CS 314 Principles of Programming Languages. Lecture 16

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1 CS 314 Principles of Programming Languages Lecture 16 Zheng Zhang Department of Computer Science Rutgers University Friday 28 th October, 2016 Zheng Zhang 1 University

2 Class Information Reminder: midterm exam this coming Wednesday class (11/2). Homework 6 posted, due Saturday 11/5 11:55pm. Zheng Zhang 2 University

3 Special (Primitive) Functions eq?: identity on names (atoms) null?: is list empty? car: selects first element of list (contents of address part of register) cdr: selects rest of list (contents of decrement part of register) (cons element list): constructs lists by adding element to front of list quote or : produces constants Zheng Zhang 3 University

4 Other Functions + - * / numeric operators, e.g., (+ 5 3) = 8, (- 5 3) = 2 (* 5 3) = 15, (/ 5 3) = = < > comparison operators for numbers Explicit type determination and test functions: All return Boolean values: #f and #t (number? 5) evaluates to #t (zero? 0) evaluates to #t (symbol? sam) evaluates to #t (list? (a b)) evaluates to #t (null? ()) evaluates to #t Note: SCHEME is a strongly typed language. Zheng Zhang 4 University

5 Other Functions (number? sam) evaluates to #f (null? (a)) evaluates to #f (zero? (- 3 3)) evaluates to #t (zero? (- 3 3)) type error (list? (+ 3 4)) evaluates to #f (list? (+ 3 4)) evaluates to #t Zheng Zhang 5 University

6 READ-EVAL-PRINT Loop The Scheme interpreters on the ilab machines are called mzscheme, racket, and drracket. drracket is an interactive environment, the others are command-line based. For example: Type mzscheme, and you are in the READ-EVAL-PRINT loop. Use Control D to exit the interpreter. READ: Read input from user: a function application EVAL: Evaluate input: (f arg 1 arg 2...arg n) 1. evaluate f to obtain a function 2. evaluate each arg i to obtain a value 3. apply function to argument values PRINT: Print resulting value: the result of the function application You can write your Scheme program in file <name>.ss and then read it into the Scheme interpreter by saying at the interpreter prompt: (load "<name>.ss") Zheng Zhang 6 University

7 READ-EVAL-PRINT Loop Example > (cons a (cons b (c d))) (a b c d) 1. Read the function application (cons a (cons b (c d))) 2. Evaluate cons to obtain a function 3. Evaluate a to obtain a itself 4. Evaluate (cons b (c d)): 4.1 Evaluate cons to obtain a function 4.2 Evaluate b to obtain b itself 4.3 Evaluate (c d) to obtain (c d) itself 4.4 Apply the cons function to b and (c d) to obtain (b c d) 5. Apply the cons function to a and (b c d) to obtain (a b c d) 6. Print the result of the application: (a b c d) Zheng Zhang 7 University

8 Quotes Inhibit Evaluation ;;Same as before: > (cons a (cons b (c d))) (a b c d) ;;Now quote the second argument: > (cons a (cons b (c d))) (a cons (quote b) (quote (c d))) ;;Instead, un-quote the first argument: > (cons a (cons b (c d))) ERROR: unbound variable: a Zheng Zhang 8 University

9 Defining Global Variables The define constructs extends the current interpreter environment by the new defined (name, value) association. > (define foo (a b c)) #<unspecified> > (define bar (d e f)) #<unspecified> > (append foo bar) (a b c d e f) > (cons foo bar) ((a b c) d e f) > (cons foo bar) (foo d e f) Zheng Zhang 9 University

10 Defining Scheme Functions (define <fcn-name> (lambda (<fcn-params>) <expression>)) Example: Given function pair? (true for non-empty lists, false o/w) and function not (boolean negation): (define atom? (lambda (object) (not (pair? object)))) Evaluating (atom? (a)): 1. Obtain function value for atom? 2. Evaluate (a) obtaining (a) 3. Evaluate (not (pair? object)) a) Obtain function value for not b) Evaluate (pair? object) i. Obtain function value for pair? ii. Evaluate object obtaining (a) Evaluates to #t Evaluates to #f Evaluates to #f Zheng Zhang 10 University

11 Conditional Execution: if (if <condition> <result1> <result2>) 1. Evaluate <condition> 2. If the result is a true value (i.e., anything but #f), then evaluate and return <result1> 3. Otherwise, evaluate and return <result2> (define abs-val (lambda (x) (if (>= x 0) x (- x)))) (define rest-if-first (lambda (e l) (if (eq? e (car l)) (cdr l) ()))) Zheng Zhang 11 University

12 Conditional Execution: cond (cond (<condition1> <result1>) (<condition2> <result2>)... (<conditionn> <resultn>) (else <else-result>)) ; optional else ; clause 1. Evaluate conditions in order until obtaining one that returns a true value 2. Evaluate and return the corresponding result 3. If none of the conditions returns a true value, evaluate and return <else-result> Zheng Zhang 12 University

13 Conditional Execution: cond (define abs-val (lambda (x) (cond ((>= x 0) x) (else (- x))))) (define rest-if-first (lambda (e l) (cond ((null? l) ()) ((eq? e (car l)) (cdr l)) (else ())))) Zheng Zhang 13 University

14 Recursive Scheme Functions: Abs-List (abs-list ( )) ( ) (abs-list ()) () (define abs-list (lambda (l) (if (null? l) () (cons (abs-val (car l)) (abs-list (cdr l))) ) ) ) Zheng Zhang 14 University

15 Recursive Scheme Functions: Append (append (1 2) (3 4 5) ( ) (append (1 2) (3 (4) 5) (1 2 3 (4) 5) (append () (1 4 5)) (1 4 5) (append (1 4 5) ()) (1 4 5) (append () ()) () (define append (lambda (x y) (cond ((null? x) y) ((null? y) x) (else (cons (car x) (append (cdr x) y))))) ) Zheng Zhang 15 University

16 Equality Checking The eq? predicate doesn t work for lists. Why not? 1. (cons a ()) produces a new list 2. (cons a ()) produces another new list 3. eq? checks if its two arguments are the same 4. (eq? (cons a ()) (cons a ())) evaluates to #f Lists are stored as pointers to the first element (car) and the rest of the list (cdr). This elementary data structure, the building block of lists, is called a pair. pair? car cdr Symbols are stored uniquely, so eq? works on them. Zheng Zhang 16 University

17 Equality Checking for Lists For lists, need a comparison function to check for the same structure in two lists (define equal? (lambda (x y) (or (and (atom? x) (atom? y) (eq? x y)) (and (not (atom? x)) (not (atom? y)) (equal? (car x) (car y)) (equal? (cdr x) (cdr y)))))) (equal? a a) evaluates to #t (equal? a b) evaluates to #f (equal? (a) (a)) evaluates to #t (equal? ((a)) (a)) evaluates to #f Zheng Zhang 17 University

18 Scheme: Functions as Values (Higher-order) Functions as arguments: (define f (lambda (g x) (g x))) (f number? 0) (number? 0) #t (f length (1 2)) (length (1 2)) 2 (f (lambda (x) (* 2 x)) 3) ((lambda (x) (* 2 x)) 3) (* 2 3) 6 REMINDER: Computation, i.e., function application is performed by reducing the initial S-expression (program) to an S-expression that represents a value. Reduction is performed by substitution, i.e., replacing formal by actual arguments in the function body. Examples for S-expressions that directly represent values, i.e., cannot be further reduced: function values (e.g.: (lambda(x) e)) constants (e.g.: 3, #t) Zheng Zhang 18 University

19 Higher-order Functions (Cont.) Functions as returned values: (define plusn (lambda (n) (lambda (x) (+ n x)))) (plusn 5) evaluates to a function that adds 5 to its argument Question: How would you write down the value of (plusn 5)? ((plusn 5) 6) 11 Zheng Zhang 19 University

20 Next Lecture Reading: Scott Chapter 11.1 to 11.3 More Scheme and higher-order functions Zheng Zhang 20 University

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