Download Functional programming 3

COP4020
Programming
Languages
Functional Programming
Prof. Xin Yuan
Topics
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
Functional programming with Scheme
Learn by examples
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Defining Global Names
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A global name is defined with the “define” special form
(define name value)
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Usually the values are functions (lambda abstractions)
Examples:
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(define my-name ''foo'')
(define determiners '(''a'' ''an'' ''the''))
(define sqr (lambda (x) (* x x)))
(define twice (lambda (f a) (f (f a))))
(twice sqr 3)  ((lambda (f a) (f (f a))) (lambda (x) (* x x)) 3) 
…  81
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Defining Global Names

A global name defined with a lambda express in essence
creates a named function.

This allows recursion – one of the most important/useful concept
in scheme.

(define fab (lambda (x) (if (= x 0) 0 (if (=x 1) 1 (+ (fab (- x 1)) (fab
(- x 2)))))))

Define a function that computes the sum of all elements in a list.
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Define a function that put an element at the end of a list
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Load program from file
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Load function
(load filename) load the program from a file
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(load “myscheme”): load the program in “myscheme.scm”
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After load, one has access to all global names in the program.
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I/O
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(display x) prints value of x and returns an unspecified
value
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(newline) advances to a new line
(read) returns a value from standard input
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(display "Hello World!")
Displays: "Hello World!"
(display (+ 2 3))
Displays: 5
(if (member (read) '(6 3 5 9)) "You guessed it!" "No luck")
Enter: 5
Displays: You guessed it!
(read-line) returns the string in a line (without the “\n”).
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I/O with files
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Open file for reading: (open-input-file filename)
Open file for writing: (open-output-file filename)
Read one character from a file: (read-char file)
Read a scheme object from file: (read file)
Check the current character in a file without consuming
the character: (peek-char file)
Check end-of-file: (eof-object? (peek-char file))
Write one character to a file: (write-char char file)
Write a scheme object to file: (write object file)
Close file: (close-port file)
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Blocks
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(begin x1 x2 … xn) sequences a series of expressions xi, evaluates
them, and returns the value of the last one xn
Examples:

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(begin
(display "Hello World!")
(newline)
)
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Example 1: define factorial
function: fact(n) = 1*2*3*…*n
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Example 1: define factorial
function: fact(n) = 1*2*3*…*n
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Recursive factorial:
(define fact
(lambda (n)
(if (zero? n) 1 (* n (fact (- n 1))))
)
)
(fact 2)
 (if (zero? 2) 1 (* 2 (fact (- 2 1))))
 (* 2 (fact 1))
 (* 2 (if (zero? 1) 1 (* 1 (fact (- 1 1)))))
 (* 2 (* 1 (fact 0)))
 (* 2 (* 1 (if (zero? 0) 1 (* 0 (fact (- 0 1))))
 (* 2 (* 1 1))
2
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Example 2

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Sum the elements of a list
(define sum
(lambda (lst)
(if (null? lst)
0
(+ (car lst) (sum (cdr lst)))
)
)
)
(sum '(1 2 3))
 (+ 1 (sum (2 3))
 (+ 1 (+ 2 (sum (3))))
 (+ 1 (+ 2 (+ 3 (sum ()))))
 (+ 1 (+ 2 (+ 3 0)))
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Example 3

Generate a list of n copies of x
(define fill
(lambda (n x)
???
)
)
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Example 3

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Generate a list of n copies of x
(define fill
(lambda (n x)
(if (= n 0)
()
(cons x (fill (- n 1) x)))
)
)
(fill 2 'a)
 (cons a (fill 1 a))
 (cons a (cons a (fill 0 a)))
 (cons a (cons a ()))
 (a a)
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Example 4

Replace x with y in list xs
(define subst
(lambda (x y xs)
???
)
)
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Example 4

Replace x with y in list xs
(define subst
(lambda (x y xs)
(cond
((null? xs)
())
((eq? (car xs) x) (cons y (subst x y (cdr xs))))
(else
(cons (car xs) (subst x y (cdr xs))))
)
)
)
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