Arithmetic Sequential Extrapolator v1.1.0

# Copyright (c) 2020 applescript_superior
# All Rights Reserved
# This product is protected by copyright and distributed under licenses restricting copying, distribution and decompilation.
# Unauthorized distribution of this software and/or any participles pertaining to it will result in a fine (not actually lol).
# Links:
#       https://www.reddit.com/r/applescript/comments/jpu9nn/how_to_determine_if_all_items_in_a_list_are_the/
#       https://macscripter.net/viewtopic.php?id=48011
#       https://apple.stackexchange.com/questions/405923/how-to-determine-if-all-items-in-a-list-are-the-same
# Created with AppleScript 2.7

# globals every variable used to prevent errors throughout the script
global common_dif
global common_dif_check
global dif_check
global extrap_num
global input_sequence
global local_dif
global occurrence
global selected_item
global sequence
global x

set title to "Arithmetic Sequential Extrapolator"
global title

my input()

on input()
    # input sequence of numbers
    set input_sequence to text returned of (display dialog "Enter Linear Sequence of Numbers" default answer "1,3,5,7,9,50" with icon 1 buttons {"Cancel", "Extrapolate"} default button 2 with title title) as string

    # sets sequence to result of string_to_list
    set sequence to my string_to_list(input_sequence, ",")
    if ((number of items of sequence) < 2) or ((number of characters of input_sequence) < 3) then
        my input()
    end if

    try
        set extrap_num to (last item of sequence) as integer
    on error
        my input()
    end try
    set sequence to reverse of (rest of (reverse of sequence))
    my extrap_sequence()
end input

on extrap_sequence()
    # determines local difference between every item of sequence
    set x to 0
    set dif_check to {}
    set common_dif_check to true
    repeat ((number of items of sequence) - 1) times
        try
            set x to (x + 1)
            set selected_item to (item x of sequence)
            set local_dif to ((item (x + 1) of sequence) - selected_item)

            # determines if the selected item equals the rest of dif_check
            # dissect this code later
            if (dif_check ≠ {}) and (dif_check does not contain local_dif) then
                set common_dif_check to false
                set common_dif to "n/a"
                exit repeat
            end if
            set common_dif to (local_dif) as number
            set dif_check to dif_check & {local_dif}
        on error
            my input()
        end try
    end repeat

    # determines answer and returns result depending on the input parameters
    if common_dif_check = true then
        set answer to my arithmetic_progression(sequence, extrap_num, common_dif)
        return ("item " & extrap_num & " of sequence is " & answer & "; common difference is " & common_dif) as string
        (* set action to button returned of (display alert extrap_num & "ᵃ = " & answer message "Common Difference: " & common_dif buttons {"Close", "OK"} default button 2)
        if action = "Close" then
            my quit_script()
        else if action = "OK" then
            my input()
        end if *)
    else if common_dif_check = false then
        return ("item " & extrap_num & " of sequence is undefined; common difference is " & common_dif) as string
        (* set action to button returned of (display alert extrap_num & "ᵃ = undefined" message "Common Difference: " & common_dif buttons {"Close", "OK"} default button 2) as string
        if action = "Close" then
            my quit_script()
        else if action = "OK" then
            my input()
        end if *)
    end if
end extrap_sequence

on arithmetic_progression(sequence, extrap_num, common_dif)
    # formula for arithmetic progression of linear sequences
    set answer to ((first item of sequence) + ((extrap_num - 1) * common_dif)) as number
    return answer
end arithmetic_progression

on string_to_list(input, input_delimiter)
    # separates string into individual items using string delimiters
    set old_delimiters to AppleScript's text item delimiters
    set AppleScript's text item delimiters to input_delimiter
    set sequence to every text item of input
    set AppleScript's text item delimiters to old_delimiters
    return sequence
end string_to_list

on quit_script()
    # just a handler to safely quit the script
end quit_script