1. Comparative Programming Languages Functional Languages Comparison: Scheme, Smalltalk, Python, Ruby, Perl, Prolog, ML, C++/STL, Java

2. CS 363 Spring 2005 GMU2 Fundamentals of Functional Programming Languages The objective of the design of a functional programming language (FPL) is to mimic mathematical functions to the greatest extent possible The basic process of computation is fundamentally different in a FPL than in an imperative language –In an imperative language, operations are done and the results are stored in variables for later use –Management of variables is a constant concern and source of complexity for imperative programming In an FPL, variables are not necessary, as is the case in mathematics

3. CS 363 Spring 2005 GMU3 Fundamentals of Functional Programming Languages In an FPL, the evaluation of a function always produces the same result given the same parameters –This is called referential transparency

4. CS 363 Spring 2005 GMU4 Lisp Lisp – based on lambda calculus (Church) –Uniform representation of programs and data using single general data structure (list) –Interpreter based (written in Lisp) –Automatic memory management –Evolved over the years –Dialects: COMMON LISP, Scheme

5. 5 Smalltalk Smalltalk – a dynamically typed object oriented programming and functional language designed at Xerox PARC by Alan Kay, Dan Ingalls, Ted Kaehler, Adele Goldberg, during the 1970s. –Released as Smalltalk-80 –Influenced the development of languages such as Objective- C, Java and Ruby –Everything is an object –Everything is available for modification. If you want to change the IDE, you can do it –Types are dynamic -- you don't have to define types in the code –Garbage collection is built in, invisible to the developer.

6. 6 Squeak Squeak is an open, highly-portable Smalltalk-80 implementation whose virtual machine is written entirely in Smalltalk –The image below was created in Squeak, and illustrates several of Squeak's abilities, including the ability to scale and rotate bitmap images at any colour depth, anti- aliased TrueType fonts and vector graphics

7. 7 Ruby Ruby – combines syntax inspired by Ada and Perl with Smalltalk-like object-oriented features –Also shares some features with Python, Lisp –Ruby is an interpreted language. –Created by Yukihiro "Matz" Matsumoto, started working on Ruby in Feb. 1993 and released it to the public in 1995. –Name chosen to reflect the language's Perl heritage. –Designed Ruby to follow the principle of least surprise - the language should be free from traps and inconsistencies of other languages

8. 8 Python Python is an interpreted, interactive programming language created by Guido van Rossum in 1990 –Originally as a scripting language for Amoeba OS capable of making system calls. – Amoeba distributed operating system is a microkernel- based research operating system written by Andrew S. Tanenbaum at Vrije Universiteit – The aim of the project was to build a timesharing system that appeared to the user as a single machine even though it was running on multiple machines.

9. 9 Python –Often compared to Tcl, Perl, Scheme, Java, and Ruby –Developed as an open source project, managed by the non- profit Python Software Foundation. –Python is a multi-paradigm language, like Perl, Oz or C++ and unlike Smalltalk or Haskell –Rather than forcing coders to adopt one particular style of coding, it permits several –Object orientation, structured programming, functional programming are all supported –Python is dynamically type-checked and uses garbage collection for memory management –origin of the name - after the television series Monty Python's Flying Circus

10. 10 Python Python (from wikipedia) –Many similarities to Perl –However, Python's designers reject Perl's exuberant syntax in favor of a more spare, less cluttered one –As with Perl, Python's developers expressly promote a particular "culture" or ideology (http://python.org/dev/culture.html) based on what they want the language to be, favoring language forms they see as "beautiful", "explicit" and "simple". –Although Python is sometimes classified as a "scripting language", it has been used to develop many large software projects such as the Zope application server

11. 11 Python Python (from wikipedia) –Though the designer of Python is somewhat hostile to functional programming and the Lisp tradition, there are significant parallels between the philosophy of Python and that of minimalist Lisp-family languages such as Scheme –Many past Lisp programmers have found Python appealing for this reason –Python is a dynamically typed language, like Lisp and unlike Java or C

12. CS 363 Spring 2005 GMU12 Scheme (dr scheme, guile) (define (gcd u v) (if ( = v 0) u (gcd v (remainder u v)) ) (define (reverse l) (if (null? l) l (append (reverse (cdr l))(list (car l))) )

13. CS 363 Spring 2005 GMU13 Scheme (dr scheme, guile) Using guile (gnu scheme): (load "slides.scm") (gcd 56 108) --> 4 (reverse '(2 3 556)) --> (556 3 2)

14. 14 Common Lisp (clisp) (defun mygcd (u v) (if (= v 0) u (mygcd v (rem u v)) ) (defun myreverse (l) (if (null l) l (append (myreverse (cdr l))(list (car l))) ) ;; (load "slides.lsp"), (mygcd 56 108) --> 4 ;; (myreverse '(2 3 556)) --> (556 3 2)

15. 15 Smalltalk (Squeak - inisqueak) myGcd: numTwo " 112 myGcd: 224 --> 112” (numTwo = 0) ifTrue: [^self]. ^numTwo myGcd: self \\ numTwo. myReverse "#(1 2 3 43 a b) myReverse -> ($b $a 43 3 2 1 )" (self size = 0) ifTrue: [^self]. ^self allButFirst myReverse, self first asOrderedCollection.

16. 16 Gnu-Smalltalk – gst !SequenceableCollection methodsFor: 'algorithms'! "Or use Array, but that limits your objects." myCount " #(1 2 3 $a $b $c myCount! --> 6 In gst: Filestream inFile: count.st " (self size = 0) ifTrue: [^0]. ^(1 + (self copyFrom: 2) myCount). !

17. 17 Gnu-Smalltalk – gst (cont.) myReverse "#(1 2 3 43 a b) myReverse -> » ($b $a 43 3 2 1 )" | temp | (self size = 0) ifTrue: [^self]. temp := OrderedCollection new: 1. temp add: self first. ^(self copyFrom: 2) myReverse, temp. !!

18. 18 Gnu-Smalltalk – gst (cont.) !Number methodsFor: 'algorithms'! myGcd: numTwo "120 myGcd: 200! --> 40" (numTwo = 0) ifTrue: [^self]. ^numTwo myGcd: self \\ numTwo. !!

19. 19 Ruby (ruby) def myGcd(numOne, numTwo) if numTwo == 0 return numOne end return myGcd(numTwo, numOne % numTwo) end def myReverse(list) if list.length == 1 return list end return myReverse(list[1..list.length- 1]).concat([list[0]]) end

20. 20 Ruby - “Class version” count.rb class Integer def myGcd(numTwo) if numTwo == 0 return self else return numTwo.myGcd(self % numTwo) end - load “file.rb” into the Ruby interpreter (eval.rb) - 120.myGcd(500) --> 20

21. 21 Ruby - “Class version” class Integer def greet print "Hello world\n" end def plus(numTwo) return self + numTwo end def times(numTwo) return self * numTwo end - load “file.rb” into the Ruby interpreter (eval.rb) - 120.greet --> “Hello..”, 3.plus(4).times(5) -> 35

22. 22 Ruby (non-class vers.) def myCount (mylist) if mylist.length == 0 return 0 else return 1 + myCount(mylist[1..mylist.length-1]) end print "Length of [1,2,3,4,5,6]= ", myCount([1,2,3,4,5,6]), "\n" To run: ruby count.rb

23. 23 Ruby (class vers.) class Array def myCount if self.length == 0 return 0 else return 1 + self[1..self.length].myCount end This version is “object oriented”... [3,4,5,6,7,78].myCount --> 6

24. 24 Python (python) def myGcd(numOne, numTwo): if(numTwo == 0): return numOne return myGcd(numTwo, numOne % numTwo) def myReverse(mylist): if len(mylist) == 1: return mylist return myReverse(mylist[1:len(mylist)]) + myReverse([mylist[0]])

25. 25 Python (python) def myCount (mylist): if len(mylist) == 0: return 0 else: return 1 + myCount(mylist[1:len(mylist)]) print "Length of [1,2,3,4,5,6]= ", myCount([1,2,3,4,5,6]) To run: python count.py

26. 26 Perl sub gcd { if ($_[1] == 0) { return $_[0]; } else { return gcd($_[1], $_[0] % $_[1]); } sub count { my @ls; @ls = @_; if (scalar(@ls) == 1) { 1; } else { count(@ls[1..$#ls]) + 1; }

27. 27 Perl sub myReverse { my @templis; if (scalar(@_) == 0) { return (); } else { @templis = myReverse(@_[1..$#_]); push(@templis, $_[0]); return @templis; }

28. 28 Prolog gcd(Num1, 0, Num1). gcd(Num1, Num2, GCD) :- Rem is Num1 mod Num2, gcd(Num2, Rem, GCD). count([],Total, Total). count([_|Rest], Counter, TotalCount) :- NewCount is Counter + 1, count(Rest, NewCount,TotalCount). /* consult('gcd.pl'). gcd(28, 100, X). count([3,4,5,6,7],0, X). */

29. 29 Prolog append([],List, List). append([First|Rest], List2, [First|List3]) :- append(Rest, List2, List3). myreverse([],[]). myreverse([First|[]],[First]). myreverse([First|Rest], NewList) :- myreverse(Rest, ReversedList), append(ReversedList,[First], NewList). /* ?- consult('reverse.pl'). ?- myreverse([11,23, 0,42,18,90, 1],X). X = [1, 90, 18, 42, 0, 23, 11] */

30. 30 ML (sml) fun gcd(num1, 0) = num1 |gcd(num1,num2) = gcd(num2, num1 mod num2); fun count([]) = 0 |count(first::rest) = 1 + count(rest); (* - use "gcdcount.sml"; - gcd(28, 124); val it = 4 : int - count([45,2,7,8,1,23,18]); val it = 7 : int *)

31. 31 ML (sml) fun reverse(L) = if L = nil then nil else reverse(tl(L)) @ [hd(L)]; fun reverse2([]) = [] |reverse2(first::rest) = reverse2(rest) @ [first] (* [] can be used for nil - use "reverse.sml"; - reverse2([1,2,3,4]); val it = [4,3,2,1] : int list -val x = [[1,2],[3,4]] : int list list - reverse(x); - val it = [[3,4],[1,2]] : int list list *)

32. 32 C++ int gcd(int num1, int num2) { if (num2 == 0) return num1; else return gcd(num2, num1 % num2); }

33. 33 C++ (STL) int count(list lis) { if (lis.size() == 0) return 0; else { lis.pop_front(); return 1 + count(lis); }

34. 34 C++ (STL) list reverse(list lis) { if (lis.size() == 0) return lis; else { int first = *lis.begin(); lis.pop_front(); list reversed; reversed = reverse(lis); reversed.push_back(first); return reversed; }

35. 35 Java int gcd(int num1, int num2) { if (num2 == 0) return num1; else return gcd(num2,num1 % num2); }

36. 36 Java int count(List lis) { if (lis.isEmpty()) // or lis.size() == 0 return 0; else return 1 + count(lis.subList(1, lis.size())); }

37. 37 Java List reverse(List lis) { if (lis.isEmpty()) return lis; else { Integer first = (Integer)lis.get(0); List temp = reverse(lis.subList(1,lis.size())); temp.add(temp.size(), first); return temp; }

38. Squeak Browser Window – Lists classes and methods in classes

39. Squeak Workspace Window To “run” each line, middle-button click, choose “do it” or “print it”

40. Squeak Transcript Window To “run” each line, middle-button click, choose “do it” or “print it”

41. Gnu Smalltalk Browser Window

42. Gnu Smalltalk, X11 Worksheet and Transcript Worksheet window Transcript window To “run” a line, right click and choose “do it” and/or “print it”

43. Gnu Smalltalk - gst Note the use of “!” at the end of each line. Also, printNl is specific to gst.

44. Ruby – example run, see count.rb

45. Ruby – example run from eval.rb

46. Python – example run, see count.rb

47. CS 363 Spring 2005 GMU47 Introduction to Scheme A mid-1970s dialect of LISP, designed to be a cleaner, more modern, and simpler version than the contemporary dialects of LISP Uses only static scoping Functions are first-class entities –They can be the values of expressions and elements of lists –They can be assigned to variables and passed as parameters

48. CS 363 Spring 2005 GMU48 Scheme (define (gcd u v) (if ( = v 0) u (gcd v (remainder u v)) ) Once defined in the interpreter:  (gcd 25 10)  5

49. CS 363 Spring 2005 GMU49 Scheme Syntax expression  atom | list atom  number | string | identifier | character | boolean list  ‘(‘ expression-sequence ‘)’ expression-sequence  expression | expression-sequence expression simplest elements

50. CS 363 Spring 2005 GMU50 Scheme atoms Constants: –numbers, strings, #T = True, … Identifier names: Function/operator names –pre-defined & user defined

51. CS 363 Spring 2005 GMU51 Scheme Expression vs. C In Scheme: (+ 3 (* 4 5 )) (and (= a b)(not (= a 0))) (gcd 10 35) In C: 3 + 4 * 5 (a = = b) && (a != 0) gcd(10,35)

52. CS 363 Spring 2005 GMU52 Smalltalk Expressions vs. C In Smalltalk: 3 + 4 * 5 ( = 35, “ + 4 mess. sent to 3, then * 5 mess.) (a = = b) & (a ~= 0) 10 gcd: 35 gcd: 35 mess. sent to 10 In C: 3 + 4 * 5 (a = = b) && (a != 0) gcd(10,35)

53. CS 363 Spring 2005 GMU53 Ruby/Python Expressions vs. C (very similar) In Ruby/Python: 3 + 4 * 5 (a = = b) && (a != 0) gcd(10,35) In C: 3 + 4 * 5 (a = = b) && (a != 0) gcd(10,35)

54. CS 363 Spring 2005 GMU54 Ruby Expressions vs. C Class version In Ruby: 3.plus(4).times(5) (= 35) (a = = b) && (a != 0) 10.gcd(35) In C: 3 + 4 * 5 (a = = b) && (a != 0) gcd(10,35)

55. CS 363 Spring 2005 GMU55 Evaluation Rules for Scheme Expressions 1.Constant atoms (numbers, strings) evaluate to themselves 2.Identifiers are looked up in the current environment and replaced by the value found there (using dynamically maintained symbol table) 3.A list is evaluated by recursively evaluating each element in the list as an expression; the first expression must evaluate to a function. The function is applied to the evaluated values of the rest of the list.

56. CS 363 Spring 2005 GMU56 Scheme Evaluation To evaluate (* (+ 2 3)(+ 4 5)) 1.* is the function – must evaluate the two expressions (+ 2 3) and (+ 4 5) 2.To evaluate (+ 2 3) 1.+ is the function – must evaluation the two expressions 2 and 3 2.2 evaluates to the integer 2 3.3 evaluates to the integer 3 4.+ 2 3 = 5 3.To evaluate (+ 4 5) follow similar steps 4.* 5 9 = 45 * ++ 2345

57. CS 363 Spring 2005 GMU57 Scheme Conditionals If statement: (if ( = v 0) u (gcd v (remainder u v)) ) (if (= a 0) 0 (/ 1 a)) Cond statement: (cond (( = a 0) 0) ((= a 1) 1) (else (/ 1 a)) ) Both if and cond functions use delayed evaluation for the expressions in their bodies (i.e. (/ 1 a) is not evaluated unless the appropriate branch is chosen).

58. CS 363 Spring 2005 GMU58 Smalltalk Conditionals If statement: (v = 0) ifTrue: [^u]. ^v gcd: u \\ v) (a = 0) ifTrue: [^0]. ^ 1/a (or use ifFalse: for the else portion above) Cond statement: None in Smalltalk(?) http://c2.com/cgi/wiki?CaseSt atementsConsideredHarmful Case statements considered harmful??

59. CS 363 Spring 2005 GMU59 Ruby Conditionals If statement: if v == 0 return u else return gcd(v, u % v) end if a == 0 return 0 else return 1/a end Use elsif for “else if” Cond statement: case a when 0 0 when 1 1 else 1/a end

60. CS 363 Spring 2005 GMU60 Python Conditionals If statement: if v == 0: return u else: return gcd(v, u % v) if a == 0: return 0 else: return 1/a Blocks are indented. Use elif for “else if” Cond statement: Use: if elif...

61. CS 363 Spring 2005 GMU61 Example of COND (DEFINE (compare x y) (COND ((> x y) (DISPLAY “x is greater than y”)) ((< x y) (DISPLAY “y is greater than x”)) (ELSE (DISPLAY “x and y are equal”)) )

62. CS 363 Spring 2005 GMU62 Example of COND compare: y (self > y) ifTrue: [ Transcript show: “x is greater than y” printString. Transcript show: cr.] ifFalse: [ (self < y) ifTrue: [ Transcript show: “y is greater than x” printString. Transcript show: cr.] ifFalse: [ Transcript show: “x and y are equal” printString. Transcript show: cr.]].

63. CS 363 Spring 2005 GMU63 Example of COND – Ruby class vers. class Integer def compare(y) if self > y print “x is greater than y\n” elsif self < y print “y is greater than x\n” else print “x and y are equal\n” end Syntax: 4 compare(5)

64. CS 363 Spring 2005 GMU64 Example of COND – Ruby non-class vers. def compare(x, y) if x > y print “x is greater than y\n” elsif x < y print “y is greater than x\n” else print “x and y are equal\n” end Syntax: compare(4,5)

65. CS 363 Spring 2005 GMU65 Example of COND – Python def compare(x, y): if x > y: print “x is greater than y” elif x < y: print “y is greater than x” else: print “x and y are equal\n” Syntax: compare(4,5) (Also – blocks are indented)

66. CS 363 Spring 2005 GMU66 Predicate Functions 1. EQ? takes two symbolic parameters; it returns #T if both parameters are atoms and the two are the same e.g., (EQ? 'A 'A) yields #T (EQ? 'A '(A B)) yields () –Note that if EQ? is called with list parameters, the result is not reliable –EQ? does not work for numeric atoms (use = )

67. CS 363 Spring 2005 GMU67 Predicate Functions 2. LIST? takes one parameter; it returns #T if the parameter is a list; otherwise () 3. NULL? takes one parameter; it returns #T if the parameter is the empty list; otherwise () Note that NULL? returns #T if the parameter is () 4. Numeric Predicate Functions =, <>, >, =, <=, EVEN?, ODD?, ZERO?, NEGATIVE?

68. CS 363 Spring 2005 GMU68 Predicate Functions - Python 1. == returns T rue if both parameters are the same e.g., 'A' == 'A' yields True ' A' == 'A B' False 2. != returns True if both parameters are not the same. e.g., 'A' != 'A' yields False ' A' != 'A B' True

69. CS 363 Spring 2005 GMU69 Predicate Functions - Python 3. type() returns the type of an object. type([1,2,3]) == list returns True 4. len([]) returns True if the parameter is the empty list; otherwise the length of the list 5. Numeric Predicate Functions ==, !=, >, =, <=

70. CS 363 Spring 2005 GMU70 let function Allows values to be given temporary names within an expression –(let ((a 2 ) (b 3)) ( + a b)) –5 Semantics: Evaluate all expressions, then bind the values to the names; evaluate the body

71. CS 363 Spring 2005 GMU71 List Comprehensions - Python provide a concise way to create lists without resorting to use of map(), filter() and/or lambda. – >>> freshfruit = [' banana', ' loganberry ', 'passion fruit '] – >>> [weapon.strip() for weapon in freshfruit] – ['banana', 'loganberry', 'passion fruit']

72. CS 363 Spring 2005 GMU72 List Comprehensions - Python >>> vec = [2, 4, 6] – >>> [3*x for x in vec] – [6, 12, 18] – >>> [3*x for x in vec if x > 3] – [12, 18] – >>> [3*x for x in vec if x < 2] – [] – >>> [[x,x**2] for x in vec] – [[2, 4], [4, 16], [6, 36]]

73. CS 363 Spring 2005 GMU73 for statements - Python >>> # Measure some strings:... a = ['cat', 'window', 'defenestrate'] >>> for x in a:... print x, len(x) cat 3 window 6 defenestrate 12

74. CS 363 Spring 2005 GMU74 for statements - Python >>> # Measure some strings:... a = ['cat', 'window', 'defenestrate'] >>> for x in a:... print x, len(x) cat 3 window 6 defenestrate 12

75. CS 363 Spring 2005 GMU75 for statements - Python >>> for x in a[:]: # make a slice copy of the entire list... if len(x) > 6: a.insert(0, x)... >>> a ['defenestrate', 'cat', 'window', 'defenestrate']

76. CS 363 Spring 2005 GMU76 range() function - Python >>> range(10) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] >>> range(5, 10) [5, 6, 7, 8, 9] >>> range(0, 10, 3) [0, 3, 6, 9] >>> range(-10, -100, -30) [-10, -40, -70]

77. CS 363 Spring 2005 GMU77 range() function - Python >>> a = ['Mary', 'had', 'a', 'little', 'lamb'] >>> for i in range(len(a)):... print i, a[i] 0 Mary 1 had 2 a 3 little 4 lamb

78. CS 363 Spring 2005 GMU 78 More looping - Python >>> knights = {'gallahad': 'the pure', 'robin': 'the brave'} >>> for k, v in knights.iteritems():... print k, v... gallahad the pure robin the brave

79. CS 363 Spring 2005 GMU 79 More looping - Python >>> for i, v in enumerate(['tic', 'tac', 'toe']):... print i, v... 0 tic 1 tac 2 toe

80. CS 363 Spring 2005 GMU 80 More looping - Python >>> for i in reversed(xrange(1,10,2)):... print i... 9 7 5 3 1

81. CS 363 Spring 2005 GMU 81 More looping - Python >>> basket = ['apple', 'orange', 'apple', 'pear', 'orange', 'banana'] >>> for f in sorted(set(basket)):... print f apple banana orange pear

82. CS 363 Spring 2005 GMU82 Quote (‘) function A list that is preceeded by QUOTE or a quote mark (‘) is NOT evaluated. QUOTE is required because the Scheme interpreter, named EVAL, always evaluates parameters to function applications before applying the function. QUOTE is used to avoid parameter evaluation when it is not appropriate –QUOTE can be abbreviated with the apostrophe prefix operator Can be used to provide function arguments –(myfunct ‘(a b) ‘(c d))

83. CS 363 Spring 2005 GMU83 Output functions Output Utility Functions: (DISPLAY expression) (NEWLINE)

84. CS 363 Spring 2005 GMU84 Output functions - Python print print "Hello, World!" print "(33 + 2) / 5 + 11.5 = ",(33 + 2) / 5 + 11.5 print "Halt!" s = raw_input("Who Goes there? ") print "You may pass,", s

85. CS 363 Spring 2005 GMU85 define function Form 1: Bind a symbol to a expression: (define a 2) (define emptylist ‘( )) (define pi 3.141593)

86. CS 363 Spring 2005 GMU86 assignment and def functions - Python Form 1: Bind a symbol to a expression: a = 2 emptylist = [] pi = 3.141593

87. CS 363 Spring 2005 GMU87 “define” function - Smalltalk Form 1: Bind a symbol to a expression: a := 2 mylist := OrderedCollection new: 0 mylist addAll: #(1 2 3 $a $b) pi := 3.141593

88. CS 363 Spring 2005 GMU88 “define” function - Ruby/Python Form 1: Bind a symbol to a expression: a = 2 emptylist = [] mylist = [1,2,3,'a'] pi = 3.141593

89. CS 363 Spring 2005 GMU89 define function Form 2: To bind names to lambda expressions (define (cube x) (* x (* x x )) ) (define (gcd u v) (if ( = v 0) u (gcd v (remainder u v)) ) function name and parameters function body – lambda expression

90. CS 363 Spring 2005 GMU90 define function - Smalltalk Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) cube ^(self * self * self) gcd: v (v = 0) ifTrue: [^self]. ^(self gcd: (self \\ v)) syntax: 50 cube syntax: 50 gcd: 2020

91. CS 363 Spring 2005 GMU91 define function - Ruby Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) class Integer def cube return self * self * self end def gcd(v) if v == 0 return self else return v.gcd(self % v) end syntax: 50.cube syntax: 50.gcd(2020)

92. CS 363 Spring 2005 GMU92 define function - Ruby non-class vers. Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) def cube(x) return x * x * x end def gcd(u, v) if v == 0 return u else return gcd(v, u % v) end syntax: cube(50) syntax: gcd(50, 2020)

93. CS 363 Spring 2005 GMU93 define function - Python Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) def cube(x): return x * x * x def gcd(u, v): if v == 0: return u else: return gcd(v, u % v) Note: blocks are indented syntax: cube(50) syntax: gcd(50, 2020)

94. CS 363 Spring 2005 GMU94 define function - Perl Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) sub cube { return $_[0] * $_[0] * $_[0]; } sub gcd { if ($_[1] == 0) { return $_[0]; } else { return gcd($_[1], $_[0] % $_[1]); } syntax: cube(50) syntax: gcd(50, 2020)

95. CS 363 Spring 2005 GMU95 define function - Prolog Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) cube(X, Cube) :- Cube is X*X*X. gcd(Num1, 0, Num1). gcd(Num1, Num2, GCD) :- Rem is Num1 mod Num2, gcd(Num2, Rem, GCD). syntax: cube(50, X). syntax: gcd(50, 2020, X).

96. CS 363 Spring 2005 GMU96 define function - ML Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) fun cube(x) = x*x*x; fun gcd(num1, 0) = num1 |gcd(num1,num2) = gcd(num2, num1 mod num2); syntax: cube(50); syntax: gcd(50, 2020);

97. CS 363 Spring 2005 GMU97 define function - C++/Java Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition) int cube(int x) { return x*x*x; } int gcd(int num1, int num2) { if (num2 == 0) return num1; else return gcd(num2, num1 % num2); } syntax: cube(50); syntax: gcd(50, 2020);

98. CS 363 Spring 2005 GMU98 Function Evaluation Evaluation process (for normal functions): 1. Parameters are evaluated, in no particular order 2. The values of the parameters are substituted into the function body 3. The function body is evaluated 4. The value of the last expression in the body is the value of the function (Special forms use a different evaluation process)

99. CS 363 Spring 2005 GMU99 Data Structures in Scheme: Box Notation for Lists first element (car)rest of list (cdr) 1 List manipulation is typically written using ‘car’ and ‘cdr’

100. CS 363 Spring 2005 GMU100 Data Structures in Scheme 1 23 (1,2,3) c da b ((a b) c (d))

101. CS 363 Spring 2005 GMU101 Basic List Manipulation ( car L) – returns the first element of L ( cdr L) – returns L minus the first element (car ‘(1 2 3)) = 1 (car ‘((a b)(c d))) = (a b) (cdr ‘(1 2 3)) = (2 3) (cdr ‘((a b)(c d))) = ((c d))

102. CS 363 Spring 2005 GMU102 Basic List Manipulation - Python L[0] – returns the first element of L L[1:] – returns L minus the first element x, y = [1,2,3], [['a','b'], ['c','d']] x[0] = 1 y[0] = ['a', 'b'] x[1:] = [2, 3] y[1:] = [['c', 'd']]

103. CS 363 Spring 2005 GMU103 Basic List Manipulation Smalltalk L first – returns the first element of L L allButFirst – returns L minus the first element (Squeak), in gst use L copyFrom:2 #(1 2 3) first -> 1 #(($a $b)($c $d))) first -> ($a $b) #(1 2 3) copyFrom: 2 -> (2 3) #(($a $b)($c $d))) copyFrom:2 ->(($c $d))

104. CS 363 Spring 2005 GMU104 Basic List Manipulation Ruby L.first – returns the first element of L L.slice(1..m) – returns L minus the first element [1, 2, 3].first -> 1 [['a', 'b'] ['c', 'd']].first ->[“a”,”b”] #(1 2 3) copyFrom: 2 -> (2 3) #(($a $b)($c $d))) copyFrom:2 ->(($c $d))

105. CS 363 Spring 2005 GMU105 Basic List Manipulation ( list e1 … en) – return the list created from the individual elements ( cons e L) – returns the list created by adding expression e to the beginning of list L (list 2 3 4) = (2 3 4) (list ‘(a b) x ‘(c d) ) = ((a b)x(c d)) (cons 2 ‘(3 4)) = (2 3 4) (cons ‘((a b)) ‘(c)) = (((a b)) c)

106. CS 363 Spring 2005 GMU106 Basic List Manipulation - Python >>> a = ['spam', 'eggs', 100, 1234] >>> a ['spam', 'eggs', 100, 1234] >>> a[0] 'spam' >>> a[3] 1234 >>> a[-2] 100 >>> a[1:-1] ['eggs', 100]

107. CS 363 Spring 2005 GMU107 Basic List Manipulation - Python >>> a[:2] + ['bacon', 2*2] ['spam', 'eggs', 'bacon', 4] >>> 3*a[:3] + ['Boe!'] ['spam', 'eggs', 100, 'spam', 'eggs', 100, 'spam', 'eggs', 100, 'Boe!'] List items can be changed: >>> a ['spam', 'eggs', 100, 1234] >>> a[2] = a[2] + 23 >>> a ['spam', 'eggs', 123, 1234]

108. CS 363 Spring 2005 GMU108 Basic List Manipulation - Python It is possible to nest lists (create lists containing other lists), for example: >>> q = [2, 3] >>> p = [1, q, 4] >>> len(p) 3 >>> p[1] [2, 3] >>> p[1][0] 2

109. CS 363 Spring 2005 GMU109 Basic List Manipulation - Python >>> p[1].append('xtra') >>> p [1, [2, 3, 'xtra'], 4] >>> q [2, 3, 'xtra'] Note that in the last example, p[1] and q really refer to the same object!

110. CS 363 Spring 2005 GMU110 Basic List Manipulation - Python >>> x = [3,4,5] >>> y = ['a','b','c'] >>> [y[0]] + x # like (cons (car y) x) >>> y[1:] # like (cdr y)

111. CS 363 Spring 2005 GMU111 Example Functions 1. member - takes an atom and a simple list; returns #T if the atom is in the list; () otherwise (DEFINE (member atm lis) (COND ((NULL? lis) '()) ((EQ? atm (CAR lis)) #T) ((ELSE (member atm (CDR lis))) ))

112. CS 363 Spring 2005 GMU112 Example Functions - Python 1. member - takes an atom and a simple list; returns True if the atom is in the list; [] otherwise def member(atm, lis): if len.lis == 0: return [] elif atm == lis[0]: True else member(atm, lis[1:])

113. CS 363 Spring 2005 GMU113 Example Functions - Ruby 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise def member(atm, lis) if len.lis == 0 then [] elsif atm == lis[0] then true else member(atm, lis[1..lis.length-1]) end

114. CS 363 Spring 2005 GMU114 Example Functions - Smalltalk 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise member: atm self size = 0 ifTrue: [ ^#().] ifFalse: [ atm = self first ifTrue: [ ^true.] ifFalse: [ ^self allButFirst member: atm

115. CS 363 Spring 2005 GMU115 Example Functions - Perl 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise sub member { my $atm; my @ls; ($atm, @ls) = @_; if (scalar(@ls) == 0) { return 0; } elsif ($ls[0] eq $atm) { return 1; } else { member($atm,@ls[1..$#ls]); }

116. CS 363 Spring 2005 GMU116 Example Functions - Prolog 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise member(X,[X|_). member(X,[_|Rest]) :- member(X,Rest). consult('member.pl'). ?- member(5,[3,2,1,4,5,6]).

117. CS 363 Spring 2005 GMU117 Example Functions - ML 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise fun member(_,[]) = false | member(atm,first::rest) = if atm=first then true else member(atm,rest); ( * use - use "member.sml"; val member = fn : ''a * ''a list -> bool val it = () : unit - member(3,[3,4,5]); val it = true : bool *)

118. CS 363 Spring 2005 GMU118 Example Functions – C++, STL 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise bool member(int atm, list lis) { if (lis.size() == 0) return false; else if (*lis.begin() == atm) return true; else { lis.pop_front(); return member(atm,lis); }

119. CS 363 Spring 2005 GMU119 Example Functions – Java 1. member - takes an atom and a simple list; returns t rue if the atom is in the list; [] otherwise boolean member(int atm, List lis) { if (lis.isEmpty()) return false; else if (((Integer) lis.get(0)).intValue()== atm) return true; else return member(atm, lis.subList(1, lis.size())); }

120. CS 363 Spring 2005 GMU120 Example Functions 2. equalsimp - takes two simple lists as parameters; returns #T if the two simple lists are equal; () otherwise (DEFINE (equalsimp lis1 lis2) (COND ((NULL? lis1) (NULL? lis2)) ((NULL? lis2) '()) ((EQ? (CAR lis1) (CAR lis2)) (equalsimp(CDR lis1)(CDR lis2))) (ELSE '()) ))

121. 121 Example Functions - Python 2. equalsimp - takes two simple lists as parameters; returns true if the two simple lists are equal; () otherwise def equalsimp(lis1, lis2): if len(lis1)==0 return len(lis2) == 0 elif len(lis2)==0 return [] elif lis1[0]== lis2[0]: return equalsimp(lis1[1:],lis2[1:]) else: return []

122. 122 Example Functions - Ruby 2. equalsimp - takes two simple lists as parameters; returns true if the two simple lists are equal; () otherwise def equalsimp(lis1, lis2) if lis1.length==0 lis2.length == 0 elsif lis2.length==0 [] elsif lis1[0]== lis2[0]: equalsimp(lis1[1..lis1.length- 1],lis2[1..lis2.length-1]) else [] end

123. 123 Example Functions - Smalltalk 2. equalsimp - takes two simple lists as parameters; returns true if the two simple lists are equal; () otherwise equalsimp: lis2 self size = 0 ifTrue:[ ^lis2 size = 0.] ifFalse:[ lis2=0 ifTrue: [ ^#().] ifFalse: [ self first = lis2 first ifTrue:[ self allButFirst equalsimp: lis2 allButFirst.] ifFalse: [^#().] ] end

124. CS 363 Spring 2005 GMU124 Example Functions 3. equal - takes two general lists as parameters; returns #T if the two lists are equal; () otherwise (DEFINE (equal lis1 lis2) (COND ((NOT (LIST? lis1))(EQ? lis1 lis2)) ((NOT (LIST? lis2)) '()) ((NULL? lis1) (NULL? lis2)) ((NULL? lis2) '()) ((equal (CAR lis1) (CAR lis2)) (equal (CDR lis1) (CDR lis2))) (ELSE '()) ))

125. CS 363 Spring 2005 GMU125 Example Functions (define (count L) (if (null? L) 0 (+ 1 (count (cdr L))) ) (count ‘( a b c d)) = (+ 1 (count ‘(b c d))) = (+ 1 (+ 1(count ‘(c d)))) (+ 1 (+ 1 (+ 1 (count ‘(d)))))= (+ 1 (+ 1 (+ 1 (+ 1 (count ‘())))))= (+ 1 (+ 1 (+ 1 (+ 1 0))))= 4

126. CS 363 Spring 2005 GMU126 Example Functions - Python def count(L): if len(L)== 0: return 0 else: return 1 + count(L[1:])

127. CS 363 Spring 2005 GMU127 Example Functions - Ruby def count(lis) if lis.length== 0 then 0 else 1 + count(lis[1..lis.length-1]) end

128. CS 363 Spring 2005 GMU128 Example Functions - Smalltalk count self size = 0 ifTrue: [ ^0.] ifFalse: [ ^(1 + self allButFirst count). ]

129. CS 363 Spring 2005 GMU129 Example Functions - Perl sub count { my @ls; @ls = @_; if (scalar(@ls) == 1) { 1; } else { count(@ls[1..$#ls]) + 1; }

130. CS 363 Spring 2005 GMU130 Example Functions - Prolog count([],Total, Total). count([_|Rest], Counter,TotalCount) :- NewCount is Counter + 1, count(Rest, NewCount,TotalCount).

131. CS 363 Spring 2005 GMU131 Example Functions - ML fun count([]) = 0 |count(first::rest) = 1 + count(rest);

132. CS 363 Spring 2005 GMU132 Example Functions – C++, STL int count(list lis) { if (lis.size() == 0) return 0; else { lis.pop_front(); return 1 + count(lis); }

133. CS 363 Spring 2005 GMU133 Example Functions – Java int count(List lis) { if (lis.isEmpty()) // or lis.size() == 0 return 0; else return 1 + count(lis.subList(1, lis.size())); }

134. CS 363 Spring 2005 GMU134 Scheme Functions Now define (define (count1 L) ?? ) so that (count1 ‘(a (b c d) e)) = 5

135. CS 363 Spring 2005 GMU135 Scheme Functions This function counts the individual elements: (define (count1 L) (cond ( (null? L) 0 ) ( (list? (car L)) (+ (count1 (car L))(count1 (cdr L)))) (else (+ 1 (count (cdr L)))) ) so that (count1 ‘(a (b c d) e)) = 5

136. CS 363 Spring 2005 GMU136 Example Functions - Python def myappend(L, M) if len(L)==0: return M else: [L[0]] + myappend(L[1:],M)) myappend(['a','b'], ['c','d'] = ['a', 'b', 'c', 'd']

137. CS 363 Spring 2005 GMU137 Example Functions - Ruby def myappend(lis, m) if lis.length==0 then M else [lis[0]] + myappend(lis[1..lis.length-1],M) end myappend(['a','b'], ['c','d'] = ['a', 'b', 'c', 'd']

138. CS 363 Spring 2005 GMU138 Example Functions - Smalltalk myappend: m) self size = 0 ifTrue: [^m.] ifFalse: [ ^(OrderedList with: self first), self allButFirst myappend: m.] #(a b) myappend: ('c' 'd') = ('a' 'b' 'c' 'd')

139. CS 363 Spring 2005 GMU139 Example Functions - Prolog4 append([],List, List). append([First|Rest],List2, [First|List3]) :- append(Rest, List2, List3).

140. CS 363 Spring 2005 GMU140 How does append do its job? (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)))) (append ‘(a b) ‘(c d)) = (cons a (append ‘(b) ‘(c d))) =

141. CS 363 Spring 2005 GMU141 How does append do its job? (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)))) (append ‘(a b) ‘(c d)) = (cons a (append ‘(b) ‘(c d))) = (cons a (cons b (append ‘() ‘(c d)))) =

142. CS 363 Spring 2005 GMU142 How does append do its job? (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)))) (append ‘(a b) ‘(c d)) = (cons a (append ‘(b) ‘(c d))) = (cons a (cons b (append ‘() ‘(c d)))) = (cons a (cons b ‘(c d))) =

143. CS 363 Spring 2005 GMU143 How does append do its job? (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)))) (append ‘(a b) ‘(c d)) = (cons a (append ‘(b) ‘(c d))) = (cons a (cons b (append ‘() ‘(c d)))) = (cons a (cons b ‘(c d))) = (cons a ‘(b c d)) =

144. CS 363 Spring 2005 GMU144 How does append do its job? (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)))) (append ‘(a b) ‘(c d)) = (cons a (append ‘(b) ‘(c d))) = (cons a (cons b (append ‘() ‘(c d)))) = (cons a (cons b ‘(c d))) = (cons a ‘(b c d)) = (a b c d)

145. CS 363 Spring 2005 GMU145 append: C++/STL list append(list lis, list m) { if (lis.size() == 0) return m; else { int first = *lis.begin(); lis.pop_front(); list appendedList = append(lis, m); appendedList.push_front(first); return appendedList; }

146. CS 363 Spring 2005 GMU146 append: Java List append(List lis, List m) { if (lis.isEmpty()) return m; else { Integer first = (Integer) lis.get(0); List temp = new ArrayList(); temp.addAll( append(lis.subList(1,lis.size()), m)); temp.add(0, first); return temp; }

147. CS 363 Spring 2005 GMU147 Reverse Write a function that takes a list of elements and reverses it: (reverse ‘(1 2 3 4)) = (4 3 2 1)

148. CS 363 Spring 2005 GMU148 Reverse (define (reverse L) (if (null? L) ‘() (append (reverse (cdr L))(list (car L))) )

149. CS 363 Spring 2005 GMU149 Reverse - Python def reverse(L): if len(L)==0: return [] else: myappend (reverse (L[1:]), [L[0]])

150. CS 363 Spring 2005 GMU150 Reverse - Ruby def reverse(lis) if lis.length==0 then [] else myappend( reverse (lis[1..lis.length-1]), [lis[0]]) end

151. CS 363 Spring 2005 GMU151 Reverse - Smalltalk reverse self size = 0 ifTrue: [^ #()asOrderedCollection).] ifFalse: [ (self allButFirst reverse) myappend: (OrderedCollection with: self first).]

152. CS 363 Spring 2005 GMU152 Reverse - Perl sub myReverse { my @templis; if (scalar(@_) == 0) { return (); } else { @templis = myReverse(@_[1..$#_]); push(@templis, $_[0]); return @templis; }

153. CS 363 Spring 2005 GMU153 Reverse - Prolog myreverse([],[]). myreverse([First|[]],[First]). myreverse([First|Rest], NewList) :- myreverse(Rest, ReversedList), append(ReversedList,[First], NewList).

154. CS 363 Spring 2005 GMU154 Reverse - ML fun reverse(L) = if L = nil then nil else reverse(tl(L)) @ [hd(L)]; fun reverse2(nil) = nil | reverse2(first::rest) = reverse2(rest) @ [first]

155. CS 363 Spring 2005 GMU155 Reverse - C++/STL list reverse(list lis) { if (lis.size() == 0) return lis; else { int first = *lis.begin(); lis.pop_front(); list reversed; reversed = reverse(lis); reversed.push_back(first); return reversed; }

156. CS 363 Spring 2005 GMU156 Reverse - Java List reverse(List lis) { if (lis.isEmpty()) return lis; else { Integer first = (Integer) lis.get(0); List temp = new ArrayList(); temp.addAll(reverse(lis.subList(1,lis.size()))); //makes a copy of reveresed list, //temp = reverse... affects lis temp.add(temp.size(), first); return temp; }

157. CS 363 Spring 2005 GMU157 Selection Sort in Scheme Let’s define a few useful functions first: (DEFINE (findsmallest lis small) (COND ((NULL? lis) small) ((< (CAR lis) small) (findsmallest (CDR lis) (CAR lis))) (ELSE (findsmallest (CDR lis) small)) )

158. CS 363 Spring 2005 GMU158 Selection Sort in Scheme (DEFINE (remove lis item) (COND ((NULL? lis) ‘() ) ((= (CAR lis) item) (CDR lis)) (ELSE (CONS (CAR lis) (remove (CDR lis) item))) ) Cautious programming! Assuming integers

159. CS 363 Spring 2005 GMU159 Selection Sort in Scheme (DEFINE (selectionsort lis) (IF (NULL? lis) lis (LET ((s (findsmallest (CDR lis) (CAR lis)))) (CONS s (selectionsort (remove lis s)) ) )

160. CS 363 Spring 2005 GMU160 Selection Sort in Python def smallest(L, A): if len(L)==0: return A elif L[0] < A: return smallest(L[1:], L[0]) else: return smallest(L[1:], A)

161. CS 363 Spring 2005 GMU161 Selection Sort in Python def myremove(L, A): L.remove(A) return L

162. CS 363 Spring 2005 GMU162 Selection Sort in Python def selection(L): if len(L) == 0: return [] else: return [smallest(L,L[0])] + selection(myremove(L,smallest(L, L[0])))

163. CS 363 Spring 2005 GMU163 Selection Sort in Ruby def smallest(lis, a) if lis.length==0 then a elsif lis[0] < a then smallest(lis[1..lis.length-1], lis[0]) else smallest(lis[1..lis.length-1], a) end

164. CS 363 Spring 2005 GMU164 Selection Sort in Ruby def myremove(lis, a) lis.delete(a) lis end

165. CS 363 Spring 2005 GMU165 Selection Sort in Ruby def selection(lis) if lis.length == 0 then [] else [smallest(lis,lis[0])] + selection(myremove(lis,smallest(lis, lis[0]))) end

166. CS 363 Spring 2005 GMU166 Selection Sort in Smalltalk smallest: currentsmallest self size = 0 ifTrue: [^currentsmallest.] ifFalse: [ self first < currentsmallest ifTrue: [ ^self allButFirst smallest: self first.] ifFalse: [ ^self allButFirst smallest: currentsmallest]. ].

167. CS 363 Spring 2005 GMU167 Selection Sort in Smalltalk myRemove: item ^self removeAt: (self find: item). !

168. CS 363 Spring 2005 GMU168 Selection Sort in Smalltalk selection "(FileStream oldFileNamed: 'selection.st') fileIn. Numbers := #(4 3 16 1 14 25 2) asOrderedCollection. numbers selection" | currentsmallest | self size = 0 ifTrue: [ ^#() asOrderedCollection.] ifFalse: [ currentsmallest := self smallest: self first. ^(OrderedCollection with: currentsmallest), (self myRemove: (self smallest: self first)) selection. ].

169. CS 363 Spring 2005 GMU169 Selection Sort in Perl sub smallest { my ($element, @lis) = @_; if (scalar(@lis) == 0) { return $element; } elsif ($lis[0] < $element) { return smallest(@lis[1..$#lis], $lis[0]); } else { return smallest(@lis[1..$#lis], $element); }

170. CS 363 Spring 2005 GMU170 Selection Sort in Perl sub remove { my ($element, @lis) = @_; my @templis; if (scalar(@lis) == 0) { return (); } elsif ($lis[0] == $element) { return @lis[1..$#lis]; } else { @templis = remove($element, @lis[1..$#lis]); unshift(@templis, $lis[0]); return @templis; }

171. CS 363 Spring 2005 GMU171 Selection Sort in Perl sub selectionsort { my @templis; my @templis2; my $s; if (scalar(@_) == 0) { return (); } else { $s = smallest(@_[1..$#_], $_[0]); @templis = selectionsort(remove($s, @_)); unshift(@templis, $s); return @templis; }

172. CS 363 Spring 2005 GMU172 Selection Sort in Prolog smallest([], Smallest,Smallest). smallest([First|Rest], CurrSmallest, Smallest) :- First < CurrSmallest, smallest(Rest, First, Smallest). smallest([_|Rest], CurrSmallest, Smallest) :- smallest(Rest, CurrSmallest, Smallest).

173. CS 363 Spring 2005 GMU173 Selection Sort in Prolog remove([], _, []). remove([First|Rest], First, Rest). remove([First|Rest], Element, [First|NewList]) :- remove(Rest, Element, NewList).

174. CS 363 Spring 2005 GMU174 Selection Sort in Prolog selectionsort([],[]). selectionsort([First|Rest], [Smallest|SortedList]) :- smallest(Rest, First, Smallest), remove([First|Rest], Smallest, NewList), selectionsort(NewList, SortedList).

175. CS 363 Spring 2005 GMU175 Selection Sort in ML fun smallest([], a) = a | smallest(first::rest, a) = if first < a then smallest(rest, first) else smallest(rest, a);

176. CS 363 Spring 2005 GMU176 Selection Sort in ML fun remove([], _) = [] | remove(first::rest, item) = if first = item then rest else first::remove(rest, item);

177. CS 363 Spring 2005 GMU177 Selection Sort in ML fun selectionsort([]) = [] | selectionsort(first::rest) = let val s = smallest(rest, first); in s::selectionsort(remove(first::rest,s)) end;

178. CS 363 Spring 2005 GMU178 Selection Sort in ML (* - use "selection.sml"; val it = [1,2,3,5] : int list - remove([1,2,3,4,5], 5); val it = [1,2,3,4] : int list - remove([1,2,3,4,5], 1); val it = [2,3,4,5] : int list - smallest([3,14,5,1,18,2], 3); val it = 1 : int *)

179. CS 363 Spring 2005 GMU179 Selection Sort in C++/STL int smallest(list lis, int small) { if (lis.size() == 0) return small; else if (*lis.begin() < small) { int first = *lis.begin(); lis.pop_front(); return smallest(lis, first); } else { lis.pop_front(); return smallest(lis, small); }

180. CS 363 Spring 2005 GMU180 Selection Sort in C++/STL list remove(list lis, int item) { if (lis.size() == 0) return lis; else if (*lis.begin() == item) { lis.pop_front(); return lis; } else { int first = *lis.begin(); lis.pop_front(); list removedList = remove(lis, item); removedList.push_front(first); return removedList; }

181. CS 363 Spring 2005 GMU181 Selection Sort in C++/STL list selectionsort(list lis) { if (lis.size() == 0) return lis; else { int first = *lis.begin(); list rest = lis; rest.pop_front(); int s = smallest(rest, first); list sortedList = selectionsort(remove(lis,s)); sortedList.push_front(s); return sortedList; }

182. CS 363 Spring 2005 GMU182 Selection Sort in Java int smallest(List lis, int small) { if (lis.isEmpty()) return small; else if (((Integer) lis.get(0)).intValue() < small) return smallest(lis.subList(1,lis.size()), ((Integer) lis.get(0)).intValue()); else return smallest(lis.subList(1,lis.size()), small); }

183. CS 363 Spring 2005 GMU183 Selection Sort in Java List remove(List lis, int item) { if (lis.isEmpty()) return lis; else if (((Integer) lis.get(0)).intValue() == item) return lis.subList(1,lis.size()); else { Integer first = (Integer) lis.get(0); List temp = new ArrayList(); temp.addAll(remove(lis.subList(1,lis.size()),item)); temp.add(0,first); return temp; }

184. CS 363 Spring 2005 GMU184 Selection Sort in Java List selectionsort(List lis) { if (lis.isEmpty()) return lis; else { Integer first = (Integer) lis.get(0); int s = smallest(lis.subList(1,lis.size()), first.intValue()); List sorted = new ArrayList(); List removeList = new ArrayList(); removeList.addAll(remove(lis,s)); sorted.addAll(selectionsort(removeList)); sorted.add(0, new Integer(s)); return sorted; }

185. CS 363 Spring 2005 GMU185 Higher order functions Def: A higher-order function, or functional form, is one that either takes functions as parameters, yields a function as its result, or both Mapcar Eval

186. CS 363 Spring 2005 GMU186 Higher-Order Functions: mapcar Apply to All - mapcar - Applies the given function to all elements of the given list; result is a list of the results (DEFINE (mapcar fun lis) (COND ((NULL? lis) '()) (ELSE (CONS (fun (CAR lis)) (mapcar fun (CDR lis)))) ))

187. CS 363 Spring 2005 GMU187 Higher-Order Functions: mapcar Using mapcar: (mapcar (LAMBDA (num) (* num num num)) ‘(3 4 2 6)) returns (27 64 8 216)

188. CS 363 Spring 2005 GMU188 Higher Order Functions: EVAL It is possible in Scheme to define a function that builds Scheme code and requests its interpretation This is possible because the interpreter is a user-available function, EVAL

189. CS 363 Spring 2005 GMU189 Using EVAL for adding a List of Numbers Suppose we have a list of numbers that must be added: (DEFINE (adder lis) (COND((NULL? lis) 0) (ELSE (+ (CAR lis) (adder(CDR lis )))) )) Using Eval ((DEFINE (adder lis) (COND ((NULL? lis) 0) (ELSE (EVAL (CONS '+ lis))) )) (adder ‘(3 4 5 6 6)) Returns 24

190. CS 363 Spring 2005 GMU190 Other Features of Scheme Scheme includes some imperative features: 1. SET! binds or rebinds a value to a name 2. SET-CAR! replaces the car of a list 3. SET-CDR! replaces the cdr part of a list

191. CS 363 Spring 2005 GMU191 COMMON LISP A combination of many of the features of the popular dialects of LISP around in the early 1980s A large and complex language – the opposite of Scheme

192. CS 363 Spring 2005 GMU192 COMMON LISP Includes: –records –arrays –complex numbers –character strings –powerful I/O capabilities –packages with access control –imperative features like those of Scheme –iterative control statements

193. CS 363 Spring 2005 GMU193 ML A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables It is strongly typed (whereas Scheme is essentially typeless) and has no type coercions Includes exception handling and a module facility for implementing abstract data types

194. CS 363 Spring 2005 GMU194 ML Includes lists and list operations The val statement binds a name to a value (similar to DEFINE in Scheme) Function declaration form: fun function_name (formal_parameters) = function_body_expression; e.g., fun cube (x : int) = x * x * x;

195. CS 363 Spring 2005 GMU195 Haskell Similar to ML (syntax, static scoped, strongly typed, type inferencing) Different from ML (and most other functional languages) in that it is purely functional (e.g., no variables, no assignment statements, and no side effects of any kind)

196. CS 363 Spring 2005 GMU196 Haskell Most Important Features –Uses lazy evaluation (evaluate no subexpression until the value is needed) –Has list comprehensions, which allow it to deal with infinite lists

197. CS 363 Spring 2005 GMU197 Haskell Examples 1. Fibonacci numbers (illustrates function definitions with different parameter forms) fib 0 = 1 fib 1 = 1 fib (n + 2) = fib (n + 1) + fib n

198. CS 363 Spring 2005 GMU198 Haskell Examples 2. Factorial (illustrates guards) fact n | n == 0 = 1 | n > 0 = n * fact (n - 1) The special word otherwise can appear as a guard

199. CS 363 Spring 2005 GMU199 Haskell Examples 3. List operations –List notation: Put elements in brackets e.g., directions = [“north”, “south”, “east”, “west”] –Length: # e.g., #directions is 4 –Arithmetic series with the.. operator e.g., [2, 4..10] is [2, 4, 6, 8, 10]

200. CS 363 Spring 2005 GMU200 Haskell Examples 3. List operations (cont) –Catenation is with ++ e.g., [1, 3] ++ [5, 7] results in [1, 3, 5, 7] –CONS, CAR, CDR via the colon operator (as in Prolog) e.g., 1:[3, 5, 7] results in [1, 3, 5, 7]

201. CS 363 Spring 2005 GMU201 Haskell Examples Quicksort: sort [] = [] sort (a:x) = sort [b | b ← x; b <= a] ++ [a] ++ sort [b | b ← x; b > a]

202. CS 363 Spring 2005 GMU202 Applications of Functional Languages LISP is used for artificial intelligence –Knowledge representation –Machine learning –Natural language processing –Modeling of speech and vision Scheme is used to teach introductory programming at a significant number of universities

203. CS 363 Spring 2005 GMU203 Comparing Functional and Imperative Languages Imperative Languages: –Efficient execution –Complex semantics –Complex syntax –Concurrency is programmer designed Functional Languages: –Simple semantics –Simple syntax –Inefficient execution –Programs can automatically be made concurrent