VDM-10 Language Manual

Chapter 3. Data Type Definitions
Operator Name
Distributes intersection
Finite power set
Semantics Description
the resulting set is the intersection of all the elements
(these are sets themselves) of, i.e. it contains the elements
that are in all the elements/sets of ss. ss must
be non-empty.
yields the power set of s1, i.e. the set of all subsets of
s1.
Examples: Let s1 = {,,,}, s2
= {2, 4, 6, 8, 11} and s3 = {} then:
in set s1 ≡ false
10 not in set s2 ≡ true
s2 union s3 ≡ {2, 4, 6, 8, 11}
s1 inter s3 ≡ {}
(s2 \ {2,4,8,10}) union {2,4,8,10} = s2 ≡ false
s1 subset s3 ≡ false
s3 subset s1 ≡ true
s2 psubset s2 ≡ false
s2 s2 union {2, 4} ≡ false
card s2 union {2, 4} ≡ 5
dunion {s2, {2,4}, {4,5,6}, {0,12}} ≡ {0,2,4,5,6,8,11,12}
dinter {s2, {2,4}, {4,5,6}} ≡ {4}
dunion power {2,4} ≡ {2,4}
dinter power {2,4} ≡ {}
3.2.2 Sequence Types
A sequence value is an ordered collection of elements of some type indexed by 1, 2, ..., n;
where n is the length of the sequence. A sequence type is the type of finite sequences of elements
of a type, either including the empty sequence (seq0 type) or excluding it (seq1 type). The elements
of a sequence type can be arbitrarily complex; they could e.g. be sequences themselves.
In the following this convention will be used: A is an arbitrary type, L is a sequence type, S is
a set type, l, l1, l2 are sequence values, ll is a sequence of sequence values. e1, e2 and en
are elements in these sequences, i will be a natural number, P is a predicate and e is an arbitrary
expression.
Syntax:
type = seq type
| . . . ;
seq type = seq0 type
| seq1 type ;
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