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Ch 15. An Introduction to LISP

Ch 15. An Introduction to LISP. 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

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Ch 15. An Introduction to LISP

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  1. Ch 15. An Introduction to LISP • 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 Artificial Intelligence

  2. 15.0 Characteristics of LISP • Language for artificial intelligence programming • Originally designed for symbolic computing • Imperative language • 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. • Combined with a rich set of high-level tools for building symbolic data structures such as predicates, frames, networks, and objects • Popularity in the AI community • 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. Artificial Intelligence

  3. 15.1 LISP: A Brief Overview • 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 Artificial Intelligence

  4. List and S-expression • 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). Artificial Intelligence

  5. Read-Eval-Print • 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) 63 Artificial Intelligence

  6. Control of LISP Evaluation:quote & eval • 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 Artificial Intelligence

  7. Programming in LISP:Creating New Functions • Syntax of Function Definition • (defun <function-name> (<formal parameters>) <function body>) • defun : define function • Example • (defun square (x) (* x x)) • (defun hypotenuse (x y) ;the length of the hypotenuse is (sqrt (+ (square x) ;the square root of the sum of (square y)))) ;the square of the other sides. Artificial Intelligence

  8. Program Control in LISP:Conditionals & Predicates(1/2) • 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) ; whether its argument is odd or not • (minusp 6) • (numberp 17) Artificial Intelligence

  9. Conditionals & Predicates(2/2) • 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 Artificial Intelligence

  10. List as recursive structures • 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) Artificial Intelligence

  11. Nested lists, structure, car/cdr recursion • 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 Artificial Intelligence

  12. Binding variables: set(1/2) • (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. Artificial Intelligence

  13. Binding variables: set(2/2) • Examples of set / setq • (setq x 1) ==> 1 ;;; assigns 1 to x • (set a 2) ==> ERROR!! ;;; a is NOT defined • (set ‘a 2) ==> 2 ;;; assigns 2 to a • (+ a x) ==> 3 • (setq l ‘(x y z)) ==> (x y z) • (set (car l) g) ==> g • l ==> (g 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) Artificial Intelligence

  14. Local variables: let(1/2) • 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))))) Artificial Intelligence

  15. Local variables: let(2/2) • Any variables within letclosure are NOT bound at top level. • More improvement (binding values in local variables) • (defun quad-roots3 (a b c)(let ((temp (sqrt (- (* b b) (* 4 a c)))) ((denom (*2 a))) (list (/ (+ (- b) temp) denom) (/ (- (- b) temp) denom)))) Artificial Intelligence

  16. For Homework • 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. Artificial Intelligence

  17. For Homework • 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) Artificial Intelligence

  18. For Homework (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))) Artificial Intelligence

  19. Recursion Templates • 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 Artificial Intelligence

  20. Double-Test Tail Recursion • Template : (DEFUN func (X) (COND (end-test-1 end-value-1) (end-test-2 end-value-2) (T (func reduced-x)))) • Example : Func : ANYODDP End-test-1 : (NULL X) End-value-1 : NIL End-test-2 : (ODDP(FIRST X)) E nd-value-2 : T Reduced-x : (REST X) (defun anyoddp (x) (cond ((null x) nil) ((oddp (first x)) t) ((t (anyoddp (rest x)))) Artificial Intelligence

  21. Single-Test Tail Recursion • Template : (DEFUN func (X) (COND (end-test end-value) (T (func reduced-x)))) • Example : Func : FIND-FIRST-ATOM End-test : (ATOM X) End-value : X Reduced-x : (FIRST X) (defun find-first-atom (x) (cond ((atom x) x) ((t (find-first-atom (first x)))) Artificial Intelligence

  22. Single-Test Augmenting Recursion(1/2) • 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 : 0 Aug-fun : + Aug-val : 1 Reduced-x : (REST X) (defun count-slices (x) (cond ((null x) 0) (t (+ 1 (count-slices (rest x)))))) Artificial Intelligence

  23. Single-Test Augmenting Recursion(2/2) • Example2: The Factorial Function (defun fact (n) (cond ((zerop n) 1) (t (* n (fact (- n 1)))))) Artificial Intelligence

  24. 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 : LAUGH End-test : (ZEROP N) New-element : ‘HA Reduced-n : (- N 1) (defun laugh (n) (cond ((zerop n) nil) (t (cons ‘ha (laugh (- n 1)))))) Artificial Intelligence

  25. Simultaneous Recursion on Several Variables(Using the Single-Test Recursion Template) • Template : (DEFUN func (N X) (COND (end-testend-value) (T (func reduced-n reduced-x)))) • Example : Func : MY-NTH End-test : (ZEROP N) End-value : (FIRST X) Reduced-n : (- N 1) Reduced-x : (REST X) (defun my-nth (n x) (cond ((zerop n) (first X) (t (my-nth (- n 1) (rest x))))) Artificial Intelligence

  26. Conditional Augmentation (1/2) • Template (DEFUN func (X) (COND (end-testend-value) (aug-test (aug-fun aug-val (func reduced-x))) (T (func reduced-x)))) • Example Func : EXTRACT-SYMBOLS End-test : (NULL X) End-value : NIL Aug-test : (SYMBOLP (FIRST X)) Aug-fun : CONS Aug-val : (FIRST X) Reduced-x : (REST X) Artificial Intelligence

  27. Conditional Augmentation (2/2) (defun extract-symbols (X) (cond ((null x) nil) ((symbolp (first x)) (cons (first x) (extract-symbols (rest x)))) (t (extract-symbols (rest x))))) Artificial Intelligence

  28. Multiple Recursion(1/2) • Template : (DEFUN func (X) (COND (end-test1end-value-1) (end-test2end-value-2) (T (combiner (func first-reduced-n) (func second-reduced-n))))) • Example : Func : FIB End-test-1 : (EQUAL N 0) End-value-1 : 1 End-test-2 : (EQUAL N 1) End-value-2 : 1 Combiner : + First-reduced-n : (- N 1) Second-reduced-n : (- N 2) Artificial Intelligence

  29. Multiple Recursion(2/2) (defun fib (n) (cond (equal n 0) 1) (equal n 1) 1) (t (+ (fib (- n 1)) (fib (- n 2)))))) Artificial Intelligence

  30. CAR/CDR Recursion(A Special Case of Multiple Recursion)(1/2) • Template : (DEFUN func (X) (COND (end-test-1end-value-1) (end-test-2end-value-2) (T (combiner (func CAR X)) (func (CDR X)))))) • Example : Func : FIND-NUMBER End-test-1 : (NUMBERP X) End-value-1 : X End-test-2 : (ATOM X) End-value-2 : NIL Combiner : OR Artificial Intelligence

  31. 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)))))) Artificial Intelligence

  32. 연습문제 • 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)))))) Artificial Intelligence

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