VDM-10 Language Manual

Chapter 6. Expressions
✡✝
mk_Score(-,w2,-,-,p2) = sc2
in (p1 > p2) or (p1 = p2 and w1 > w2)
✆
In this particular example we extract the second and fifth components of the two scores.
Note that don’t care patterns (page 73) are used to indicate that the remaining components
are irrelevant for the processing done in the body of this expression.
Let-be-such-that expressions are useful for abstracting away the non-essential choice of an
element from a set, in particular in formulating recursive definitions over sets. An example
of this is a version of the sequence filter function (page 40) over sets:
✞
✡✝
set_filter[@elem] : (@elem -> bool) -> (set of @elem) ->
(set of @elem)
set_filter(p)(s) ==
if s = {}
then {}
else let x in set s
in (if p(x) then {x} else {}) union
set_filter[@elem](p)(s \ {x});
We could alternatively have defined this function using a set comprehension (described in
section 6.7):
✞
✡✝
set_filter[@elem] : (@elem -> bool) -> (set of @elem) ->
(set of @elem)
set_filter(p)(s) ==
{ x | x in set s & p(x)};
The last example shows how the optional “be such that” part (be st) can be used. This
part is especially useful when it is known that an element with some property exists but an
explicit expression for such an element is not known or difficult to write. For instance we
can exploit this expression to write a selection sort algorithm:
✞
remove : nat * seq of nat -> seq of nat
remove (x,l) ==
let i in set inds l be st l(i) = x
in
l(1,...,i-1) ˆ l(i+1,...,len l)
pre x in set elems l;
selection_sort : seq of nat -> seq of nat
43
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