sml - How to get a list of months by giving two days of a year? -

i have function named month_range takes 2 days of year input (e.g., 65 , 128, assuming year has 365 days) , returns list number of month days day1 through day2 belongs to.

the size of list must "day2 - day1 + 1".

example : month_range(25,35) should return : [1,1,1,1,1,1,1,2,2,2,2]

i wrote following code

fun month_range (day1:int,day2:int) =     let       val month_days= [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31];       fun what_month(day :int) =           let             fun aux(sum :int,  numbers: int list) =                 let                   val numbers_tail = tl numbers                 in                   if sum <= (hd numbers)                   1                   else                     1 + aux(sum, (hd numbers + hd numbers_tail)                             :: (tl numbers_tail))                 end           in             aux(day, month_days)           end     in       if (day1>day2)       []       else what_month(day1) @ what_month(day1 + 1)@::what_month(day2)     end 

but gives me following error

/tmp/emacs-region5156f3r:21.51-21.54 error: unbound variable or constructor: @:: /tmp/emacs-region5156f3r:21.12-21.70 error: operator not function [literal]   operator: int   in expression:     (what_month (day1 + 1)) <errorvar> /tmp/emacs-region5156f3r:21.12-21.70 error: operator , operand don't agree [literal]   operator domain: 'z list * 'z list   operand:         int * _   in expression:     what_month day1 @ (((what_month <exp>) <errorvar>) what_month) day2  uncaught exception error   raised at: ../compiler/toplevel/interact/evalloop.sml:66.19-66.27              ../compiler/toplevel/interact/evalloop.sml:44.55              ../compiler/toplevel/interact/evalloop.sml:296.17-296.20 

first off can see error message, using @::, doesn't make sense.

you have made function what_month assignment, there no reason putting inside let-expression.

now if simplify code bit

val month_days= [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]; fun what_month(day :int) =     let       fun aux(sum :int,  numbers: int list) =           let             val numbers_tail = tl numbers           in             if sum <= (hd numbers)             1             else               1 + aux(sum, (hd numbers + hd numbers_tail)::(tl numbers_tail))           end     in       aux(day, month_days)     end   fun month_range (day1:int,day2:int) =       if (day1>day2)       []       else what_month(day1) 

then see still doesn't type. because type of what_month function int -> int, if-expression inside body of month_range returns list in branch, must return list in else branch. fix that.

currently function returns number of month day1 belongs (theoretically, doesn't type yet). wan't return list days day1 ... day2.
recursion comes in. if return what_month(day1) concatenated recursive call month_range( day1 + 1, day2) end building list

what_month(day1) :: what_month(day1 + 1) :: what_month(day1 + 1 + 1) ... 

and since return empty list, when reach condition day1 > day2, recursion give result this

what_month(day1) :: what_month(day1 + 1) :: what_month(day1 + 1 + 1)  :: ...                  :: what_month(day2) ::[] 

the resulting code looks this

fun month_range (day1:int,day2:int) =     if (day1>day2)     []     else what_month(day1) :: month_range(day1 + 1, day2)  - month_range(25,35); val = [1,1,1,1,1,1,1,2,2,2,2] : int list