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LISP

Lecture Notes

LISP

• LISP was the first functional programming language.

• With the exception of the first version all LISP dialects

include imperative language features such as, imperative

style variables, assignment statements, and iteration.

Symbolic Expressions, the Syntactic Basis

of LISP

• The syntactic elements of the LISP programming language are

symbolic expressions.

• Both programs and data are represented as s-expressions. An s-

expression may be either an atom or a list.

• Symbolic atoms are composed of letters numbers and certain non-

alphanumeric characters (* - + $ % ^ &_ > < )

• A list is a sequence of either atoms or other lists separated by blanks

and enclosed in parentheses.

Examples

• ‘(A B C D)

• ‘(A (B C) D (E (F G)))

(function_name arg_1 … arg_n)

Example

( + 5 7 )

evaluates to 12.

Examples

• ‘(1 2 3 4)

• ‘(likes bill ?X)

• (- (+ 3 4) 7)

• (=(+ 2 3) 5)

• (list 1 2 3 4)

• (nth 0(list a b c d))

0

t

(1 2 3 4)

a

Concepts Behind LISP

• From this emerged a universal LISP function that could

evaluate any other function in LISP.

• The first requirement for the universal LISP function was a

notation that allowed functions to be expressed in the same

way data was expressed.

• Function calls were specified in a prefix list form called

Cambridge Polish

• In evaluating a function LISP first evaluates its arguments

and then applies the function indicated by the first element

of the expression to the results of these evaluations. For

example in evaluating the expression

(+ (* 2 3) (* 3 5))

• LISP first evaluates the arguments (* 2 3) and (* 3 5).

These results are then passed to the top level addition

which is evaluated, returning 21.

Definition

S-Expression

An s-expression is defined recursively:

1. An atom is an s-expression.

2. If s1, s2,...,sn are s-expressions,

then so is the list (s1, s2,...,sn).

Evaluating an s-expression

• A list is a non-atomic expression.

• In evaluating an s-expression:

– If the s-expression is a number, return the value of the

number.

– If the s-expression is an atomic symbol, return the value

bound to that symbol; if it is not bound then it is an

error.

– If the s-expression is a list, evaluate the second through

the last arguments and apply the function indicated by

the first argument to the result.

Control of LISP Evaluation: quote and eval

The purpose of the quote is to prevent evaluation of s-

expression that should be treated as data rather than an

evaluable form.

(quote(a b c ))

(quote(+1 3))

(list(+1 2) (+ 3 4))

(list ‘(+ 1 2) ‘(+ 3 4))

(>(* 5 6) (+ 4 5))

(‘(a b c )) (a b c)

(‘(+ 1 3)) (+ 1 3 )

(3 7)

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

t

eval is a complement to quote.

(quote(+ 2 3)) (+ 2 3)

(eval(quote(+ 2 3))) 5

Programming in LISP: Creating New Functions

LISP supports a large number of built in functions

– Arithmetic functions supporting both integers and real numbers.

– Program control functions

– List manipulation and other data structuring functions.

– Input/Output functions

– Forms for the control of function evaluation

– Functions for the control of the environment and operating system.

(defun square(x)

(* x x))

>(square 5) ; causes 5 to be bound to x

25

(defun <function name> (<formal parameters>)

(<function body) )

(defun hypotenuse(x y)

(sqrt (+ (square(x)) (square(y))))

Program Control in LISP: Conditionals

and Predicates

cond takes as arguments a number of condition - action pairs.

(cond (<condition1> <action1>)

(<condition2> <action2>)

................

(<conditionn> <actionn>) )

(defun absolute-value(x)

(cond ((< x 0) (-x))

((> = x 0) (x))))

(defun absolute-value(x)

(cond ((< x 0) (-x))

(t x)))

If clause

if takes three arguments

(defun absolute-value(x)

(if (< x 0 ) (-x) x ))

Predicates

A predicate is a LISP function that returns nil to indicate ‘false’ and

anything other than nil to indicate ‘true’.

> (= 9 (+ 4 5))

t

>(oddp 4)

nil

Examples to arithmetic predicates are: <, >, =, oddp, evenp, zerop, plusp,

minusp.

>(member 3 ‘(1 2 3 4 5))

(3 4 5)

All Boolean functions are short circuit in Common LISP. They return a value as soon as the result is determined.

>(and(t t nil t))

nil

>(or( t nil t t))

t

Lists as Recursive Structures

The basic functions for accessing the components of a list are

car and cdr.

car (first) - Takes a list as its argument and returns the

first element of the list.

cdr (rest) - Takes a list as its argument and returns the

list with the first argument removed.

>(car ’(a b c ))

a

>(cdr ’(a b c))

(b c)

>(car(cdr ’(a b c d)))

b

A recursive approach to manipulate list structures to perform

an operation on each of the elements of a list

1. If the list is empty quit

2. Perform the operation on the first element of the list and

recur on the remainder of the list.

Common LISP predicates for list processing are

member : Determines whether an s-expression

is a member of a list.

length : Determines the length of a list.

Example:

Define ‘my-member’ which takes an atom and a list

as arguments and returns nil if the atom is not

present in the list, otherwise returns the portion of

the list containing the atom as the first element.

(defun my-member(element list)

(cond((null list) nil)

((equal element(car list)) list)

(t (my-member element (cdr list))))

>(my-member 4 ‘(1 2 3 4 5 6))

(4 5 6)

(defun my-length(list)

(cond((null list) 0)

(t (+ (my-length (cdr list) 1)))))

cons is a basic list constructor

(cons ’A ’(L I S)) (A L I S)

(cons ’A ’B) (AB)

(cons ’(A) ’(L I S)) ((A) L I S)

car and cdr tear lists apart and drive the recursion ; cons

selectively constructs the result as the recursion unwinds.

Recursion is used to scan the list element by element, as the

recursion unwinds the cons function reassembles the solution.

If cons is called with two lists as arguments it makes the

first of these a new first element of the second list,

whereas append returns a list whose elements are the

elements of the two arguments:

>(cons ’(1 2) ‘(4 5 6))

((1 2) 4 5 6))

>(append ’(1 2) ‘(4 5 6))

(1 2 4 5 6)