The Z notation: A reference manual

Automated verification of shape, size and bag properties via user-defined predicates in separation logic

“…However, we envisage the use of more complex constraint domains in the future, with the adoption of new constraint solvers/provers in our system. In the rest of the paper, we will use the following bag operators [55]: bag union ⊔, bag intersection ⊓, bag subsumption ⊏, and bag cardinality |B|.…”

Implementations are not specifications: Specification, replication and experimentation in computational cognitive modeling

“…This was effectively the approach taken in describing early models of short-term memory (e.g., Atkinson & Shiffrin, 1968;Waugh & Norman, 1965). More formally, one might adopt mathematical methods to specify the functional decomposition of processes and their interactions, such as combinatorial logic (e.g., Hindley & Seldin, 1986), calculi for concurrent communicating systems (e.g., Milner, 1989), or formal specification languages (e.g., Spivey, 1989). Such approaches have additional benefits, beyond implementation-independent specification of theory.…”

“…One approach is to reason over properties of the specification, as was done informally by Broadbent (1958) and more formally in the context of a well-specified cognitive model by Barnard and colleagues (e.g., Duke, Barnard, May, & Duce, 1995). This kind of reasoning is one of the key motivations for computer science specification languages such as Z (Spivey, 1989).…”

Executable formal specifications of complex distributed systems with CoreASM

“…State-based formal methods that view the states of a system in terms of mathematical structures are common for practical system design and analysis. In addition to ASM, one can point to methods such as Alloy [41], B [42], CASL [43], the Vienna Development Method (VDM) [44], and the Z notation [45] as the most popular approaches that share many similar concepts and rely on tool support for analysis of specifications. In fact, the ingredients of the ASM method are not original.…”