B$.$ Lambda Expression Command

Syntax: $($lambda $($arg$-$id $...)$ body $...+)$

A lambda expression creates a function. In the simplest case, a lambda expression has

the form

Example $1$:

$(($lambda $($x$)(+$ x x$))4)$ Output: $8$

Example $2$:

$($define foo

$($let $(($x $4))$

$($lambda $($y$)(+$ x y$))))$

$($foo $6)$

Output: $10$

C$.$ Lexical Binding or scoping

This is necessary for preserving lexical scope$--$the meanings of variable names must

be obvious at the point where the procedure is defined.

$($let $(($x $2)($y $3))$

$(*$ x y$))$

Output: $6$

Write expression after converting to prefix

Example $1$:

X $=10$ y$=5$ z$=3$

$($x$-$y$)*$z

Output: $15$

Example $2$:

w $=15$ x $=10$ y$=5$ z$=3$

w$/$y$-$z$*$x

Output: $-27$

Example $3$:

v$=20$ w $=15$ x $=10$ y$=5$ z$=3$

z$*5+$ y $-$ w$/$y$-$v$*$x

Output: $-183$

Lexical binding and lambda

Example $1$:

$($let $(($x $2)($y $3))$

$($let $(($foo $($lambda $($z$)(+$ x y z$)))$

$($x $7))$

$($foo $4)))$

Output: $9$

Example $2$:

$($let $(($x $2)($y $3))$

$($let$*(($x $7)$

$($z $(+$ x y$)))$

$(*$ z x$)))$

Output: $70$

D$.$ Internal Definitions

Example $1$:

$($let $(($x $5))$

$($define foo $($lambda $($y$)($bar x y$)))$

$($define bar $($lambda $($a b$)(+(*$ a b$)$

a$)))$

$($foo $(+$ x $3)))$

Output: $45$

Code Explanation: first X will be $5$ and Y will be based on input of foo, thus,

y$=5+3=8,$ foo will call bar function. In bar function output will be $5*8+5=45$

E$.$ Exercises:

$1-$ Define three variables x$,$ y z and give them the value $10,5$ and $3$

respectively. Calculate the expression $($x$-$y$)*$z using lambda.

$2-$ Explain and predict the output of this code:

$($define x $2)$

$(+$ x $1)$

$3-$ Explain and predict the output of this code:

$($set$!$ x $4)$

$(-$ x $1)$

F$.$ Quoting

Syntax: quote or $\text{'}$

This notation is used to include literal constants in Scheme code. $($quote

$)$ may be abbreviated as $\text{'}.$ The two notations are equivalent in

all respects.

Code Output

$($quote a$)$ a

$($quote #$($a b c$))$ #$($a b c$)$

$($quote $(+12))(+12))$

Example:

$\text{'}"$abc$"$ Output: a

"abc" Output: a

G$.$ Exercises: Write the corresponding expression using quoting

to display:

$1-145932$

$2-$ #t

$3-$ #$\backslash$a

H$.$ Sequencing

Syntax: begin $...$

The s are evaluated sequentially from left to right, and the value$($s$)$ of the

last is$($are$)$ returned. This expression type is used to sequence side effects

such as input and output.

Example $1$:

$($define x $0)$

$($begin $($set$!$ x $5)$

$(+$ x $1))$

Output: $6$

Example $2$:

$($begin $($display $"4$ plus $1$ equals $")$

$($display $(+41)))$

Output: $4$ plus $1$ equals $5=>$

unspecified