VDM-10 Language Manual

VDM-10 Language Manual
of scores and returns the corresponding pair of teams:
✞
promoted : seq of Score -> Team * Team
promoted([sc1,sc2]ˆ-) == mk_(sc1.team,sc2.team);
✡✝
✆
Here sc1 is bound to the head of the argument sequence, and sc2 is bound to the second
element of the sequence. If promoted is called with a sequence with fewer than two
elements then a runtime error occurs. Note that as we are not interested in the remaining
elements of the list we use a don’t care pattern for the remainder.
The preceding example also demonstrated the use of sequence concatenation patterns. Another
example of this is the function quicksort which implements a standard quicksort
algorithm:
✞
quicksort : seq of nat -> seq of nat
quicksort (l) ==
cases l:
[] -> [],
[x] -> [x],
[x,y] -> if x < y then [x,y] else [y,x],
-ˆ[x]ˆ- -> quicksort ([y | y in set elems l & y < x]) ˆ
[x] ˆ
quicksort ([y | y in set elems l & y > x])
end
✡✝
Here, in the second cases clause a sequence concatenation pattern is used to decompose l
into an arbitrary pivot element and two subsequences. The pivot is used to partition the list
into those values less than the pivot and those values greater, and these two partitions are
recursively sorted.
Tuple patterns can be used to bind tuple components to identifiers. For instance since the
function promoted defined above returns a pair, the following value definition binds the
winning team of GroupA to the identifier Awinner:
✞
values
✆
✡✝
mk_(Awinner,-) = promoted(GroupA);
✆
Record patterns are useful when several fields of a record are used in the same expression.
For instance the following expression constructs a map from team names to points score:
✞
{ t |-> w * 3 + l | mk_Score(t,w,l,-,-) in set elems GroupA}
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