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Functional Programming 02 Lists

Functional Programming 02 Lists. Review. > (cons ‘a ‘(b c d)) (A B C D) > ( list ‘a ‘b ‘c ‘d) (A B C D) > (car ‘(a b c d)) A > ( cdr ‘(a b c d)) (B C D). Review. Exercises

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Functional Programming 02 Lists

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  1. Functional Programming 02 Lists

  2. Review • > (cons ‘a ‘(b c d))(A B C D) • > (list ‘a ‘b ‘c ‘d)(A B C D) • > (car ‘(a b c d))A • > (cdr ‘(a b c d))(B C D)

  3. Review • Exercises • What does this function do?(defun enigma (x) (and (not (null x)) (or (null (car x)) (enigma (cdr x))))) • > (enigma ‘((a b) (c nil d) e)) • NIL • > (enigma nil) • NIL • > (enigma ‘((a b) nil c)) • T

  4. Lists-Cons • LisPListProcessor • Cons • Combine two objects into a two-part object • A cons is a pair of pointers • Car • Cdr • Provide a convenient representation for pairs of any type

  5. Lists-Cons • > (setf x (cons ‘a nil))(A) • The resulting list consists of a single cons • > (car x)A • > (cdr x)NIL

  6. Lists-Cons • > (setf y (list ‘a ‘b ‘c))(A B C) • > (cdr y)(B C)

  7. Lists-Cons • > (setf z (list ‘a (list ‘b ‘c) ‘d))(A (B C) D)) • > (car (cdr z)) • (B C)

  8. Lists-Cons • (defun our-listp (x) (or (null x) (consp x))) ; either null or a cons • (defun our-atom (x) (not (consp x))) • NIL is both an atom and a list

  9. Lists-Equality • Each time we call cons, Lisp allocates a new piece of memory with room for two pointers • > (eql (cons ‘a nil) (cons ‘a nil))NIL • The two objects look the same, but are in fact distinct • eql • Returns true only if its arguments are the same object • > (setf x (cons ‘a nil))(A)> (eql x x)T

  10. Lists-Equality • equal • Returns true if its arguments would print the same • > (equal x (cons ‘a nil))T • (defun our-equal (x y) (or (eql x y) (and (consp x) (consp y) (our-equal (car x) (car y)) (our-equal (cdr x) (cdr y)))))

  11. Lists-Why Lisp Has No Pointers • Variables have values ～Lists have elements • Variables have pointers to their values • Lisp handles pointers for you • > (setfx ‘(a b c))(A B C)> (setf y x)(A B C) • > (eql x y)T

  12. Lists-Why Lisp Has No Pointers • Assign a value to a variable orStore a value in a data structure→ store a pointer to the value x→ ▼☆◆□ • When you ask for the value of the variable or the contents of the data structure, Lisp returns what it points to →?? • All this happens beneath the surface → you don’t have to think about it

  13. Lists-Building Lists • > (setfx ’(a b c)) y (copy-list x))(A B C) • x and (copy-list x) will always be equal, and never eql unless x is nil

  14. Lists-Building Lists • (defun our-copy-list (lst) (if (atom lst)lst (cons (car lst) (our-copy-list (cdrlst))))) • > (append ‘(a b) ‘(c d) ‘(e))(A B C D E)

  15. Exercise • Show the following lists in box notation • (a b (c d)) • (a (b (c (d)))) • (((a b) c) d)

  16. Lists-Example: Run-length coding > (compress ‘(1 1 1 0 1 0 0 0 0 1))((3 1) 0 1 (4 0) 1) • (defun compress (x) (if (consp x) (compr (car x) 1 (cdr x)) x)) • (defuncompr (elt n 1st) ;find elt from lst, the current length is n (if (null lst) (list (n-elts elt n)) (let ((next (car lst))) (if (eql next elt) (compr elt (+ n 1) (cdr lst)) (cons (n-elts elt n) (compr next 1 (cdrlst) ) ) ) ) ) ) • (defun n-elts (elt n) ;output (n elt) (if (> n 1) (list n elt) elt ) )

  17. Lists-Example: Run-length coding • (defun uncompress (lst) (if (null lst) nil (let ((elt (car lst)) (rest (uncompress (cdr lst)))) (if (consp elt) (append (apply #’list-of elt) rest (cons elt rest))))) • (defun list-of (n elt) ;output n elt (if (zerop n) nil (cons elt (list-of (- n 1) elt)))) > (list-of 3 ‘ho)(HO HOHO) > (uncompress ‘((3 1) 0 1 (4 0) 1) (1 1 1 0 1 0 0 0 0 1))

  18. Lists-Access • > (nth 0 ‘(a b c))A • > (nthcdr 2 ‘(a b c))(C) • nth ≡ car of nthcdr • (defun our-nthcdr (n lst) (if (zerop n)lst (our-nthcdr (- n 1) (cdrlst))))

  19. Lists-Mapping Functions • > (mapcar#’(lambda (x) (+ x 10)) ‘(1 2 3))(11 12 13) • > (mapcar#’list ‘(a b c) ‘(1 2 3 4))((A 1) (B 2) (C 3)) • > (maplist#’(lambda (x) x) ‘(a b c))((A B C) (B C) (C))

  20. Lists-Trees • Conses can also be considered as binary trees • Car: left subtree • Cdr: right subtree • (a (b c) d)

  21. Lists-Trees • Common Lisp has several built-in functions for use of trees • copy-tree • subst • (defun our-copy-tree (tr) (if (atom tr)tr (cons (our-copy-tree (car tr)) (our-copy-tree (cdrtr))))) • Compare it with copy-list

  22. Lists-Trees • >(substitute ‘y ‘x ‘(and (integerp x) (zerop (mod x 2))))(AND (INTEGERP X) (ZEROP (MOD X 2))) • Substitute: replaces elements in a sequence • > (subst ‘y ‘x ‘(and (integerp x) (zerop (mod x 2)))(AND (INTEGERP Y) (ZEROP (MOD Y 2))) • Subst: replaces elements in a tree

  23. Lists-Trees • (defunour-subst (newoldtree) ( if (eql tree old) new ( if (atom tree) tree (cons (our-substnewold(car tree)) (our-substnewold(cdr tree ) ) ) ) ))

  24. Lists-Recursion • Advantage: let us view algorithms in a more abstract way • (defunlen (lst) (if (null lst) 0 (+ (len (cdrlst)) 1))) • We should ensure that • It works for lists of length 0 • It works for lists of length n, and also for lists of length n+1

  25. Lists-Recursion • Don’t omit the base case of a recursive function • Exercises (defun our-member (objlst) ;it’s a wrong prog (if (eql (car lst) obj)lst (our-member obj (cdrlst))))

  26. Lists-Sets • Lists are a good way to represent small sets • Every element of a list is a member of the set it represent • > (member ‘b ‘(a b c))(B C) • > (member ‘(b) ‘((a) (b) (c)))NIL Why? • Equal: the same expression? • Eql: the same symbol or number? • member compares objects using eql • > (member ‘(a) ‘((a) (z)) :test #’equal) ;:test-> keyword argument((A) (Z))

  27. Lists-Sets • > (member ‘a ‘((a b) (c d)) :key #’car)((A B) (C D)) • Ask if there is an element whose car is a • Ask if there is an element whose car is equal to 2 • > (member 2 ‘((1) (2)) :key #’car :test #’equal) ((2)) • > (member 2 ‘((1) (2)) :test #’equal :key #’car) ((2))

  28. Lists-Sets • > (member-if #’oddp ‘(2 3 4))(3 4) • (defunour-member-if (fnlst) (and (consplst) (if (funcall fn (car lst))lst (our-member-iffn(cdrlst)))))

  29. Lists-Sets • > (adjoin ‘b ‘(a b c))(A B C) • > (adjoin ‘z ‘(a b c))(Z A B C) • > (union ‘(a b c) ‘(c b s))(A C B S) • > (intersection ‘(a b c) ‘(b b c))(B C) • > (set-difference ‘(a b c d e) ‘(b e))(A C D)

  30. Lists-Sequences • > (length ‘(a b c))3 • > (length ‘((a b) c (d e f)))? • > (subseq ‘(a b c d) 1 2)(B) • > (subseq ‘(a b c d) 1)(B C D) • > (reverse ‘(a b c))(C B A)

  31. Lists-Sequences • Palindrome: a sequence that reads the same in either direction • (defun mirror? (s) (let ((len (length s))) (and (evenplen) (let ((mid (/ len 2))) (equal (subseq s 0 mid) (reverse (subseq s mid))))))) • > (mirror? ‘(a b b a))T

  32. Lists-Sequences • > (sort ‘(0 2 1 3 8) #’>)(8 3 2 1 0) • Sort is destructive!! • Exercise • Use sort and nth to write a function that takes an integer n, and returns the nth greatest element of a list • (defunnthmost (n lst) (nth (- n 1) (sort (copy-list lst) #’>)))

  33. Lists-Sequences • > (every #’oddp ‘(1 3 5)) ;everyone is …T • > (some #’evenp ‘(1 2 3)) ;someone is …T • > (every #’> ‘(1 3 5) ‘(0 2 4))T

  34. Lists-Stacks • (push objlst)pushes obj onto the front of the list lst • (pop lst)removes and returns the first element of the list lst • > (setf x ‘(b))(B) • > (push ‘a x)(A B) • > x(A B) • > (setf y x)(A B) • > (pop x)A • > x(B) • > y(A B)

  35. Lists-Dotted Lists • Proper list: is either nil, or a cons whose cdr is a proper list • (defun proper-list? (x) (or (null x) (and (consp x) (proper-list? (cdr x))))) • Dotted list:is an n-part data structure • (A . B) • (setf pair (cons ‘a ‘b))(A . B)

  36. Lists-Dotted Lists • > ‘(a . (b . (c . nil)))(A B C) • > (cons ‘a (cons ‘b (cons ‘c ‘d)))(A B C . D)

  37. Lists-Example: Shortest Path • (setf my-net ‘((a b c) (b c) (c d)) • > (cdr (assoc ‘a my-net))(B C)

  38. Lists-Example: Shortest Path • (defunshortest-path(start end net) (bfsend (list (list start)) net)) • (defunbfs (end queuenet) (if (null queue) nil (let ((path (car queue))) (let ((node (car path))) (if (eql node end) (reverse path) (bfsend (append (cdr queue) (new-paths pathnodenet)) net)))))) • (defunnew-paths (pathnodenet) (mapcar #'(lambda (n) (cons n path)) (cdr (assoc node net))))

  39. Lists-Example: Shortest Path • > (shortest-path ‘a ‘d my-net)(A C D) • Queue elements when calling bfs successively • ((A)) • ((B A) (C A)) • ((C A) (C B A)) • ((C B A) (D C A)) • ((D C A) (D C B A))

  40. Lists-Garbage • Automatic memory management is one of Lisp’s most valuable features • The Lisp system maintains a segment of memory→ HeapMemory is allocated from a large pool of unused memory area called the heap (also called the free store). • Consing: allocating memory from the heap • Garbage collection (GC): the system periodically search through the heap, looking for memory that is no longer needed • > (setflst (list ‘a ‘b ‘c)(A B C) • > (setflst nil)NIL

  41. Lists • Homework • Suppose the function pos+ takes a list and returns a list of each element plus its position:> (pos+ ‘(7 5 1 4))(7 6 3 7)Define this function using (a) recursion, (b) iteration, (c) mapcar.(Due March 17) • Bonus assignment • Write a C program to find the shortest path in a network, just like the program in page 38, and analyze the differences between these two programs(Due March 24)

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