An approach to writing precise specifications is to build a model of the intended system using languages such as Z, VDM, or B that describe the system state and the operations that change states.
System states are typically described using sets, sequences, relations, mappings, and functions, and operations are described by pre- and post-conditions. There are a number of ways to structure such a specification. In Z, for instance, a specification consists of schemas made of declarations (variables, etc.) together with predicates that constrain the schema.
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