VDM-10 Language Manual

Chapter 6. Expressions
where e1 is a boolean expression, while e2 and e3 are expressions of any type. The if
expression denotes the value of e2 evaluated in the given context if e1 evaluates to true in
the given context. Otherwise the if expression denotes the value of e3 evaluated in the given
context. The use of an elseif expression is simply a shorthand for a nested if then else
expression in the else part of the expression.
The cases expression has the form
✞
✡✝
cases e :
p11, p12, ..., p1n -> e1,
... -> ...,
pm1, pm2, ..., pmk -> em,
others
-> emplus1
end
where e is an expression of any type, all pij’s are patterns which are matched one by one
against the expression e. The ei’s are expressions of any type, and the keyword others
and the corresponding expression emplus1 are optional. The cases expression denotes the
value of the ei expression evaluated in the context in which one of the pij patterns has been
matched against e. The chosen ei is the first entry where it has been possible to match the
expression e against one of the patterns. If none of the patterns match e an others clause
must be present, and then the cases expression denotes the value of emplus1 evaluated in
the given context.
Examples: The if expression in the VDM languages corresponds to what is used in most programming
languages, while the cases expression in the VDM languages is more general than most
programming languages. This is shown by the fact that real pattern matching is taking place,
but also because the patterns do not have to be constants as in most programming languages.
An example of the use of conditional expressions is provided by the specification of the
mergesort algorithm:
✞
lmerge : seq of nat * seq of nat -> seq of nat
lmerge (s1,s2) ==
if s1 = []
then s2
elseif s2 = []
then s1
elseif (hd s1) < (hd s2)
then [hd s1] ˆ (lmerge (tl s1, s2))
else [hd s2] ˆ (lmerge (s1, tl s2));
mergesort : seq of nat -> seq of nat
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✆