Assertions and Abstract Data Types

Even though we have defined assertions in terms of programs, notion can be extended to abstract data types (which are mathematical entities). An ADT assertion is a statement that should always be true of the carrier set values or the operations in ADT. ADT assertions can describe many things about an ADT, but generally they help describe the operations of ADT. Especially helpful in this regard are operation preconditions, which generally constrain parameters of operations, operation post conditions, which define results of the operations, and axioms that make statements about properties of operations, often showing how operations are related to one another.