Provide expressions $($without type annotations$)$ that have the following types

$($ a $>$ int $)>$a $>$ int

$($f$)(1/2$ point$)$a $>($ a $>$b$)$ list $>$b list $.$

$($g$)(1$ point$)$ Define a function f that when used in the following expression will not produce

any type errors:

f o l d $\_$ l e f t f $([],0)[5$ ; $4$ ; $3$ ; $2$ ; $1]$

The implementation and type of fold$\_$le are given for reference, below.

l e t r e c f o l d $\_$ l e f t f a l $=$ match l with

$|[]>$ a

$|$ h : : t $>$ f o l d $\_$ l e f t f $($ f a h $)$ t

$($h$)(1$ point$)$ What would you put in place for the blank such that the following code returns

$44?$

l e t f $=$ fun x y z $>$

L i s t $.$ f o l d $\_$ l e f t $($ fun a c c e $>$ a c c $+$ e $+($ y z $))0$ x in

f $[1$ ; $1$ ; $1$ ; $1]\_\_\_\_\_\_\_\_\_4$

hat would you put in place for the blank such that sublist $[1]0=[]$ and

sublist $[1$; $0$; $2$; $3]1=[1$; $0]?$

l e t s u b l i s t l t $=$

f o l d $\_$ r i g h t $($ fun x a $>\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)$ l $[]$

The implementation of fold$\_$right is given for reference, below.

l e t r e c f o l d $\_$ r i g h t f l a c c $=$ match l with

$|[]>$ a c c

$|$ x : : x s $>$ f x $($ f o l d $\_$ r i g h t f x s a c c $)$

$($j$)(1$ point$)$ What would you put in place for the blank such that the following program

returns $(10\mathrm{.}0,40\mathrm{.}0)?$

type t a x p a y e r $=$

$|$ P e r s o n of f l o a t

$|$ Company of f l o a t

l e t t a x y $=$

l e t i n c o m e $\_$ t a x a x $=\_\_\_\_\_\_\_\_\_\_$ in

match y with

$|$ P e r s o n i $>$ i n c o m e $\_$ t a x i $0.1$

$|$ Company j $>$ i n c o m e $\_$ t a x j $0.2$ in

$($ t a x $($ P e r s o n $100.0),$ t a x $($ Company $200.0)$