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)
> (enigma ‘((a b) nil c)) T

4. Lists-Cons LisP  List Processor 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
> (setf x ‘(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 or Store 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 > (setf x ’(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 (cdr lst)))))
> (append ‘(a b) ‘(c d) ‘(e)) (A B C D E)

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

16. Lists-Example: Run-length coding
(defun compress (x)
(if (consp x)
(compr (car x) 1 (cdr x))
x))
(defun compr (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 (cdr lst) ) ) ) ) ) )
(defun n-elts (elt n) ;output (n elt)
(if (> n 1)
(list n elt)
elt ) )
> (compress ‘( )) ((3 1) 0 1 (4 0) 1)

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 HO HO)
> (uncompress ‘((3 1) 0 1 (4 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) (cdr lst))))

19. Lists-Mapping Functions
> (mapcar #’(lambda (x) (+ x 10)) ‘( )) ( )
> (mapcar #’list ‘(a b c) ‘( )) ((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 (a (b c) d)
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 (cdr tr)))))
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 (defun our-subst (new old tree) ( if (eql tree old) new
( if (atom tree)
tree
(cons (our-subst new old (car tree))
(our-subst new old (cdr tree ) ) ) ) ))

24. Lists-Recursion
Advantage: let us view algorithms in a more abstract way
(defun len (lst) (if (null lst) (+ (len (cdr lst)) 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 (obj lst) ;it’s a wrong prog (if (eql (car lst) obj) lst (our-member obj (cdr lst))))

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)

28. Lists-Sets > (member-if #’oddp ‘(2 3 4)) (3 4)
(defun our-member-if (fn lst) (and (consp lst) (if (funcall fn (car lst)) lst (our-member-if fn (cdr lst)))))

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 (evenp len)
(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
(defun nthmost (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 obj lst) 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
(defun shortest-path (start end net)
(bfs end (list (list start)) net))
(defun bfs (end queue net)
(if (null queue)
nil
(let ((path (car queue)))
(let ((node (car path)))
(if (eql node end)
(reverse path)
(bfs end
(append (cdr queue)
(new-paths path node net))
net))))))
(defun new-paths (path node net)
(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 → Heap Memory 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
> (setf lst (list ‘a ‘b ‘c) (A B C)
> (setf lst nil) NIL

41. Lists Homework Bonus assignment
Suppose the function pos+ takes a list and returns a list of each element plus its position: > (pos+ ‘( )) ( ) 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)