In the nested array model, a simple array is an array whose elements are all simple scalars. A non-empty array is simple if and only if it has a depth of 1. Empty arrays are considered simple in most contexts, although they may have depth greater than 1 in languages that use the prototype to determine depth.
The simple arrays are a superset of the arrays allowed in flat array theory without boxes (or those which have depth 0 in flat array theory): they include all arrays of a single type, as well as arrays which mix types like numbers and characters. Arrays which would not be representable in flat array theory—those which contain a mixture of simple scalar types, or contain both simple scalars and other arrays—are called mixed.
The term "simple" is not typically used in flat APLs. On the APL Wiki, it may be used to mean a non-boxed array.