When working with List Boxes the documentation is not especially clear regarding how to type the arrays and variables involved. Here are the appropriate data types for List Boxes:

• The list box itself is a boolean array (e.g. ARRAY BOOLEAN(listbox1;0)).
  
• The headers are longints (e.g. C_LONGINT(header1)).
  
• The columns are arrays of the data type they hold (e.g. ARRAY TEXT(Column1;0)).
  

An example of how to type a list box array is listed at the bottom of the Management of List box objects page in the language reference:

https://www.4d.com/docs/CMU/CMU10040.HTM

Note: The List Box Boolean array keeps track of which rows are selected (True = selected, False = not selected). The above link goes into more detail regarding list box management.