Question

(a) Explain the method of making composed functions in Scheme. Show an example of a composed function (f(g(x))). (b) Write a scheme function f(r) which returns three functions of two variables as follows. If r=0 the returned function should be Vxy. If r = 1 the returned function should be (x + y)/2. If r = 2 the returned function should be 70.5x² +0.5y2. In all other cases the returned value should be 0.

Answer 1

Answer:

a)

A compose function is defined between the two functions or more functions.

Here for simplicity, the compose function accepts two functions and are considered as single argument.

In a compose function, depending on the defining the functional flow, the value is evaluated.

To compose (f, g) on x, then it will be computed as, f(g(x)).

Method in Scheme:

Define the function called compose, on two functions called f and g with a value x.

Internally define a lambda function on x where

• It first evaluates the g(x).

• The obtained resultant from g(x) will pass as value into function f.

• Then final result obtained from the f(g(x)) will be returned to the call function.

The value calculation is based on the functions that are passed in place of f and g.

Example:

Compute the value of acos(sin(0)).

Here sin() is function g,acos() is function f and x = 0.

Scheme:

; define the function compose on two functions

; f and g and return the value computed by f(g(x))

(define (compose f g)

(lambda (x) (f (g x))))

; function call to find the value of acos(sin(0))

; first test case

(display ((compose acos sin) 0))

(newline)

; function call to find the value of cos(sin(0))

; first test case

(display ((compose cos sin) 0))

(newline)

Sample Output:

Code screen shot:

b)

Scheme function screen shot: