# CS 314 Principles of Programming Languages

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1 CS 314 Principles of Programming Languages Lecture 17: Functional Programming Zheng (Eddy Zhang Rutgers University April 4, 2018

2 Class Information Homework 6 will be posted later today. All test cases for project 1 have been released. If a small issue in project 1 results in your code not working for most test cases, you can submit a patch (using the linux utility tool patch to generate the difference of two versions of a file by the end of this week. We will review the change before we determine if you will get partial credit back. 2

3 Special (Primitive Functions eq?: identity on names (atoms null?: is list empty? car: select first element of the list (contents of address part of register cdr: select rest of the list (contents of decrement part of register (cons element list: constructs lists by adding element to the front of list quote or ': produces constants Do not evaluate the ' the content after '. Treat them as list of literals. 3

4 Quotes Inhibit Evaluation > ( cons 'a (cons 'b '(c d (a b c d ;; Now if we quote the second argument > ( cons 'a '(cons 'b '(c d (a cons 'b '(c d ;; If we unquote the first argument > ( cons a (cons 'b '(c d a: undefined; cannot reference undefined identifier context 4

5 Review: 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: 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 iii. Evaluates to #t c Evaluates to #f 4. Evaluates to #f (define atom? ( lambda (object (not (pair? object 5

6 Review: 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 '( 6

7 Review: 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 #t value 2. Evaluate and return the corresponding result 3. If none of the conditions returns a true value, evaluate and return <else-result> 7

8 Conditional Execution: cond (define rest-if-first (lambda (e l (cond ( (null? l '( ( (eq? e (car l ( cdr l ( else '( Example 1 Example 2 (define abs-val (lambda ( x ( cond ( (>= x 0 x (else (- x 8

9 Recursive Scheme Functions: abs-list (define abs-list (lambda (l (if (null? l '( (cons (abs (car l (abs-list (cdr l (abs-list '( ( (abs-list '( ( 9

10 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 10

11 Equality Checking The eq? predicate does not work for lists. Why not? (cons 'a '( produces a new list (cons 'a '( produces another new list eq? checks whether two arguments are the same (eq? (cons 'a '( (cons 'a '( evaluates to #f 11

12 Equality Checking 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 a list, is called a pair car cdr Symbols are stored uniquely, so eq? works on them. 12

13 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 13

14 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 14

15 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 15

16 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 16

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 17

18 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 18

19 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 19

20 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 20

21 Scheme: Functions as First Class Values 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 (* ((lambda (x (* (*

22 Scheme: Functions as First Class 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 (* ((lambda (x (* (*

23 Scheme: Functions as First Class Values (Higher-Order 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 parameters 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 Computation completes when S-expression cannot be further reduced. 23

24 Higher-Order Functions (Cont. Functions as returned value: (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

25 Higher-Order Functions (Cont. In general, any n-ary function (lambda (x_1 x_2 x_n e can be rewritten as a nest of n unary functions: (lambda (x_1 (lambda (x_2 ( (lambda(x_n e 25

26 Higher-Order Functions (Cont. In general, any n-ary function (lambda (x_1 x_2 x_n e can be rewritten as a nest of n unary functions: (lambda (x_1 (lambda (x_2 ( (lambda(x_n e This translation process is called currying. It means that having functions with multiple parameters do not add anything to the expressiveness of the language: ( (lambda (x_1 x_2... x_n e v_1 v_2... v_n ( (((lambda (x_1 (lambda (x_2... (lambda (x_n e... v_1 v_2... v_n 26

27 Higher-order Functions: map (define map (lambda (f l (if (null? l '( ( cons ( f (car l (map f (cdr l map takes two arguments: a function and a list map builds a new list by applying the function to every element of the (old list 27

28 Higher-order Functions: map (define map (lambda (f l (if (null? l '( ( cons ( f (car l (map f (cdr l map takes two arguments: a function and a list map builds a new list by applying the function to every element of the (old list 28

29 Higher-Order Functions: map Example: (map abs '( ( (map (lambda (x (+ 1 x '( (0 3 4 Actually, the built-in map can have more than two arguments: (map + '(1 2 3 '(4 5 6 (

30 Next Lecture Things to do: Read Scott, Chapter (4th Edition or Chapter (3rd Edition, Chapter (4th Edition or Chapter (3rd Edition 30

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