Description
1. (5 points) In Scala, write a more general version of the sum_fun function called
apply_combine that applies a function f(taken as a parameter) to the integers from 1 to
x(taken as a parameter), then combines those values using another function g(taken as a
parameter). So combine takes in three parameters: a function f that takes in an Int and
returns an Int, an Int x, and a function g that takes in two Ints and returns an Int. It then
returns the result of using the function g to combine the values gained by applying f to 1, 2, …, x.
For example, if I define
def add(x:Int, y:Int) :Int = x+y
def square(x:Int):Int = x*x
then
combine(square, 4, add)
would return 30
And if I define
def mult(x:Int, y:Int) :Int = x*y
then
combine(x=>x, 4, mult)
would return 24
2. (10 points) Write a curried version of the function from problem 1. This function,
apply_combine2, takes in one parameter, the function f:Int=>Int. apply_combine2
then returns a function that takes in one Int parameter, and returns yet another function
which in turn takes in a function g:(Int, Int)=>Int and returns the same Int value as
apply_combine. It’s up to you whether you wish to use named or anonymous functions.
For example, we could use this function in the following ways:
def apply_square = apply_combine2(x=>x*x)
def apply_square_5 = apply_square(5)
println(apply_combine2(x=>x*x)(5)((x, y)=>x*y))
Hint: When figuring out your types, start by figuring out the (overall) type of the function that
takes in g (it’s NOT(Int, Int)=>Int) and use that to figure out the return type of the
function that takes in the Int parameter.
3. Theory (5 points) a. Reduce the following expression in the λ-Calculus:
((λm. λn. λf. λx.((m f) ((n f) x)) λf. λx.(f x)) λf. λx.(f (f x)))
Note: there are several bound xs and fs with different scopes. You may wish to rewrite some of
the expressions with different variable names.
b. What arithmetic operation do you think is represented in the λ-Calculus by
λm. λn. λf. λx.((m f) ((n f) x))? Wait until after class Monday to try to answer part b. Hint:
Given our discussion on Monday, how would you interpret the two parameters sent in to this
function in part a?
See the syllabus for instructions on how to start a Scala project in Eclipse.
Submission instructions: You will print out your code for each problem, stapling together
multiple sheets (there will be deductions for unstapled homework!). Turn in the hardcopy at the
beginning of class. You will ALSO submit all of your .scala files as attachments, to
cs169@math.scu.edu (NOT Dr. Linnell’s email!!) The subject line of the email should be “CS169
HW6 YourLastName YourIDNumber “
