What is a specification language ?

data types: Z, VDM, Larch. Z, a formal method based on set theory, can be used in both model-oriented and property-oriented styles. Figure 4 gives a modeloriented specification of a symbol table, following the Z notation of Spivey.h The state of the table is modeled by a partial mapping from keys to values (X -H Y denotes a set of partial mappings from set X to set Y; a partial mapping relates each member of X to at most one member of Y). By convention, unprimed variables in Z stand for the state before an operation is performed and primed variables for the state afterwards. I will use the same convention in the VDM and Larch specifications. The table contains four operations: INIT, INSERT, LOOKUP, and DELETE. INIT initializes the symbol table st to be empty. INSERT modifies the table by adding a new binding to sf, in the case the key k is not already in the domain of st. LOOKUP requires that the key k be in the domain of the mapping, returns the value to which k is mapped, and does not change the state of the symbol table (sr’ = sf). DELETE also requires that the key k be in the domain of the mapping and modifies the table by deleting the binding associated with k from st (+I is a domain subtraction operator). The proof checker B has been used to prove theorems based on Z specifications. VDM supports a model-oriented speci-