1. Procedures with optional parameters which do not require matching arguments
Example: consider the exponent function which may take one argument, m, in
which case it returns the square of m, or two arguments, m and n, in which
case it returns n power of m.
* (defun exponent (m &optional n) ; here n is an optional parameter.
(if n ; if the value for an optional parameter is
(if (zerop n) ; not provided, it is assumed NIL. 1
(* m (exponent m (- n 1))))
(* m m)))
EXPONENT
* (exponent 2) 4
* (exponent 2 3) 8

2. Optional parameters may be given default values, if we do not want their default value to be NIL.
Example: the exponent procedure
* (defun exponent (m &optional (n 2))
(if (zerop n) 1
(* m (exponent m (- n 1)))))
EXPONENT
* (exponent 2) 4
* (exponent 2 3) 8

3. Optional parameters eliminate the need for auxiliary procedures, because the first call uses the default value, while all other recursive calls ignore it
* (trace exponent) (EXPONENT) * (exponent 4) | 1 Entering: EXPONENT, argument-list: (4) | 2 Entering: EXPONENT, argument-list: (4 1) | | 3 Entering: EXPONENT, argument-list: (4 0) | | 3 Exiting: EXPONENT, value 1 | 2 Exiting: EXPONENT, value 4 | 1 Exiting: EXPONENT, value 16 16

4. Example
Consider math-quiz, a function which posts n math problems to the user
(who can set n as she wants) tutoring her in arithmetic (+, -, * or / is to be
set by the user, as well as the range of numbers to be exercised).
(defun math-quiz (&optional (op '+) (range 100) (n 3))
(dotimes (i n)
(exercise (random range) op (random range))))
(defun exercise (num1 op num2)
(format t "~%The expression is ")
(format t "~a ~a ~a" num1 op num2)
(format t "~% ... and the answer is ...")
(print (eval (list op num1 num2))))
* (math-quiz) ;all parameters are optional, no argument is required.
The expression is
... and the answer is ...
182
The expression is
101
The expression is
107

5. Example (cont.)
Optional parameters are position-dependent. To provide a non-default
value for n, we must specify values for all optional parameters that come
before n (even if they are their default values).
* (math-quiz ' ) ; ”+” and “100” are the default values for the first two arguments
The expression is ; they must be provided if we want to change the default value
... and the answer is ... ; of the last argument.
107
The expression is
... and the answer is ... 72
The expression is
110
The expression is
The expression is 81

6. Keyword parameters.
Keyword parameters are similar to optional parameters, except that they are
position-independent because bindings are determined by keywords not by
order.
Example: the math-quiz function.
(defun math-quiz2 (&key (op '+) (range 100) (n 3))
(dotimes (i n)
(exercise (random range) op (random range))))
(defun exercise (num1 op num2)
(format t "~%The expression is ")
(format t "~a ~a ~a" num1 op num2)
(format t "~% ... and the answer is ...")
(print (eval (list op num1 num2))))
* (math-quiz2 :n 2)
The expression is
... and the answer is ... 84
The expression is
127

7. The rest parameter.
This takes as its value the list of all arguments that have been unaccounted for.
Example: consider function sum-two which takes only two arguments and adds them.
(defun sum-two (number &rest numbers)
(sum-two-aux number numbers))
(defun sum-two-aux (sum list-of-numbers)
(if (endp list-of-numbers)
sum
(sum-two-aux (+ sum (first list-of-numbers))
(rest list-of-numbers))))
* (trace sum-two sum-two-aux)
(SUM-TWO-AUX SUM-TWO)
* (sum-two )
| 1 Entering: SUM-TWO, argument-list: ( )
| 2 Entering: SUM-TWO-AUX, argument-list: (2 ( ))
| | 3 Entering: SUM-TWO-AUX, argument-list: (6 (6 3 7))
| | 4 Entering: SUM-TWO-AUX, argument-list: (12 (3 7))
| | | 5 Entering: SUM-TWO-AUX, argument-list: (15 (7))
| | | 6 Entering: SUM-TWO-AUX, argument-list: (22 NIL)
| | | 6 Exiting: SUM-TWO-AUX, value 22
| | | 5 Exiting: SUM-TWO-AUX, value 22
..... 22

8. The aux parameter
This is not matched to any argument, because it is intended to define auxiliary
local variables similar to let*.
Example: the both-ends procedure.
* (setf whole-list '(a b c d)) ; the value of whole-list must be provided before
(A B C D) ; function definition, otherwise an error will occur
* (defun both-ends-new (whole-list &aux (first-el (first whole-list))
(last-list (last whole-list)))
(cons first-el last-list))
* (trace both-ends-new)
(BOTH-ENDS-NEW)
* (both-ends-new whole-list)
| 1 Entering: BOTH-ENDS-NEW, argument-list: ((A B C D))
| 1 Exiting: BOTH-ENDS-NEW, value (A D)
(A D)
Various parameters can be combined in the following order: optional
parameters come first after regular parameters, next are sole rest
parameters followed by key parameters, followed by aux parameters.

9. Representing structures in Lisp
We can create user-defined data types to represent any data type in Lisp. These are called structure types, and they come with automatically created access procedures. defstruct is the primitive that creates new structure types. (defstruct <structure name> (<field name 1> <default value 1>) (<field name 2> <default value 2>) (<field name n> <default value n>)) Example: (defstruct person (sex nil) (personality 'nice))

10. Lisp structures (cont.)
Structures are implemented as vectors, where the type (structure name) is the
zero element, field 1 is the first element, … field n is the n-th element. This means
that structures are more efficient than lists, because each element can be
accessed in a single step.
Notes: 1. ) defstruct defines a new data type.
2.) defstruct does not create instances of that data type, but automatically
creates a data-constructor procedure, data-reader procedures (a
separate one for each field), data type predicate, as well as
generalizes the setf primitive to handle the new data type.
Example:
(setf person-instance-1 (make-person)) ; make-person with no parameters creates a
;new instance of type person with fields filled with default values in defstruct
(setf person-instance-2 (make-person :sex 'female)) ; default value changes by
;providing a new value for keyword :sex.

11. Lisp structures (cont.)
To read data from created instances: * (person-sex person-instance-2) FEMALE * (person-personality person-instance-1) NICE Because data is accessed by an automatically generated reader procedure, it is said to be procedurally indexed. To change the values of existing fields: * (setf (person-sex person-instance-1) 'female) * (person-sex person-instance-1)

12. Lisp structures (cont.)
defstruct also creates a data type predicate: * (person-p person-instance-1) T * (person-p '(a b c)) NIL Example: Define a data type rock that contains fields for color, size and worth. Assume that the default color is gray, default size – pebble, default worth – nothing. (defstruct rock (color 'gray) (size 'pebble) (worth 'nothing)) (setf high-hopes-rock (make-rock :color 'gold :worth 'high))

13. Lisp structures (cont.)
A big advantage of structure types is that one structure can include fields of
another structure, thus forming a representational hierarchy.
Example: Consider structure employee
employee
salesperson hacker …
* (defstruct employee
(length-of-service 0)
(payment 'salary))
EMPLOYEE
* (defstruct (hacker (:include employee))
(preferred-language 'lisp))
HACKER
* (setf employee-example (make-employee))
#S(EMPLOYEE :LENGTH-OF-SERVICE 0 :PAYMENT SALARY)
* (setf hacker-example (make-hacker))
#S(HACKER :LENGTH-OF-SERVICE 0 :PAYMENT SALARY :PREFERRED-LANGUAGE LISP)
* (employee-length-of-service employee-example)
* (employee-length-of-service hacker-example)

14. To print the contents of an instance of a structure:
One structure can include another with one or more of the fields repeated in both. In such
case, the default value in more specialized structure shadows the default value in more
general structure.
* (setf employee-example (make-employee))
#S(EMPLOYEE :LENGTH-OF-SERVICE 0 :PAYMENT SALARY)
* (defstruct (salesperson (:include employee (payment 'commission)))
(preferred-car 'mercedes))
SALESPERSON
* (setf salesperson-example (make-salesperson))
#S(SALESPERSON :LENGTH-OF-SERVICE 0 :PAYMENT COMMISSION :PREFERRED-CAR MERCEDES)
* (employee-payment hacker-example)
SALARY
* (employee-payment salesperson-example)
COMMISSION
To print the contents of an instance of a structure:
* (describe hacker-example)
#S(HACKER :LENGTH-OF-SERVICE 0 :PAYMENT SALARY :PREFERRED-LANGUAGE LISP) is a named structure of type HACKER.
It has as an included structure EMPLOYEE.
Its slot names and values are:
LENGTH-OF-SERVICE - 0
PAYMENT - SALARY
PREFERRED-LANGUAGE - LISP

15. included in the structure’s definition. Example:
To print the structure itself, however, a special printing procedure must be defined and
included in the structure’s definition.
Example:
* (defstruct (employee2 (:print-function print-employee2))
(name 'anna)
(ss# 'unknown)
(length-of-service 5)
(payment 'salary))
EMPLOYEE2
* (defun print-employee2 (structure &rest ignore)
(format t "structure for ~a with ss# ~a"
(employee2-name structure)
(employee2-ss# structure)))
PRINT-EMPLOYEE2
* (setf employee-anna (make-employee2))
structure for ANNA with ss# UNKNOWN
* (describe employee-anna)
structure for ANNA with ss# UNKNOWN is a named structure of type EMPLOYEE2.
Its slot names and values are:
NAME - ANNA
SS# - UNKNOWN
LENGTH-OF-SERVICE - 5
PAYMENT - SALARY

16. Representing tables as association lists: the ASSOC and RASSOC primitives.
Consider a two-column table, where the first column contains properties of a given object, and the second column contains the values of these properties. Such object descriptions can be represented by expressions called association lists (or a-lists). These have two different formats: Format 1: ((key-1 value-1) (key-2 value-2) .... (key-n value-n)) Format 2: ((key-1 . value-1) (key-2 . value-2) .... (key-n . value-n)) The assoc primitive searches a-lists by key. Its format is the following: (assoc <key> <a-list>) The rassoc primitive searches a-lists by value, but it works only on a-lists of dotted pairs. Its format is the following: (rassoc <value> <a-list>)

17. Example: a table of days of the week and their average temperatures.
* (setf week-7-1 '((Mon 28) (Tue 32) (Wed 37) (Th 31) (Fri 33) (Sat 26) (Sun 29))) ((MON 28) (TUE 32) (WED 37) (TH 31) (FRI 33) (SAT 26) (SUN 29)) * (assoc 'fri week-7-1) (FRI 33) * (second (assoc 'fri week-7-1)) 33 * (rassoc 26 week-7-1) NIL
* (setf week-7-2 '((Mon . 28) (Tue . 32) (Wed . 37) (Th . 31) (Fri . 33) (Sat . 26) (Sun . 29))) ((MON . 28) (TUE . 32) (WED . 37) (TH . 31) (FRI . 33) (SAT . 26) (SUN . 29)) * (assoc 'fri week-7-2) (FRI . 33) * (rest (assoc 'fri week-7-2)) 33 * (rassoc 26 week-7-2) (SAT . 26) * (first (rassoc 26 week-7-2)) SAT

18. Another example on a-list of dotted pairs:
* (setf state-table '((al . alabama) (az . arizona)))
((AL . ALABAMA) (AZ . ARIZONA))
* (assoc 'al state-table)
(AL . ALABAMA)
* (rest (assoc 'al state-table))
ALABAMA
* (assoc 'ct state-table)
NIL
* (rassoc 'alabama state-table)
* (first (rassoc 'alabama state-table)) AL

19. Representing tables as property lists: the GET primitive.
There are two types of values that can be assigned to symbols:
Ordinary values. Example: (setf number 5)
Property values. These are placed together in a list, called property list (or p-list) and are “attached” to the symbol (i.e. can be accessed only through the symbol itself). Example: consider symbol day-1 with the following properties: avg-temp, sun-rise, and sun-set:
* (setf (get 'day-1 'avg-temp) 37) ;setf and get are used in combination
; to get to and set a value for a property
* (setf (get 'day-1 'sun-rise) '6h45m) ; of day-1
6H45M
* (setf (get 'day-1 'sun-set) '17h10m)
17H10M
* (get 'day-1 'sun-rise) ; after a value has been assigned to
6H45M ; a property, get retrieves that value

20. The DESCRIBE and REMPROP primitives
The describe primitive can be used to see the contents of the p-list:
* (describe 'day-1)
DAY-1 is an internal symbol in package USER.
Its value is unbound.
Its function definition is unbound.
Its property list contains:
Property: SUN-SET, Value: 17H10M
Property: SUN-RISE, Value: 6H45M
Property: AVG-TEMP, Value: 37
The remprop primitive removes a property from the p-list:
* (remprop 'day-1 'avg-temp) T

21. Representing tables as arrays
Arrays are represented in the same way as in JAVA, and their indexes start
with 0.To declare an array, a combination of SETF and MAKE-ARRAY
primitives is used as follows:
* (setf array-1 (make-array 10)) ; the first array element is in position 0, the last in position 9
#( )
* (setf array-2 (make-array '(5 2))) ; the first array element is in position 0, 0
#2A((0 0) (0 0) (0 0) (0 0) (0 0))
* (setf array-3 (make-array '(2 5 3)))
#3A(((0 0 0) (0 0 0) (0 0 0) (0 0 0) (0 0 0)) ((0 0 0) (0 0 0) (0 0 0) (0 0 0) (0 0 0)))
To initialize an array at the same time:
* (setf array-1 (make-array 10 :initial-contents '( )))
#( )
* (setf array-2 (make-array '(5 2) :initial-contents '((1 2) (3 4) (5 6) (7 8) (9 10))))
#2A((1 2) (3 4) (5 6) (7 8) (9 10))
The size of array dimension can be determined by the ARRAY-DIMENSION primitive:
* (array-dimension array-2 0) 5

22. Retrieving and changing array elements
To retrieve an item from an array, we use the AREF primitive as follows:
* array-1
#( )
* (aref array-1 5) ; retrieves the 6-th item 6
* array-2
#2A((1 2) (3 4) (5 6) (7 8) (9 10))
* (aref array-2 2 1) ; retrieves the item in the 3-rd raw, 2-nd column
To change the value stored in a specified position, we use a combination of
SETF and AREF primitives:
* (setf (aref array-1 5) 33) 33
#( )
* (setf (aref array-2 2 1) 66) 66
#2A((1 2) (3 4) (5 66) (7 8) (9 10))

23. Hash tables: yet another way to represent tables
Primitives on hash tables:
* (setf table (make-hash-table)) ; initializes the table
#<HASH-TABLE 0/37 9B:19F6>
* (setf (gethash 'al table) 'alabama) ; modifies the table
ALABAMA
* (gethash 'al table) ; retrieves values T
* (gethash 'ct table)
NIL
* (remhash 'al table) ; removes a key-value pair from the table
* (gethash 'al table)
* (clrhash table) ; removes all key-value pairs from the table