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Ch 15. An Introduction to LISP
KU NLP
 15.0 Introduction
 15.1 LISP: A Brief Overview
 15.1.1 Symbolic Expressions, the Syntactic Basis of LISP
 15.1.2 Control of LISP Evaluation: quote and eval
 15.1.3 Programming in LISP: Creating New Functions
 15.1.4 Program Control in LISP: Conditionals and Predicates
 15.1.5 Functions, Lists, and Symbolic Computing
 15.1.6 Lists as Recursive Structures
 15.1.7 Nested Lists, Structure, and car/cdr Recursion
 15.1.8 Binding Variables Using set
 15.1.9 Defining Local Variables Using let
 15.1.10 Data Types in Common LISP
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15.0 Characteristics of LISP
KU NLP
1.
Language for artificial intelligence programming
a.
2.
Imperative language
a.
b.
3.
Originally designed for symbolic computing
Describe how to perform an algorithm
Contrasts with declarative languages such as PROLOG
Functional programming
Syntax and semantics are derived from the mathematical theory of
recursive functions.
b. Combined with a rich set of high-level tools for building symbolic
data structures such as predicates, frames, networks, and objects
a.
4.
Popularity in the AI community
a.
b.
Widely used as a language for implementing AI tools and models
High-level functionality and rich development environment make it
an ideal language for building and testing prototype systems.
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15.1 LISP: A Brief Overview
KU NLP
 Syntactic elements of LISP
 Symbolic expressions : S-expressions
 Atom : basic syntactic units
 List
 Both programs and data are represented as s-expressions
 Atom




Letters (upper, lower cases)
Numbers
Characters : * + - / @ $ % ^ & _ < > ~ .
Example
3.1416
 Hyphenated-name
 *some-global*
 nil


x
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List and S-expression
KU NLP
 List
 A sequence of either atoms or other lists separated by
blanks and enclosed in parentheses.
 Example
 (1 2 3 4)
 (a (b c) (d (e f)))
 Empty list “( )” : nil
 nil is the only s-expression that is considered to be both an
atom and a list.
 S-expression
 An atom is an s-expression.
 If s1, s2,…, sn are s-expressions,
then so is the list (s1 s2 … sn).
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Read-Eval-Print
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 Interactive Environment
 User enters s-expressions
 LISP interpreter prints a prompt
 If you enter
 Atom: LISP evaluates itself (error if nothing is bound to the
atom)
 List: LISP evaluates as an evaluation of function, i.e. that the
first item in the list needs to be a function definition (error if
no function definition is bound for the first atom), and
remaining elements to be its arguments.
 > (* 7 9)
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Control of LISP Evaluation:
quote & eval
KU NLP
 quote : ‘
 prevent the evaluation of arguments
 (quote a) ==> a
 (quote (+ 1 3)) ==> (+ 1 3)
 ‘a ==> a
 ‘(+ 4 6) ==> (+ 4 6)
 eval
 allows programmers to evaluate s-expressions at will
 (eval (quote (+ 2 3))) ==> 5
 (list ‘* 2 5) ==> (* 2 5)
 (eval (list ‘* 2 5)) ==> 10
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Programming in LISP:
Creating New Functions
KU NLP
 Syntax of Function Definition
 (defun <function-name> (<formal parameters>)
<function body>)
 defun : define function
 Example
 (defun square (x)
(* x x))
 (defun hypotenuse (x y)
(sqrt (+ (square x)
(square y))))
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;the length of the hypotenuse is
;the square root of the sum of
;the square of the other sides.
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Program Control in LISP:
Conditionals & Predicates(1/2)
KU NLP
 Conditions
 (cond (<condition 1> <action1>)
(<condition 2> <action 2>)
...
(<condition n> <action n))
 Evaluate the conditions in order until one of the condition returns a
non-nil value
 Evaluate the associated action and returns the result of the action
as the value of the cond expression
 Predicates
 Example
(oddp 3)
 (minusp 6)
 (numberp 17)

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; whether its argument is odd or not
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Conditionals & Predicates(2/2)
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 Alternative Conditions
 (if test action-then action-else)
 (defun absolute-value (x)
(if (< x 0) (- x) x))
 it returns the result of action-then if test return a non-nil value
 it return the result of action-else if test returns nil
 (and action1 ... action-n)
; conjunction
 Evaluate arguments, stopping when any one of arguments evaluates to
nil
 (or action1 ... action-n)
; disjunction
 Evaluate its arguments only until a non-nil value is encountered
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List as recursive structures
KU NLP
 Cons cell: data structure to hold a list in LISP
 car - holds the first element.
 cdr - holds the rest in the list.
 Accessing a list





(car ‘(a b c)) ==> a
(cdr ‘(a b c)) ==> (b c)
(first ‘(a b c)) ==> a
(second ‘(a b c)) ==> b
(nth 1 ‘(a b c)) ==> b
 Constructing a list
 (cons ‘a ‘(b c)) ==> (a b c)
 (cons ‘a nil) ==> (a)
 (cons ‘(a b) ‘(c d)) ==> ((a b) c d)
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Nested lists, structure,
car/cdr recursion
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 More list construction
 (append ‘(a b) ‘(c d)) ==> (a b c d)
 (cons ‘(a b) ‘(c d)) ==> ((a b) c d)
 Counting the number of elements in the list
 (length ‘((1 2) 3 (1 (4 (5))))) ==> 3
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Binding variables: set(1/2)
KU NLP
 (setq <symbol> <form>)
 bind <form> to <symbol>
 <symbol> is NOT evaluated.
 (set <place> <form>)
 replace s-expression at <place> with <form>
 <place> is evaluated. (it must exists.)
 (setf <place> <form>)
 generalized form of set: when <place> is a symbol, it behaves like setq;
otherwise, it behaves like set.
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Binding variables: set(2/2)
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 Examples of set / setq
 (setq x 1) ==> 1 ;;;
 (set a 2) ==> ERROR!!
 (set ‘a 2) ==> 2 ;;;
 (+ a x) ==> 3
 (setq l ‘(x y z)) ==>
 (set (car l) g) ==> g
 l ==> (g y z)
assigns 1 to x
;;; a is NOT defined
assigns 2 to a
(x y z)
 Examples of setf
 (setf x 1) ==> 1
 (setf a 2) ==> 2
 (+ a x) ==> 3
 (setf l ‘(x y z)) ==> (x y z)
 (setf (car l) g) ==> g
 l ==> (g y z)
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Local variables: let(1/2)
KU NLP
 Consider a function to compute roots of a quadratic equation:
ax2+bx+c=0
 (defun quad-roots1 (a b c)
(setq temp (sqrt (- (* b b) (* 4 a c))))
(list (/ (+ (- b) temp) (* 2 a))
(/ (- (- b) temp) (* 2 a))))
 (quad-roots1 1 2 1) ==> (-1.0 -1.0)
 temp ==> 0.0
 Local variable declaration using let
 (defun quad-roots2 (a b c)
(let (temp)
(setq temp (sqrt (- (* b b) (* 4 a c))))
(list (/ (+ (- b) temp) (* 2 a))
(/ (- (- b) temp) (* 2 a)))))
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Local variables: let(2/2)
KU NLP
 Any variables within let closure are NOT bound at top level.
 More improvement (binding values in local variables)
 (defun quad-roots3 (a b
(let ((temp (sqrt (- (*
((denom (*2 a)))
(list (/ (+ (- b)
(/ (- (- b)
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c)
b b) (* 4 a c))))
temp) denom)
temp) denom))))
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For Homework
KU NLP
 Representing predicate calculus with LISP
 ∀x likes (x, ice_cream)
(Forall (VAR X) (likes (VAR X) ice_cream))
 ∃x foo (x, two, (plus two three))
(Exist (VAR X) (foo (VAR X) two (plus two three)))
 Connectives
 ¬S
(nott S)
 S1 ∧ S2
(ANDD S1 S2)
 S1 ∨ S2
(ORR
S1 S2)
 S1 → S2
(imply
S1 S2)
 S1 ≡ S2
(equiv
S1 S2)
 Do not use the builtin predicate names.
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For Homework
KU NLP
 숙제를 간략하게 하기 위해서 다음 predicate만을
atomic sentence라고 가정한다.
 true, false
 likes (george, kate)
likes (x, george)
likes (george, susie)
likes (x, x)
likes (george, sarah, tuesday)
friends (bill, richard)
friends (bill, george)
friends (father_of(david), father_of(andrew))
helps (bill, george)
helps (richard, bill)
equals (plus (two, three), five)
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For Homework
KU NLP
(DEFUN atomic_s (Ex)
(cond ((member Ex ‘(true false)) T)
((member (car Ex) ‘(likes …))
(Test_term (cdr Ex)))
(T nil)))
(DEFUN Test_term (ex1)
(cond ((NULL ex1) T)
((member (car ex1) ‘(george …..)
(test_term (cdr ex1)))
((VARP (car ex1)) (test_term (cdr ex1)))
((functionp (car ex1)) (test_term (cdr ex1)))
(T nil)))
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Recursion Templates
KU NLP
 Recursion template
 A few standard forms of recursive Lisp functions.
 You can create new functions by choosing a template and filling in
the blanks.
 Recursion templates의 종류
① Double-Test Tail Recursion
② Single-Test Tail Recursion
③ Single-Test Augmenting Recursion
④ List-Consing Recursion
⑤ Simultaneous Recursion on Several Variables
⑥ Conditional Augmentation
⑦ Multiple Recursion
⑧ CAR/CDR Recursion
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Double-Test Tail Recursion
KU NLP
 Template :
(DEFUN func (X)
(COND (end-test-1 end-value-1)
(end-test-2 end-value-2)
(T (func reduced-x))))
 Example :
Func :
End-test-1 :
End-value-1 :
End-test-2 :
E nd-value-2 :
Reduced-x :
ANYODDP
(NULL X)
NIL
(ODDP(FIRST X))
T
(REST X)
(defun anyoddp (x)
(cond ((null x) nil)
((oddp (first x)) t)
((t (anyoddp (rest x))))
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Single-Test Tail Recursion
KU NLP
 Template :
(DEFUN func (X)
(COND (end-test end-value)
(T (func reduced-x))))
 Example :
Func :
FIND-FIRST-ATOM
End-test :
(ATOM X)
End-value :
Reduced-x :
X
(FIRST X)
(defun find-first-atom (x)
(cond ((atom x) x)
((t (find-first-atom (first x))))
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Single-Test Augmenting Recursion(1/2)
KU NLP
 Template :
(DEFUN func (X)
(COND (end-test end-value)
(T (aug-fun aug-val)
(func reduced-x))))
 Example1 :
Func :
COUNT-SLICES
End-test :
(NULL X)
End-value :
Aug-fun :
Aug-val :
Reduced-x :
0
+
1
(REST X)
(defun count-slices (x)
(cond ((null x) 0)
(t (+ 1 (count-slices (rest x))))))
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Single-Test Augmenting Recursion(2/2)
KU NLP
 Example2: The Factorial Function
(defun fact (n)
(cond ((zerop n) 1)
(t (* n (fact (- n 1))))))
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KU NLP
List-Consing Recursion
(A Special Case of Augmenting Recursion)
 Template :
(DEFUN func (N)
(COND (end-test NIL)
(T (CONS new-element
(func reduced-n)))))
 Example :
Func :
End-test :
New-element :
Reduced-n :
LAUGH
(ZEROP N)
‘HA
(- N 1)
(defun laugh (n)
(cond ((zerop n) nil)
(t (cons ‘ha (laugh (- n 1))))))
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KU NLP
Simultaneous Recursion on Several Variables
(Using the Single-Test Recursion Template)
 Template :
(DEFUN func (N X)
(COND (end-test end-value)
(T (func reduced-n reduced-x))))
 Example :
Func :
End-test :
End-value :
Reduced-n :
Reduced-x :
MY-NTH
(ZEROP N)
(FIRST X)
(- N 1)
(REST X)
(defun my-nth (n x)
(cond ((zerop n) (first X)
(t (my-nth (- n 1) (rest x)))))
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Conditional Augmentation (1/2)
KU NLP
 Template
(DEFUN func (X)
(COND (end-test end-value)
(aug-test (aug-fun aug-val
(func reduced-x)))
(T (func reduced-x))))
 Example
Func :
End-test :
End-value :
Aug-test :
Aug-fun :
Aug-val :
Reduced-x :
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EXTRACT-SYMBOLS
(NULL X)
NIL
(SYMBOLP (FIRST X))
CONS
(FIRST X)
(REST X)
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Conditional Augmentation (2/2)
KU NLP
(defun extract-symbols (X)
(cond ((null x) nil)
((symbolp (first x))
(cons (first x)
(extract-symbols (rest x))))
(t (extract-symbols (rest x)))))
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Multiple Recursion(1/2)
KU NLP
 Template :
(DEFUN func (X)
(COND (end-test1 end-value-1)
(end-test2 end-value-2)
(T (combiner (func first-reduced-n)
(func second-reduced-n)))))
 Example :
Func :
End-test-1 :
End-value-1 :
End-test-2 :
End-value-2 :
Combiner :
First-reduced-n :
Second-reduced-n :
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FIB
(EQUAL N 0)
1
(EQUAL N 1)
1
+
(- N 1)
(- N 2)
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Multiple Recursion(2/2)
KU NLP
(defun fib (n)
(cond (equal n 0) 1)
(equal n 1) 1)
(t (+ (fib (- n 1))
(fib (- n 2))))))
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KU NLP
CAR/CDR Recursion
(A Special Case of Multiple Recursion)(1/2)
 Template :
(DEFUN func (X)
(COND (end-test-1 end-value-1)
(end-test-2 end-value-2)
(T (combiner (func CAR X))
(func (CDR X))))))
 Example :
Func :
End-test-1 :
End-value-1 :
End-test-2 :
End-value-2 :
Combiner :
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FIND-NUMBER
(NUMBERP X)
X
(ATOM X)
NIL
OR
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CAR/CDR Recursion
(A Special Case of Multiple Recursion)(2/2)
(defun find-number (x)
(cond ((numberp x) x)
((atom x) nil)
(t (or (find-number (car x))
(find-number (cdr x))))))
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연습문제
KU NLP
 VECTORPLUS X Y
: Write a function (VECTORPLUS X Y) which takes two lists
and adds each number at the same position of each list.
 예) (VECTORPLUS ‘(3 6 9 10 4) ‘(8 5 2))
→ (11 11 11 10 4)
 답)
(DEFUN VECPLUS (X Y)
(COND
((NULL X) Y)
((NULL Y) X)
(T (CONS (+ (CAR X) (CAR Y)
(VECPLUS (CDR X) (CDR Y))))))
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