Define the following Common Lisp functions and macros.

$$ Assignment$5.$lisp is expected to contain only the methods described in this assignment manual. $($load $$Assignment$5.$lisp$)$ should return T and print no other information to the console.

$$ Parameter names can be arbitrary.

o Function and macro names, on the other hand, must be exactly as specified.

$$ Parameters must be in the order they are listed in the assignment manual.

$$ You may use as many optional parameters as you like, even if no optional parameters

are described in the assignment manual.

$$ Functions are expected to return values, not print values to the console.

o Functions should not print any information to the console when executed.

$$ Do not use defun inside of a function body.

$$ Do not define any global variables with defvar. For local variables inside functions, use let and let$*$ blocks.

$$ Assume all inputs are valid, you do not need to do any parameter validation in your functions.

$$ You must comment your Common Lisp code. The ; character is used to denote comments.

$$ You cannot use any destructive operations in any of your functions. This includes: the setq special operator, setf, delete, nconc, push, or any derivatives of the setq special operator. Destructive operations go against the functional paradigm described in class.

o A non$-$destructive alternative to nconc is the append function

$$ I highly recommend against using looping macros and online compilers for the development of this assignment, historically they have caused significant confusion.

$$ SBCL can be installed onto almost any modern operating system. You can download and install the SBCL compiler here

$1.[5$ points$]$ Write a Common Lisp function named myList which creates the following list and returns it $(4(722)$ "art" $("$math$"(8)99)100)$

$2.[10$ points$]$ Write a Common Lisp function named leapYear which takes no required parameters and returns an ordered list containing all leap years from $1800$ though $2024.$ The list of leapyears must be calculated, no points will be given for a hard$-$coded list.

$3.[10$ points$]$ Write a Common Lisp function named union$-$ which takes two list parameters. union$-$ returns a single list which contains the separate unique entities from both lists, with no duplication. You are not allowed to use the predefined union function for this function.

$4.[10$ points$]$ Write a Common Lisp function named avg with a single parameter named

aList. avg returns the average of all elements in aList. Assume all elements in aList are numbers. If given an empty list, avg should return NIL. The avg function must be tail recursive.

$5.[15$ points$]$ Write a Common Lisp function named isType which takes a single parameter named dataType. isType will return an anonymous function which takes a single parameter and returns true if the parameters data type is the data type specified in dataType. Otherwise the anonymous function returns false.

$6.[15$ points$]$ Write a Common Lisp function named taxCalculator with three parameters: limit$,$ rate, and values. limit and rate will be numbers, values will be a list. taxCalculator returns a list with the same elements and ordering of the values parameter EXCEPT every element which is greater than limit is multiplied by rate. Assume that all elements of the values list are numbers. BONUS: Make taxCalculator tail recursive $+5$ points

$7.[20$ points$]$ Write a Common Lisp function named clean which takes two parameters: aFunc and aList. aFunc will be a function and aList a list. aFunc is expected to be a function which takes a single parameter and returns a boolean value. clean will return a list which contains all values in aList which, when passed to aFunc, return true. If aList contains sublists, clean should create a new sublist with only the values which return true when passed to aFunc

$8.[15$ points$]$ Define a Common Lisp macro named threeWayBranch, which takes three parameters: x$,$ y$,$ and z$.$ All parameters will be lists containing an arbitrary number of sublists where the first sublist is a conditional. $(($conditional$)($sublist$-1)($sublist$-2)...)$ The threeWayBranch macro will behave similarly to the cond macro. It will first evaluate the conditional in parameter x and if it evaluates to true, execute the remaining sublists in z$.$ If no conditionals evaluate to true, threeWayBranch will return NIL. You are not allowed to use the cond macro to implement threeWayBranch.