Question $6[15]$

Let L$1,$ L$2$ and L denote lists of terms. Write Prolog programs to realise the following:

$($Note that the lengths of lists L$1$ and L$2$ should be equal in all cases$)$:

a$)$ Interleave alternate elements of L$1$ and L$2$ into L$.$

For example, if L$1=[$a$,$b$,$c$]$ and L$2=[1,2,3],$

then L $=[$a$,1,$b$,2,$c$,3].$

Are the input$-$output roles of variables in your program reversible?

b$)$ Transpose L$1$ and L$2$ into L$.$ That is$,$ if L$1=[$a$,$b$,$c$]$ and L$2=[1,2,3],$ then

L $=[($a$,1),($b$,2),($c$,3)].$

Are the input$-$output roles of your variables reversible?

c$)$ Suppose that L$1$ and L$2$ are lists of numeric values. Write a procedure

inner$\_$prod$($L$1,$L$2,$X$)$ that defines X to be the inner$-$product of the two vectors L$1$

and L$2.$

The inner$-$product X is calculated as follows:

If we have two vectors $[$a$1,$ a$2,...,$ an$]$ and $[$b$1,$ b$2,...,$ bn$]$ then

X $=$ a$1\backslash$times b$1+$ a$2\backslash$times b$2+...+$ an$\backslash$times bn$.$

Are the input$-$output roles of the variable in your program reversible?