PLEASE READ!!!! please have the code in Ocaml not Python.

Part $1$: Non$-$Recursive Functions

Implement the following functions that do not require recursion. Accordingly, these functions are defined

without the rec keyword, but you MAY add the rec keyword to any of the following functions or write a

recursive helper function. Just remember that if you write a helper function, it must be defined in the file

before it is called.

rev$\_$tup $($tup:$(\text{'}$a $*\text{'}$b$))$

Type: $\text{'}$a $*\text{'}$b $*\text{'}$c $->\text{'}$c $*\text{'}$b $*\text{'}$a

Description: Returns a tuple in the reverse order of tup $.$

Examples:

$re{v}_{t}up(1,2)=(2,1)$

revtup$(1,1)=(1,1)$

rev$+$tup$(a,1)=(1,a)$

rev$\_$triple $($triple:$(\text{'}$a $*\text{'}$b $*\text{'}$c $))$

Type: $\text{'}$a $*\text{'}$b $*\text{'}$c $->\text{'}$c $*\text{'}$b $*\text{'}$a

Description: Returns a triple in the reverse order of triple $.$

Examples:

$re{v}_t$riple$((1,2,3))=(3,2,1)$

$re{v}_t$riple$((1,1,1))=(1,1,1)$

$re{v}_t$riple$((a,1,c))=(c,1,a)$

is$\_$odd$($x:int$)$

Type: int $->$ bool

Description: Returns whether or not x is odd.

Examples:

$i{s}_{o}dd1=$ true

$i{s}_{o}dd4=$ false

$i{s}_{o}dd9=$ true is$\_$older$($date$1$ :$($int $*$ int $*$ int$),$ date$2$:$($int $*$ int $*$ int$))$

Type: $($int $*$ int $*$ int$)->($int $*$ int $*$ int$)->$ bool

Description: Returns whether date$1$ comes before the date$2.$

Examples:

is$\_$older $(2021,1,15),(2020,1,16)=$ false

is$\_$older $(2022,1,15),(2021,2,16)=$ false

is$\_$older $(2022,1,16),(2021,2,1)=$ false

is$\_$older $(2021,1,14),(2021,1,15)=$ true

to$\_$us$\_$format$($date$1$ :$($int $*$ int $*$ int$)$

Type: $($int $*$ int $*$ int$)->($int $*$ int $*$ int$)$

Description: Convert date which appears as $($Year$,$ Month, Day$)$ to US format $($Month$,$ Day, Year$).$

Examples:

to$\_$us$\_$format $(2021,1,15)=(1,15,2021)$

to$\_$us$\_$format $(2022,1,15)=(1,15,2022)$

to$\_$us$\_$format $(2022,10,16)=(10,16,2022)$

to$\_$us$\_$format $(2021,12,6)=(12,6,2021)$

Part $2$: Recursive Functions

Implement the following functions using recursion.

pow $($x:int, p:int$)$

Type: int $->$ int $->$ int

Description: Returns $x$ raised to the power p $.$

Assumptions: p is non$-$negative, and we will not test your code for integer overflow cases.

Examples:

pow $3,1=3$

pow $3,2=9$

pow $(-3),3=-27$

fac $($x:int$)$

Type: int $->$ int

Description: Returns the factorial of x as an integer.

Assumptions: You may assume the answer is non$-$negative, $x1.$

Examples:

fac $4=24$

fac $5=120$

fac $7=5040$

fac $2=2$

get$\_$nth $(($idx : int$),($lst: 'a list$))$

Type: int $->$ 'a list $->\text{'}$a

Description: Returns the element at the index idx in the list lst$.$

Assumptions: idx is non$-$negative.

Examples:

README

$ge{t}_{n}th2,[26$;$11$;$99]=99$

$ge{t}_{n}th0,[a$; $b]=a$

$ge{t}_{n}th1[a$; $b]=b$

larger $(($lst$1$: 'a list$),($lst$2$: 'a list$))$

Type: 'a list $->$ 'a list $->$ 'a list

Description: Returns the longer list provided as an argument, returns the

empty list if the two lists are the same length.

Examples:

larger $[][]=[]$

larger $[1][2$;$3]=[2$;$3]$

larger $[2$;$4][2]=[2$;$4]$

larger $[4$;$1$;$2][3$;$5$;$7]=[]$

sum$(($lst$1$: int list$),($lst$12$: int list$))$