CSCI 320, Homework 2

Collaboration policy in effect for this assignment: SEE last page before starting the assignment.1. Read sections 2.3 Lists, Iteration, and Recursion and 2.4 Pairs, Lists, and Racket Syntax, in The Racket Guide <• Complete the following programming exercises, from your text: Chapter 15, pages 698, 699, numbers: 5, 6,7, 8, 9, 11, 12, 14, 16• Note: you may use existing basic scheme functions. If, however, there is already a scheme function thatsolves a given problem, say #5 for example, you can’t use it. You must write it yourself. In solving theproblems above, you may write other worker functions.• All code requiring repetition, should accomplish it through recursion.2. Functional programming characteristics include:• first class functions – this means that the language supports passing functions as arguments to otherfunctions, returning them as the values from other functions, and assigning them to variables or storingthem in data structures. (Extracted from Wikipedia, “first class functions” on September 13, 2011).• higherorderfunctions – the term used by Sebesta means the same thing as “first class functions”. Sebestaalso refers to these as “functional forms.” (See page 659.)Higherorderfunctions or functional forms include:Composition: a function that takes two functional parameters and yields a function whose value is the firstactual parameter function applied to the result of the second. Composition is denoted by:€h ≡ f  gFor example, if€f (x) ≡ x + 2g(x) ≡ 3* x then€h(x) ≡ f (g(x)), or€h(x) ≡ (3* x) + 2Construction: a function that takes a list of functions as parameters. When applied to an argument, aconstruction applies each of its functional parameters to that argument and collects the results in a list orsequence.Let€g(x) ≡ x * xh(x) ≡ 2* xi(x) ≡ x /2then€[g,h,i](4) yields€(16,8,2)Applytoall:a function that takes a single function as a parameter. If applied to a list of arguments, apply‐to‐allapplies its functional parameter to each of the values in the list argument and collects the results in a list orsequence.Let€h(x) ≡ x * x then€α(h,(2,3,4)) yields€(4,9,16)Assignment: Write functional, (referentially transparent, no side‐effects and hence loop‐less)Scheme code to implement the function forms composition, construction and apply‐to‐all:• composition(f, g) – named composition, its parameters, f and g, are any two functions – will becalled with different functions different timesCollaboration policy in effect for this assignment: SEE last page before starting the assignment.2• construction(lstOfFuncts, a) – takes as arguments, an arbitrarily long list of functions and asingle argument• applyToAll(f, lstOfArgs) – takes as arguments a function, f, and an arbitrarily long list ofargumentsWARNING: Solutions (and the next assignment) will be posted immediatelyafter the due date/time, so late assignments will not be accepted.EARLY submissions are always accepted.What to submit: Two files one called• Part 1, which contains the solutions to problem 1 above, with calls tothe functions embedded.• Part 2, which contains the solutions to problem 2 above, with calls tothe functions embedded.Collaboration policy in effect for this assignment: SEE last page before starting the assignment.• You may only submit solutions generated by your own work.• You may discuss DrRacket with classmates and instructors.• You may discuss Racket with classmates and instructors.• You may discuss these problems with classmates and instructors. If it helps you to learn from othershow to solve the problem, that is fine. The objective is that you CAN and DO solve the problem. YouMUST acknowledge these discussions.• You MAY NOT copy the work of others.• You MAY NOT give your work to others.• You should not look for solutions on the internet, you should craft your own.I can’t give you a grade for someone else’s work!!!! If you do run into asolution that you use or that influences your solution, you must acknowledgethat.• Your name must be in every file you submit.