VDM-10 Language Manual

Chapter 4
Algorithm Definitions
In the VDM languages algorithms can be defined by both functions and operations. However,
they do not directly correspond to functions in traditional programming languages. What separates
functions from operations in the VDM languages is the use of local and global variables. Operations
can manipulate both the global variables and any local variables. Both local and global
variables will be described later. Functions are pure in the sense that they cannot access global
variables and they are not allowed to define local variables. Thus, functions are purely applicative
while operations are imperative.
Functions and operations can be defined both explicitly (by means of an explicit algorithm definition)
or implicitly (by means of a pre-condition and/or a post condition). An explicit algorithm
definition for a function is called an expression while for an operation it is called a statement. A
pre-condition is a truth-valued expression which specifies what must hold before the function/operation
is evaluated. A pre-condition can only refer to parameter values and global variables (if
it is an operation). A post-condition is also a truth valued expression which specifies what must
hold after the function/operation is evaluated. A post-condition can refer to the result identifier,
the parameter values, the current values of global variables and the old values of global variables.
The old values of global variables are the values of the variables as they were before the operation
was evaluated. Only operations can refer to the old values of global variables in a post-condition
as functions are not allowed to change the global variables.
However, in order to be able to execute both functions and operations by the interpreter they
must be defined explicitly 1 . In the VDM langugaes it is also possible for explicit function and
operation definitions to specify an additional pre- and a post-condition. In the post-condition of
explicit function and operation definitions the result value must be referred to by the reserved word
RESULT.
1 Implicitly specified functions and operations cannot in general be executed because their post-condition does not need
to directly relate the output to the input. Often it is done by specifying the properties the output must satisfy.
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