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- CS320 Lab 12 LISP Laboratory Number 2
- : Check out New things on the Course Web Page
- : Goal
- : Deliverables
- : Hints
- : Review
- : Creating new functions
- : Case sensitive guile
- : Functions with a single parameter
- : Functions with two parameters
- : A Binary Search
- : Optional experiments if you have time
- : : Higher powers
- : : Classic factorial
- : : What does this function calculate
- : : An example of top-down design in LISP
- : Leave LISP
- Check the Preparation for next class

- To run LISP open a terminal window. No source to edit..... in this lab!
- To leave XLISP send EOT by holding down CTRL and tapping D
- Parentheses (...) are the must important things in LISP.
- A comment in XLISP starts with a ";" and runs to the end of the line.
- Keep your handout on LISP open beside you and look in it for the rules of LISP.
- Open many windows and use your hilight-and-paste feature to save time.
- Use an editor to write your functions and their test cases then either
- Any test editor is good for LISP, but vi can help you track the parentheses.
- Put XLISP code in files that end ".lsp".
- In 'vi' you can track parentheses if you do the following
:set showmatch

- Copy and paste into a window running XLisp to run them...
- or
- Save the version ( :w in vi) and run xlisp on it. (:!xlisp % in vi)

- In 'vi' you can track parentheses if you do the following
- Some browser may panic if you link to a ".lsp" file. If you put source code in a ".txt" file every browser in the world will read it and your user's will love you.
- n^4 = (n^2)^2.
Test it. And save it...

## Functions with two parameters

Functions of more arguments/parameters are done the same way using the syntax - ( DEFINE (name w x y z ...) expression)
Here is a definition of a function with two arguments in LISP:

(DEFINE (pythagoras x y) (+ (square x) (square y)))

(pythagoras 3 4)

Some common errors(pythagoras 4)

(pythagoras 1 3 4)

(pythagoras )

In our XLISP the value of the function name is an expression defining a function:pythagoras

Here is a function that return the larger of two expressions:

(define (max2 a b) (if (> a b) a b))

(max2 1 17)

(max2 17 1)

(max2 (max2 3 5) (max2 4 1))

(max2 (square 3) (cube 2))

Define a function called min2 that returns the smallest of two arguments. Test it and save it....

## A Binary Search

Here is a function that searches for the positive square root of a positive number. It uses the square function. It has four arguments:- target: the number for which you need a root. Must be >=0.
- lo: a number that is less than the root.
- hi: a number that is greater than the root.
- error: a number indicating the desired accuracy of the approximation.

(define (binroot target lo hi error )

(let (( mid (/ (+ lo hi) 2.0))) ; this saves the time to recalculate mid

(if (<= (- hi lo) error)

mid

(if (< (square mid) target)

(binroot target mid hi error)

(binroot target lo mid error)

)

)

)

)

Here is how I tested it:(binroot 50 0 100 0.05)

Test it further and trace it.The above algorithm will find roots of any monotonic increasing function. Modify it to find cube roots and fourth roots of positive numbers.

## Optional experiments if you have time

- If n is 0 then power(x,n) = 1.
- If n is 1 then power(x,n) = x.
- If n is even then n=2*k for some k and so power(x,n)=square(power(x,k)).
- If n is odd then n=2*k+1 for some k and so power(x,n)=x*square(power(x,k)).

### Higher powers

The following function works out the value of x to the power n when n is a whole number greater than or equal to 0.(define (power x n)

(cond

((= n 0) 1)

((= n 1) x)

(T (* x (power x (- n 1))))

)

)

Here are two test cases(power 2 3)

(power 3 2)

Test with the trace function....However this is not a very fast way to calculate powers. There is another one based on these facts:

Net

(End of Net)

We have LISP function EVENP and ODDP to detect parity and (/ n 2) works out a k for us by rounding down.Can you figure out how to speed up the original power function?

### Classic factorial

We now define a new function, command and kind of expression that calculates the factorial of a positive integer. The factorial of the number 0 is 1, and for all other positive integers n you work out n times the factorial of n-1. In LISP we say:(define (factorial n)

(if (= n 0) 1 (* n ( factorial ( - n 1 ) ))

)

)

Here you print out the definition of factorial:

factorial

Here you input expressions that apply factorial to simple numbers:(factorial 0)

(factorial 3)

(factorial 5)

Trace how it works:

(trace factorial)

(factorial 0)

(factorial 3)

(factorial 5)

(untrace factorial)

Below you can use factorial is more complicated ways:

(factorial (factorial 3))

(setq n 3)

(factorial n)

(setq f (factorial n))

f

(setq f (factorial f))

f

The problem with this factorial is that n! quite a small n is too large to be represented as an integer. Worse n! when n<0 is infinitely small! As a result we should define a safe factorial that returns a string "error" when n<0 or n is too big.

Program and test this one.

### What does this function calculate

[ fibo.lsp ]### An example of top-down design in LISP

[ primes.html ]. . . . . . . . . ( end of section Optional experiments if you have time) <<Contents | End>>

## Leave LISP

To exit lisp, input the EOT character CTRL/D

To earn full credit the work must be done before the end of the lab and should contain a list of at least 3 notes. Each note is a short paragraph with one or two sentences and a new LISP function (or link to a file containing the function). The sentences should say what the function does and what you learned by writing it.

Let me know by calling me across to your workstation when done.

Net

(End of Net)

Here are some simple LISP expressions/commands. Load the LISP interpreter and input each in turn. Try to predict what each will return as a value before inputting it:

()

(+ 1 2)

(1 + 2)

(* (+ 1 2) (+ 3 4))

(+ 1 2 3 4)

(A B C)

'(A B C)

A

'A

(A)If you get one wrong... you may need to go back to [ 11.html ] again.

( define (a) 4321)

(a)

a

'a

(a 1)Copy and paste the above XLISP commands into XLISP in a terminal window.

Then define and test a new function called answer that returns the value 42.

(DEFINE (square x) (* x x))Here is how you test it...

(square 3)

(square 4)

(square 5)

Here is how you can use it:

(square (+ 1 2 3))

(+ (square 3) (square 4) )

(+ 3 (square 3) )Test the above!

Here is how XLISP can list it:

squareXLISP does not let you edit a function however!

Do not leave LISP until you complete the next two steps.

Here is a function for the cube:

(DEFINE (cube x) (* x (square x)))Test it.

Define a function called fourth that returns the fourth power of a number. Use the fact that the fourth power on n is the square of the square of n:

. . . . . . . . . ( end of section CS320 Lab 12 LISP Laboratory Number 2) <<Contents | End>>