Lisp Tutorial | MAPCAR and LAMBDA in Lisp

Applicative Programming in Lisp
Usually, the input to a Lisp function is some sort of data.

Functions are data too, so applicative programming takes this idea and uses Lisp functions in the same way other data: as inputs to other functions and functions returned as values. Today's Programming Lisp Tutorial introduces Applicative Programming in Lisp, MAPCAR and LAMBDA.

And of course we have the answer to the Lisp Programming Challenge from our last post.

Using COND in Common Lisp

Our last post looked at IF THEN statements using the IF function in Lisp. Here's the answer to the challenge set in that post, to write a MY-ABSOLUTE function using an IF function:

(defun my-absolute (x)
              (if (>= x 0) x
                (* -1 x)))

COND

It's possible to use multiple IF functions but if you have lots of things to test it can be more convenient to use a COND function.

COND is a conditional function. It consists of any number of
test and consequent clauses.

(COND (first-test first-consequent)
(second-test second-consequent)
....
(last-test last-consequent))

COND works by progressing through each clause in turn. If the test part is true, COND evaluates the consequent part and returns its value, it does not evaluate any further clauses.

If the test evaluates to NIL (false), COND jumps to the next clause. If all clauses are false, COND returns NIL.

Here's an example COND function:

(defun what-is (x)
  (cond ((equal x ’apple) ’fruit)
    ((equal x ’asparagus) ’vegetable)
    ((equal x ’pork-chop) ’meat)
    (t ’unknown)))

As shown in the example above, it's useful to put a T as the last COND clause. This allows you to return a value or perform another task if all of the preceeding clauses are false.

Today's Challenge:
Write a function called MY-COMPARE using COND that will take two numbers as input and return one of these statements as appropriate:

THE FIRST NUMBER IS LARGER
THE SECOND NUMBER IS LARGER
THE TWO NUMBERS ARE EQUAL

If.. then.. else..

Previously we looked at using a predicates to test whether something was TRUE or FALSE, on in Lisp T or NIL:


(oddp 5)
T

Predicates can form part of an IF THEN statement: if something is true then do something.
The IF function takes three arguments: a test, a true part, and a
false part.

For example, using the ODDP function to test if a number is odd and then returning a statement|:

(if (oddp 3) '(the number is odd) '(the number is even))
(THE NUMBER IS ODD)

(if (oddp 4) '(the number is odd) '(the number is even))
(THE NUMBER IS EVEN)

As well as returning simple statements as in the above example, we can also get Lisp to perform further functions is a test is T or nil. This function for example:

• takes a single number (n) as its input argument.
• tests to see if a number is odd using the ODDP function,
• if the number is odd we add 1 to it to make it even,
• if the ODDP test returns NIL we simply return our original odd number.

;make odd
(defun make-odd (n)
  (if (evenp n) ; the test
      (+ 1 n) ;the true statement
    n)) ; the false statement

Today's Challenge
Write a function in Lisp called MY-ABSOLUTE that returns the absolute value of a number. Absolute values are always non-negative. For negative numbers the absolute value multiply the number by -1; for zero and positive numbers the absolute value is the number itself.

Remember the IF function takes three arguments:

• a test
• a true part, and a
• false part

We'll post the answer in our next http://programminglisp.blogspot.com/ blogpost.

Lists in Lisp

Lists are are one of Lisp's most flexible and powerful data types. Here are some examples of lists:

(red orange yellow green blue indigo violet)

(10 green bottles)

(9 18 27 36 45 54 63 72 81 90 99 108)

(thisisalist)

((a)(list of) (lists))

To get the length of a list, we can use the LENGTH function. We have to put the quote mark ' in front of each word here, otherwise Lisp would try to evaluate or understand what we mean:

length '(red orange yellow green blue indigo violet))

7

(length '(10 green bottles))

3

(length '(9 18 27 36 45 54 63 72 81 90 99 108))

12

(length '(thisisalist))

1

(length '((a)(list of) (lists)))

3

As you can see from the final example, lists can contain other lists. The elements of the list are the things that appear inside only one level of parentheses, so in the final example the LENGTH function returns 3 because there are only 3 elements to the list:

(a)

(list of)

(lists)

As we saw briefly in the first steps with Lisp post we can extract individual elements from lists using these functions:

(first '(a b c d e))
A

(second '(a b c d e))
B

(third '(a b c d e))
C

(rest '(a b c d e))
(B C D E)

(last '(a b c d e))
(E) 

(first (first '((a)(list of) (lists))))

A

Creating a new list is very easy using the LIST function:

(list 'banana)

(banana) 

(list 'water 'malt 'hops 'yeast)
(WATER MALT HOPS YEAST)

Again we have to put the quote mark ' in front of each word here, otherwise Lisp would try to evaluate or understand what we mean by water, malt, hops and yeast i.e. had we assigned values to these.

We'll look more at using, creating and extracting data from lists in future posts.

Using Cons To Create Lists In Lisp

Today's post looks at creating lists in Lisp. Before we do that let's have a look at the answer to yesterday's post:

Write a function called square-odd-p. This function takes a single number as input, it squares this number and tests to see if the square of the number is odd.

(defun square-odd-p (x)
   (oddp (* x x)))

Creating Lists in Lisp
cons is a Common Lisp primitive, that creates lists from an atom
(number or letter) and a list:

(cons 1 '(2 3))
(1 2 3)

 We'll use cons to help us write a function to replace the first member of a list. In order to do this we'll:

• Have to take two inputs to our function: the new item and the list
• We'll use the rest function to return everything but the first member of the list
• We can then cons our new item to the start of this list:

(defun replace-first (new-item the-list)
   (cons new-item (rest the-list)))

And an example:

(replace-first 'peter-pan '(one flew over the cuckoos nest))
   (PETER-PAN FLEW OVER THE CUCKOOS NEST)

In the next post we'll look at some more examples of building and manipulating lists.

Predicates In Lisp

Today we're looking at predicates. Predicates are tests that we can use to see if something is true or false.

Before we do that let's look at the answers from yesterday:

(defun minus-one (x)
   (- x 1))

(defun ten-times-bigger (x)
   (* x 10))

(defun weeks-to-days (weeks)
   (* weeks 7))

It doesn't matter if you called weeks x or something entirely different, it is often useful to give our arguments names that are useful.

Predicates
As mentioned earlier predicates are tests that return either True or False. In lisp:

T = True
Nil = False

Here are some examples:

oddp checks to see if a number is odd:

(oddp 5)
T

(oddp 6)
NIL

evenp checks to see if a number is even:

(evenp 5)
NIL

(evenp 6)
T

Here are some other common predicates with examples:
(zerop 0)
T

(= 3 4)
NIL

(> 3 4)
NIL

(< 5 10)
T



Predicate Summary

• (evenp n) true if n is even
• (floatp n) true if n is a floating point number
• (integerp n) true if n is an integer
• (minusp n) true if n is less than zero
• (numberp n) true if n is a number 
• (oddp n) true if n is an odd number (0 is considered even) 
• (plusp n) true if n is greater than 0 
• (zerop n) true if n is 0
• (> x y) true if x is greater than y
• (< x y) true if x is less than y
• (>= x y) true if x is greater than or equal to y
• (<= x y) true if x is less than or equal to y

Using Predicates In Functions
In yesterday's post we wrote our own functions. We can include predicates in these functions. For example, this function adds two numbers together and checks to see if the result is even, again we could all it almost anything but as it's a predicate that check to see if the sum of two numbers is even we'll call it sum-even-p:

(defun sum-even-p (x y)
   (evenp (+ x y)))


Notice the order of the function

    (evenp (+ x y)))

the input element to evenp is the + function and x y


Today's Challenge
Today's challenge write a function called square-odd-p. This function takes a single number as input, it squares this number and tests to see if the square of the number is odd.

Check tomorrow's post for the answer and more Lisp tutorials.

Writing A Function In Lisp

There are a large number of built in functions in Lisp, it's also possible, useful and very easy to write your own functions in Lisp. Have a look at this function:

(defun my-square (x)
(* x x))

Let's break this down:

defun is a function used to define new functions.
my-square is the name that we've given to our function, we could call it almost anything we like but it makes to give it a useful name so that we can remember it later.
x is the argument or input to our function. Again we could call this almost anything we like.
(* x x) This is where the actual work of our function takes place, we using the multiply function and multiplying x by itself.

When you have written and evaluated this function, it can be called and used just any other function:
(my-square 5)
25

(my-square 9)
81

It's good practice to comment your function, both so that others can understand it quickly and easily and for yourself.

(defun my-square (x)
 "this function squares an input number x"
(* x x))

Using double quotes " " adds a definition to your function, these can only be used after you have defined the input arguments.

A more versatile way of adding comments that can be used anywhere is to use semicolons, anything after the semicolon is ignored:

(defun my-square (x)
 "this function squares an input number x"

(* x x)) ; this line squares x

We'll work more on writing new functions tomorrow, for now see if you can write these functions, answers in tomorrow's post:

minus-one a function that takes a single number as input and returns the number that is one less
ten-times-bigger a function that takes a single number as input and returns the number that is ten times bigger
weeks-to-days a function that takes a number of weeks as input and returns the total number of equivalent days

These examples may seem simple, however this is a really good stepping stone to learn how to build much more powerful functions in Lisp. Answers and more on building functions tomorrow...

First Steps With Lisp

Assuming you've followed yesterday's post and installed a version of Common Lisp, today we'll look at some first steps in learning Lisp.

We'll discuss background ideas and other useful theory in future posts, but for now we'll dive straight in and get our hands dirty with some Lisp programming.

1. Open your Lisp listener window, if it's not all ready showing, look for 'Listener' under your window menu.

2. As you would expect, Lisp can perform all sorts of mathematical operations, type this into your listener:
(+ 2 3)

It should of course return 5. There are a couple of useful points here:
-The function always come first
-The function and its arguments are surrounded by ()

3. Here are some more examples:
(+ 2 4 5 6)
17

(* 10 9)
90

(- 10 2.5)
7.5

and so on...
4. These operations can be nested inside one another for example:
(+ 1 (* 3 3))
10
The inner parentheses get evaluated first.

5. Aside from mathematical functions, many function access data. For example:
(first '(a b c d e))
A

6. The function 'first' returns the first item of a list. There are many other similar functions for accessing data:
(second '(a b c d e))
B

(third '(a b c d e))
C

(rest '(a b c d e))
(B C D E)

(last '(a b c d e))
(E)

7. The ' quote mark stops the Lisp from trying to evaluate the list (from trying to interpret what the list means - we could have for example assigned values to these letters).

Tomorrow we'll start building our own functions, but for now get used to using these functions in your version of Lisp