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CS 363 Comparative Programming Languages

CS 363 Comparative Programming Languages. Functional Languages: Scheme. 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

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CS 363 Comparative Programming Languages

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  1. CS 363 Comparative Programming Languages Functional Languages: Scheme

  2. 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 CS 363 Spring 2005 GMU

  3. 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 CS 363 Spring 2005 GMU

  4. Functions • A function is a rule that associates to each x from some set X of values a unique y from another set Y of values: • y = f(x) or f: X Y • Functional Forms • Def: A higher-order function, or functional form, is one that either takes functions as parameters, yields a function as its result, or both range domain CS 363 Spring 2005 GMU

  5. 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 CS 363 Spring 2005 GMU

  6. Scheme (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))) ) ) CS 363 Spring 2005 GMU

  7. 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 CS 363 Spring 2005 GMU

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

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

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

  11. 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) Scheme Expression vs. C CS 363 Spring 2005 GMU

  12. Evaluation Rules for Scheme Expressions • Constant atoms (numbers, strings) evaluate to themselves • Identifiers are looked up in the current environment and replaced by the value found there (using dynamically maintained symbol table) • 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. CS 363 Spring 2005 GMU

  13. Scheme Evaluation To evaluate (* (+ 2 3)(+ 4 5)) • * is the function – must evaluate the two expressions (+ 2 3) and (+ 4 5) • To evaluate (+ 2 3) • + is the function – must evaluation the two expressions 2 and 3 • 2 evaluates to the integer 2 • 3 evaluates to the integer 3 • + 2 3 = 5 • To evaluate (+ 4 5) follow similar steps • * 5 9 = 45 * + + 2 3 4 5 CS 363 Spring 2005 GMU

  14. 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)) ) Scheme Conditionals 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). CS 363 Spring 2005 GMU

  15. 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”)) ) ) CS 363 Spring 2005 GMU

  16. 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 = ) CS 363 Spring 2005 GMU

  17. 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? CS 363 Spring 2005 GMU

  18. 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 CS 363 Spring 2005 GMU

  19. 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)) CS 363 Spring 2005 GMU

  20. Output functions • Output Utility Functions: (DISPLAY expression) (NEWLINE) CS 363 Spring 2005 GMU

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

  22. 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 CS 363 Spring 2005 GMU

  23. 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) CS 363 Spring 2005 GMU

  24. 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’ CS 363 Spring 2005 GMU

  25. Data Structures in Scheme (1,2,3) 1 2 3 c a d ((a b) c (d)) b CS 363 Spring 2005 GMU

  26. 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)) CS 363 Spring 2005 GMU

  27. 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) CS 363 Spring 2005 GMU

  28. 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))) )) CS 363 Spring 2005 GMU

  29. 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 '()) )) CS 363 Spring 2005 GMU

  30. 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 '()) )) CS 363 Spring 2005 GMU

  31. 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 CS 363 Spring 2005 GMU

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

  33. 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 CS 363 Spring 2005 GMU

  34. Example Functions (define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M)) ) ) (append ‘(a b) ‘(c d)) = (a b c d) CS 363 Spring 2005 GMU

  35. 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))) = CS 363 Spring 2005 GMU

  36. 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)))) = CS 363 Spring 2005 GMU

  37. 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))) = CS 363 Spring 2005 GMU

  38. 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)) = CS 363 Spring 2005 GMU

  39. 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) CS 363 Spring 2005 GMU

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

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

  42. 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)) ) ) CS 363 Spring 2005 GMU

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

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

  45. 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 CS 363 Spring 2005 GMU

  46. 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)))) )) CS 363 Spring 2005 GMU

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

  48. 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 CS 363 Spring 2005 GMU

  49. 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 CS 363 Spring 2005 GMU

  50. 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 CS 363 Spring 2005 GMU

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