combine, zero)(a+1, b))
}

So mapReduce function can be used to generalize sum and product functions as follows:

def sumGN(f:Int=>Int)(a:Int,b:Int) = mapReduce(f, (x,y)=>(x+y), 0)(a, b)
def productGN(f:Int=>Int)(a:Int,b:Int) = mapReduce(f, (x,y)=>(x*y), 1)(a, b)

I took a look at the definition of map reduce in functional programming but I have a hard time why the generalized function has been named as map reduce above. I can not grasp the relation. Any help will make my very happy.

Regards

Answer 1

This is by no means an exact explanation (names are fuzzy anyway) but here’s an alternative definition:

def mapReduce(f: Int => Int, combine: (Int, Int) => Int, zero: Int)(a: Int, b: Int): Int ={
  if (a > b) zero
  else (a to b).map(f).reduce(combine)
}

Do you see the link?