$1.$ Briefly explain why the following expressions induce a "type error"? $($a$)($I$/2$ point$)[("]",4\mathrm{.}0)$; $("$R$",0\mathrm{.}0)$; $("$S$",1)]($b$)(1$ point$)$ type 'a option $-$ Some of $\text{'}$a $|$ None let f a $-$ if a a $0\mathrm{.}0$ then None else a$.2.$ Provide expressions $($without type amotations$)$ that have the following types: $($a$)(1$ point$)$ int $->$ int list $->$ bool list $($b$)(1/2$ point $)^\text{'}$ a $->($a $->$ b$^\text{'}$ b$)->\text{'}$b $($c$)(1/.$ point$)($a $->$ b$^\text{'}$ b$)->\text{'}$ a $->\text{'}$ b $->$ b bool$($e$)(//2$ point $)($a $->$ int $)->$ a $->$ int $($f$)(1/2$ point$)\text{'}$a $->(\text{'}$a $->\text{'}$b$)$ list $->\text{'}$b list. $($g$)(1$ point$)$ Defme a function f that when used in the following expression will not produce any type errors: fold left f$([],0)[5$ ; $4$ ; $3$ ; $2$ ; $1]$ The implementation and type of fold left are given for reference, below. let rec fold left f a l $-$ match I with I$]->$ a I h::t $->$ fold left f$($f a h$)$ t $($h$)(1$ point$)$ What would you put in place for the blank such that the following code returns $44?$ let f $-$ fun x y z $->$ List. fold left $($fun acc e $->$acc$+$e$+($y z$))0$ x in f $[1$ ; $1$ ; $1$ ; $1]4($i$)(1$ point$)$ What would you put in place for the blank such that sublist $[1]0-[]$ and sublist $[1$ ; $0$ ; $2$ ; $3]1-[1$ ; $0]?$ let sublist $1$ t fold right $($fun x a $->)[[]$ The implementation of fold right is given for reference, below. let rec fold right f $[$ acc $-$ match $[$ with I $[]->$acc x:: x $5->$ f x $($fold right f x $5$ acc$)($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 taxpayer $-$ Person of float Company of float let tax y$-$ let income tax a x in match y with $|$ Person i $->$ income tax i $0\mathrm{.}1|$ Company j $->$ income tax j $0\mathrm{.}2$ in $($tax $($Person $100\mathrm{.}0),$ tax $($Company $200\mathrm{.}0))$