# SICP - Solution: Exercise 2.4

##### January 6, 2019

## Exercise 2.4 #

Here is an alternative procedural representation of pairs. For this representation, verify that

`(car (cons x y))`

yields`x`

for any objects`x`

and`y`

.`(define (cons x y) (lambda (m) (m x y))) (define (car z) (z (lambda (p q) p)))``

What is the corresponding definition of cdr? (Hint: To verify that this works, make use of the substitution model of 1.1.5.)

## Solution #

Applyting the substition model on `cons`

to:

```
(car (cons x y))
```

will give:

```
(car (lambda (m) (m x y)))
```

It means that `car`

will take as a parameter the anonymous function `(lambda (m) (m x y))`

. This function takes a function `m`

as a parameter and this function `m`

will receive `x`

and `y`

as parameters.

The definition of `car`

takes a function as parameters and will evaluate this function by passing an anonymous function as argument: `(lambda (p q) p)`

. This anonymous function takes two parameters and return the first one.

We can continue our substitution by inserting the definition of `car`

:

```
((lambda (m) (m x y)) (lambda (p q) p))
```

This looks like a lot of parentheses, but it means that the first function `(lambda (m) (m x y))`

takes the anonymous function `(lambda (p q) p)`

as a parameter. When substituting `m`

for the parameter, we have:

```
((lambda (p q) p) x y)
```

which will evaluate to:

```
x
```