ProZ is a extension of the ProB animator and model checker to support Z specifications. It uses the Fuzz type checker by Mike Spivey [[1]] for extracting the formal specification from a LaTeX file. On the website you can also find documentation about the syntax of Z specifications.
Often a Z specification makes use of comprehension sets, often introduced by the underlying translation process from Z to B. Normally those comprehension sets should be treated symbolically. To support this you should set the following in the preferences menu:
Animation Preferences -> - Lazy expansion of lambdas & set comprehensions: True - Convert lazy form back into explicit form for Variables and Constants: False
To identify the components (like state, initialisation, operations) of a Z specification, ProZ expects a certain structure of the specification: There must be a schema called "Init". "Init" describes the initialisation of the state. "Init" must include exactly one schema in the declaration part, the included is assumed to be the state schema.
For example, let S be the state schema (= is used for \defs):
S = [ x,y:N ]
There are two supported styles for the initialisation:
a) Init = [ S | x=0 /\ y=1] b) Init = [ S'| x'=0 /\ y'=1 ]
If you want to use the logic of other schemas beside the state schema in the initialisation, you can do that by including those schemas in the predicate part.
ProZ identifies schemas as operations if they satisfy the following properties:
* All variables of the state and their primed counterpart are declared in the operation. Usually this is done by including "\Delta S" in the operation (with S being the state schema). * The operation is not referenced by any other schema in the specification
Example: Let S be defined as above:
A = [ \Delta S | x'=x+1 /\ y'=y ]
B = [ x,y,x',y':N | x'=x+1 /\ y'=y ]
C = [ x,x':N | x'=x+1 ]
D = [ y,y':N | y'=y ]
E = C /\ D
F = [ \Xi S | x=0 ]
Then the schemas A,B and E describe all the same operation, also F is identified as an operation that leaves the state unchanged.
If axiomatic definitions are present, the declared variables are treated like constants. In the first step of the animation, ProB searches for values that satisfy all predicates of the axiomatic definitions are searched. After the first step the predicates of the axiomatic definitions are ignored. If you want to define functions in an axiomatic definition, consider that ProB can treat lambda expressions and set comprehensions symbolically. Example: The definition of a function "square" could be
a) square : Z -> Z
b) square : Z -> Z
The preferred way when using ProZ is a), because the lambda expression can be interpreted symbolically. In case of using b) ProB will try to find a explicit set that will satisfy the given property.
You can add a B-style invariant to the specification by defining a schema "Invariant" that declares a subset of the state variables. In each explored state the invariant will be checked. The model checking feature of ProB will try to find states that violate the invariant.
It is possible to limit the search space of the model checker by adding a schema "Scope" that declares a subset of the state variables. If such a schema is present, each explored state is checked, if it satisfies the predicate. If not, the state is not further explored.
Abbreviation definitions (e.g. Abbr == {1,2,3}) are used like macros by ProZ, a reference to an abbreviation is replaced by its definition in a preprocessor phase. Thereby schemas defined by abbreviation definitions are ignored when ProZ tries to identify components. So use schema definitions instead of abbreviation definitions (\defs instead of ==) when defining state, initialisation, operations, etc.
Sometimes it is not desired to check properties of some variables. E.g. ProZ checks if the square function in 2.3.a is a total function by enumerating it (it checks the function only for a limited interval). For more complex definitions the number of entries is often too large to check. When the user is sure that those properties are satisfied (like in our example), a solution is relaxing the declaration from "square : Z -> Z" to "square : Z <-> Z". Sometimes this is not easy to do, e.g. if schema types are used which imply other constraints.
ProZ supports an operation \prozignore that instructs ProZ to ignore all constraints on the type and to use just the underlying type. E.g. the square function could be defined by:
square : \prozignore( Z -> Z )
If you want to use \prozignore, you must first define a TeX command \prozignore: {{{ \newcommand{\prozignore}{ignore_\textsl{\tiny ProZ}} }}}
You can change the definition of the macro as you like, the content is ignored by ProZ. Then you must introduce a generic definition of \prozignore. The definition is ignored by ProB, but Fuzz needs it for type checking.
{{{ %%pregen \prozignore \begin{gendef}[X]
\prozignore~\_ : \power X
\end{gendef} }}}
It is also possible to append this lines to the "fuzzlib" in the fuzz distribution.
You can inspect the result of the translation process with "Show internal representation" in the "Debug" menu. Please note, that the shown B machine is normally not syntactically correct, because of
* additional constructs like free types
* additional type information of the form "var:type"
* names with primes (') or question marks, etc.
* the pretty printer may not support every construct
Generic definitions are not supported yet.
Bags are not supported yet.
* disjoint * partition * reflexive-transitive closure * probably other?
The error messages are not very helpful yet.