VDM-10 Language Manual

Chapter 19
Static Semantics
VDM specifications that are syntactically correct according to the syntax rules do not necessarily
obey the typing and scoping rules of the language. The well-formedness of a VDM specification
can be checked by the static semantics checker. In the Toolbox such a static semantics checker (for
programming languages this is normally referred to as a type checker) is also present.
In general, it is not statically decidable whether a given VDM specification is well-formed
or not. The static semantics for the VDM languages differs from the static semantics of other
languages in the sense that it only rejects specifications which are definitely not well-formed, and
only accepts specifications which are definitely well-formed. Thus, the static semantics for the
VDM languages attach a well-formedness grade to a VDM specification. Such a well-formedness
grade indicates whether a specification is definitely well-formed, definitely not-well-formed, or
possibly well-formed.
In the Toolbox this means that the static semantics checker can be called for either possible
correctness or definite correctness. However, it should be noted that only very simple specifications
will be able to pass the definite well-formedness check. Thus, for practical use the possible wellformedness
is most useful.
The difference between a possibly well-formedness check and a definite well-formedness check
can be illustrated by the following fragment of a VDM specification:
✞
✡✝
if a = true
then a + 1
else not a
where a has the type nat | bool (the union type of nat and bool). The reader can easily
see that this expression is ill-formed if a is equal to true because then it will be impossible to
add one to a. However, since such expressions can be arbitrarily complex this can in general not
be checked statically. In this particular example possible well-formedness will yield true while
definite well-formedness will yield false.
✆
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