Consider the following ML expressions. Evaluate each expression and write down its value followed by :

and its type. For example the value of $[1]$::nil::nil is $[[1],[]]$:int list list. Another example,

nil::nil is $[[]]$:$$a list list. If the expression is invalid or will cause an error, explain why.

$1.1$::$2$::$3$::$[4,5]$

$2.$ #$2(1$::$2$::$3$::$[4,5])$

$3.$ #$1(1$::$2$::nil, $"$a$",$ #$"$a$")$

$4.[]$@$[[]]$

$5.[$nil$]$::$[[1]]$

$6.[$nil$]$::$[[]]$

$7.$ hd $($tl $[1,2,3]))$

The following three expressions are function definitions. You are asked to infer the type of each function.

$1.$ fun f x $=$ hd x

$2.$ fun f x $=$ hd x $+1$

$3.$ fun f x $=$ hd x :: x