A formal specification language is usually composed of three primary components: (1) a syntax that defines the specific notation with whic...

A formal specification language is usually composed of three primary components:

The syntactic domain of a formal specification language is often based on a syntax that is derived from standard set theory notation and predicate calculus. For example, variables such as x, y, and z describe a set of objects that relate to a problem (sometimes called the domain of discourse) and are used in conjunction with the operators . Although the syntax is usually symbolic, icons (e.g., graphical symbols such as boxes, arrows, and circles) can also be used, if they are unambiguous.

The semantic domain of a specification language indicates how the language represents system requirements. For example, a programming language has a set of formal semantics that enables the software developer to specify algorithms that transform input to output. A formal grammar (such as BNF) can be used to describe the syntax of the programming language. However, a programming language does not make a good specification language because it can represent only computable functions. A specification language must have a semantic domain that is broader; that is, the semantic domain of a specification language must be capable of expressing ideas such as, "For all x in an infinite set A, there exists a y in an infinite set B such that the property P holds for x and y". Other specification languages apply semantics that enable the specification of system behavior. For example, a syntax and semantics can be developed to specify states and state transition, events and their effect on state transition, synchronization and timing.

It is possible to use different semantic abstractions to describe the same system in different ways. Data flow and corresponding processing were described using the data flow diagram, and system behavior was depicted with the state transition diagram. Analogous notation was used to describe object-oriented systems. Different modeling notation can be used to represent the same system. The semantics of each representation provides complementary views of the system. To illustrate this approach when formal methods are used, assume that a formal specification language is used to describe the set of events that cause a particular state to occur in a system. Another formal relation depicts all functions that occur within a given state. The intersection of these two relations provides an indication of the events that will cause specific functions to occur.

A variety of formal specification languages are in use today. are representative formal specification languages that exhibit the characteristics noted previously. The Z specification language is used for illustrative purposes. Z is coupled with an automated tool that stores axioms, rules of inference, and application-oriented theorems that lead to mathematical proof of correctness of the specification.

**(1)**a syntax that defines the specific notation with which the specification is represented,**(2)**semantics to help define a "universe of objects" that will be used to describe the system, and**(3)**a set of relations that define the rules that indicate which objects properly satisfy the specification.The syntactic domain of a formal specification language is often based on a syntax that is derived from standard set theory notation and predicate calculus. For example, variables such as x, y, and z describe a set of objects that relate to a problem (sometimes called the domain of discourse) and are used in conjunction with the operators . Although the syntax is usually symbolic, icons (e.g., graphical symbols such as boxes, arrows, and circles) can also be used, if they are unambiguous.

The semantic domain of a specification language indicates how the language represents system requirements. For example, a programming language has a set of formal semantics that enables the software developer to specify algorithms that transform input to output. A formal grammar (such as BNF) can be used to describe the syntax of the programming language. However, a programming language does not make a good specification language because it can represent only computable functions. A specification language must have a semantic domain that is broader; that is, the semantic domain of a specification language must be capable of expressing ideas such as, "For all x in an infinite set A, there exists a y in an infinite set B such that the property P holds for x and y". Other specification languages apply semantics that enable the specification of system behavior. For example, a syntax and semantics can be developed to specify states and state transition, events and their effect on state transition, synchronization and timing.

It is possible to use different semantic abstractions to describe the same system in different ways. Data flow and corresponding processing were described using the data flow diagram, and system behavior was depicted with the state transition diagram. Analogous notation was used to describe object-oriented systems. Different modeling notation can be used to represent the same system. The semantics of each representation provides complementary views of the system. To illustrate this approach when formal methods are used, assume that a formal specification language is used to describe the set of events that cause a particular state to occur in a system. Another formal relation depicts all functions that occur within a given state. The intersection of these two relations provides an indication of the events that will cause specific functions to occur.

A variety of formal specification languages are in use today. are representative formal specification languages that exhibit the characteristics noted previously. The Z specification language is used for illustrative purposes. Z is coupled with an automated tool that stores axioms, rules of inference, and application-oriented theorems that lead to mathematical proof of correctness of the specification.