CMP 339/692 Programming Languages Day 4 Thursday, February 9, 2011

1. CMP 339/692Programming LanguagesDay 4Thursday,February 9, 2011 Rhys Eric Rosholt Office: Office Phone: Web Site: Email Address: Gillet Hall - Room 304 718-960-8663 http://comet.lehman.cuny.edu/rosholt/ rhys.rosholt @ lehman.cuny.edu

2. Getting Racket http://racket-lang.org/download/ • Package: Racket • Version: 5.2.1 (February 2012) • Platform: Windows x86 • Type: Windows • Installer File: racket-5.2.1-bin-i386-win32.exe • Size: 38M • (as of 5 pm today) • On the next page, choose the “Main download” site, Northeastern University, in Boston.

3. Chapter 15 Functional Programming Languages

4. Chapter 15 • Introduction • Mathematical Functions • Fundamentals of Functional Programming Languages • The First Functional Programming Language: LISP • Introduction to Scheme • COMMON LISP • ML • Haskell • Applications of Functional Languages • Comparison of Functional and Imperative Languages

5. Fundamentals of Functional Programming Languages The basic process of computation is fundamentally different in a FPL than in an imperative language • Imperative Languages • variables are necessary to mimic machine operation • operations are done and the results are stored in variables for later use • repetition done with loops made with control variables • FPLs • mathematics has unknowns, not variables • repetition done by recursion • referential transparency • FPLs are simpler than imperative languages

6. List FunctionsCONS and LIST CONS • takes two parameters, • the first can be either an atom or a list • the second is a list • returns a new list that includes • the first parameter as its first element, and • the second parameter as the rest of the list Example:(CONS 'A '(B C))returns(A B C) LIST • takes any number of parameters • returns a list with the parameters as elements

7. An Introduction to Scheme List Processing QUOTEtakes: an s-expression returns: the input without evaluation (abbreviated by apostrophe prefix operator) CONStakes: an s-expression and a list returns: a list composed of the two inputs LISTtakes: any number of parameters returns: a list with the input parameters as elements

8. Numeric Predicate Functions #T is true () is false =, <>, >, <, >=, <= EVEN?, ODD?, ZERO?, NEGATIVE?

9. Numeric Predicate Functions (define (quadratic-solutions a b c) (display (/ (+ (- 0 b) (sqrt (- (square b) (* 4 a c)))) (* 2 a))) (newline) (display (/ (- (- 0 b) (sqrt (- (square b) (* 4 a c)))) (* 2 a))) (define (square dum) (* dum dum) )

10. Control FlowIF Selection - the special form, IF (IF predicate then_exp else_exp) (IF (<> count 0) (/ sum count) 0 ) Example: (DEFINE (somefunction n) (IF (= n 0) 1 (* n (somefunction (- n 1))) ) )

11. Control FlowCOND Multiple Selection-the special form, COND (COND (predicate_1 expr {expr}) ... (predicate_n expr {expr}) (ELSE expr {expr}) ) Example: (DEFINE (compare x y) (COND ((> x y) (DISPLAY "x greater than y")) ((< x y) (DISPLAY "y greater than x")) (ELSE (DISPLAY "x and y are equal")) ))

12. An Introduction to Scheme Control Flow 1. Selection - the special form, IF (IF predicate then_exp else_exp) 2. Multiple Selection - the special form, COND (COND (predicate_1 expr {expr}) (predicate_2 expr {expr}) ... (predicate_n expr {expr}) (ELSE expr {expr}) )

13. Output Functions (DISPLAY expression) (NEWLINE)

14. List FunctionsCAR and CDR CAR • takes a list parameter • returns the first element of that list Example: (CAR '(A B C)) returnsA (CAR '((A B) C D)) returns(A B) CDR • takes a list parameter • returns the list after removing its first element Example:(CDR '(A B C)) returns(B C) (CDR '((A B) C D)) returns(C D)

15. Predicate FunctionEQ? EQ? • takes two parameters • it returns #T if both parameters are atoms and the two are the same Example:(EQ? 'A 'A) yields#T (EQ? 'A 'B) yields() Note that if EQ? is called with list parameters, the result is undefined Also EQ? does not work for numeric atoms

16. Predicate FunctionsLIST? and NULL? LIST? • takes one parameter; • returns • #T if the parameter is a list • () otherwise NULL? • takes one parameter; • returns • #T if the parameter is the empty list • () otherwise Note: NULL? returns #T if the parameter is()

17. Example Scheme Function member 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))) ))

18. Example Scheme Function equalsimp 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 '()) ))

19. Example Scheme Functionequal 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 '()) ))

20. Example Scheme Function append append • takes two lists as parameters • returns the first parameter list with the elements of the second parameter list appended at the end (DEFINE (append lis1 lis2) (COND ((NULL? lis1) lis2) (ELSE (CONS (CAR lis1) (append (CDR lis1) lis2))) ))

21. Example Scheme FunctionLET Syntax: (LET ( (name_1 expression_1) (name_2 expression_2) ... (name_n expression_n)) body ) Semantics: • Evaluate all expressions • Bind the values to the names • Evaluate the body

22. LET Example (DEFINE (quadratic_roots a b c) (LET ( ( root_prt_ovr_2a ( / (SQRT (- (* b b)(* 4 a c)))(* 2 a)) ) ( mins_b_ovr_2a ( / (- 0 b) (* 2 a)) ) ) (DISPLAY (+ mins_b_ovr_2a root_prt_ovr_2a)) (NEWLINE) (DISPLAY (- mins_b_ovr_2a root_prt_ovr_2a)) ) )

23. Scheme Functional Forms Composition The previous examples have used it (CDR (CDR ‘(A B C))) returns (C) (CAR (CDR ‘(A B C))) returns B Most lisp languages abbreviate this: (CADR ‘(A B C)) returns B Frequently, this expands farther: (CADDDR ‘(A B C D E)) returns D

24. Scheme Functional Forms Apply to All - one form in Scheme is mapcar takes: a function and a list returns: a list of results of function applied to all elements of the list; Applies the given function to all elements of the given list; (DEFINE (mapcar fun lis) (COND ((NULL? lis) '()) (ELSE (CONS (fun (CAR lis)) (mapcar fun (CDR lis)))) ))

25. Functions That Build Code Frequently, it is useful to define a function that builds code and evaluates it 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

26. Functions That Build Code (DEFINE (adder lis) (COND ((NULL? lis) 0) (ELSE (EVAL (CONS '+ lis))) ) ) The function adder is defined to do the job. The parameter lis is a list of numbers. First CONS prefixes the atom + onto lis. Note that + is quoted to prevent evaluation. The new list is given to EVAL for evaluation.

27. COMMON LISP • A combination of many of the features of the popular dialects of LISP around in the early 1980s • Includes: • records • arrays • complex numbers • character strings • powerful i/o capabilities • packages with access control • imperative features like those of Scheme • iterative control statements

28. ML • A static-scoped functional language • (types determined at compile time) • Syntax is closer to Pascal than to LISP • Usually uses type inferencing to determine the types of undeclared variables • Also has type declarations • Strongly typed and has no type coercions • (Scheme is essentially typeless) • Includes exception handling and a module facility for implementing abstract data types • Supports lists and list processing

29. ML Uses val instead of DEFINE to bind a name to a value Function declaration syntax and example: fun <name> (<parameters>) = <body>; fun cube (x: int) = x * x * x; The default numeric type is int Example of patterned parameters in functions: fun fact(0) = 1 | fact(n: int): int = n * fact(n –1); List notation: brackets and commas All elements of a list must be the same type

30. Haskell • Similarities to ML • (syntax, static scoped, strongly typed, type inferencing) • Differences from ML (and most other functional languages) • Haskell is purely functional • (no variables, no assignment statements, and no side effects of any kind) • 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

31. Haskell Function Definitions with Parameter Forms Examples 1. Factorial fact 0 = 1 fact n = n * fact(n – 1) 2. Fibonacci numbers fib 0 = 1 fib 1 = 1 fib (n + 2) = fib (n + 1) + fib n 3. Factorial using guards fact n | n == 0 = 1 | n > 0 = n * fact(n – 1)

32. Haskell List Operations • List notation: brackets and commas • directions = [“north”,“south”,“east”,“west”] • Length: # • #directions is 4 • Arithmetic series with the .. operator • [2, 4..10] is the same as [2, 4, 6, 8, 10] • Catenation with the ++ operator • [1, 3] ++ [5, 7] results in [1, 3, 5, 7] • CONS, CAR, CDR via the colon operator • (as in Prolog) • 1:[3, 5, 7] results in [1, 3, 5, 7]

33. Haskell List Operations Examples product [ ] = 1 product (a:x) = a * product x fact n = product [1..n] quadratic_root a b c = [part1 – part2, part1 + part2] where part1 = -b/(2.0*a) part2 = sqrt(b^2–4.0*a*c)/(2.0*a)

34. Haskell List Comprehensions Set Notation A list of the squares of the first 20 positive integers is given by this function: [ n * n | n <- [1..20] ] This function computes all of the factors of its given parameter: factors n = [ i | i [ 1..n div 2 ], n mod i == 0 ] Quicksort: sort [ ] = [ ] sort (h:t) = sort [ b | b <- t; b <= h ] ++ [ h ] ++ sort [ b | b <- t; b > h ]

35. Haskell Lazy Evaluation Only compute those that are necessary positives = [ 0.. ] The member function could be written as member [ ] b = False member (a:x) b = (a == b) || member x b Determining if 16 is a square number (Problem?) squares = [ n * n | n <- [ 0.. ] ] member squares 16 The following version will always work member2 (m:x) n | m < n = member2 x n | m == n = True | otherwise = False

36. Applications of Functional Languages • APL is used for throw-away programs • 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

37. Comparing Functional Languages 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

38. Summary Functional programming languages • control program execution using • function application • conditional expressions • recursion • functional forms • do not use imperative features • variables • assignments • have advantages over imperative alternatives, but lower efficiency prevents widespread use

39. Summary LISP began as a purely functional language and later included imperative features Scheme is a relatively simple dialect of LISP that uses static scoping exclusively COMMON LISP is a large LISP-based language ML is a static-scoped and strongly typed functional language which includes many features desired by programmers Haskell is a lazy functional language supporting infinite lists and set comprehension.

40. Next ClassTuesdayFebruary 14, 2011 Rhys Eric Rosholt Office: Office Phone: Web Site: Email Address: Gillet Hall - Room 304 718-960-8663 http://comet.lehman.cuny.edu/rosholt/ rhys.rosholt @ lehman.cuny.edu