Programming Languages part A

(* 1 *)
fun is_older(xs:(int*int*int), ys: (int*int*int))=
    let val first_year = #1 xs
	val first_month = #2 xs
	val first_day = #3 xs
			   
	val second_year = #1 ys
	val second_month = #2 ys
	val second_day = #3 ys

    in
	if first_year < second_year
	then true
	else if first_year = second_year andalso first_month <second_month
	then true
	else if first_year = second_year andalso first_month=second_month andalso first_day<second_day
	then true
	else false
    end		    
	     
(* 2 *)
fun number_in_month(xs:(int*int*int) list , y:int)=
    if null xs
    then 0
    else
	let
	    val date = hd xs
	    val month = #2 date
	     in
		 if month=y
		 then 1+number_in_month(tl xs,y)
		 else number_in_month(tl xs,y)
	end
	    
(* 3 *)
fun number_in_months(xs:(int*int*int) list, ys: int list)=
    if null ys
    then 0
    else let
	val y = hd ys
	 in
	     number_in_month(xs,y)+number_in_months(xs,tl ys)
    end
	     
(* 4 *)	     
fun dates_in_month(xs: (int*int*int) list, y: int)=
    if null xs
    then []
    else if #2 (hd xs) = y
    then hd xs :: dates_in_month(tl xs,y)
    else dates_in_month(tl xs,y)

(* 5 *)
fun dates_in_months(xs:(int*int*int) list, ys:int list)=
    if null ys
    then []
    else let
	val y = hd ys
	val a = dates_in_month(xs,y)		    
    in
	if null a
	then dates_in_months(xs,tl ys)
	else
	a::dates_in_months(xs,tl ys)
    end       

(* 6 *)
fun get_nth(xs: string list, y:int)=
    if y<=0 orelse null xs
    then ""
    else if y = 1 
    then hd xs
    else
	let val z = y-1
	in
	    get_nth(tl xs,z)
	end
(* 7 *)
fun date_to_string(x:(int*int*int))=
    let
	val year = Int.toString(#1 x)
	val months = ["January", "February", "March", "April", "May", "June","July", "August", "September", "October", "November", "December"]
	val day = Int.toString(#3 x)
	val month = #2 x 
	val stringMonth =  get_nth(months, month)
    in
	stringMonth^" "^day ^", " ^year 
    end


(* 8 *)
fun number_before_reaching_sum(sum : int,ws:int list) =
    let fun add(x:int,ys:int list, z:int)=
		if x+hd ys<sum
		then add(x+hd ys, tl ys,z+1)
		else z
	in
	    add(0,ws,0)
    end
	

(* 9 *)
fun what_month(x:int)=
    let val month = [31,28,31,30,31,30,31,31,30,31,30,31]
    in
	number_before_reaching_sum(x,month)+1
    end

(* 10 *)
fun month_range(x:int, y:int)=
    if x>y
    then []
    else
	let fun createList(xs:int list)=
		if hd xs = y
		then xs
		else createList(hd xs +1::xs) 
	    val range = createList([x])
	    fun series(ys:int list,zs:int list)=
		if null ys
		then zs
		else
		    series(tl ys,what_month(hd ys)::zs)   
	in
	    series(range,[])	      
	end

(* 11 *)
fun oldest(xs: (int*int*int) list)=
    if null xs
    then NONE
    else
	let
	    val tl_oldest = oldest(tl xs)
	in
	    if  isSome tl_oldest andalso not (is_older(hd xs, valOf tl_oldest))
	    then
		tl_oldest	
	    else
		SOME(hd xs)
	end