VDM-10 Language Manual

Chapter 3. Data Type Definitions
Operator Name
Tail
Semantics Description
yields the subsequence of l where the first element is
removed. l must be a non-empty sequence.
Length yields the length of l.
Elements yields the set containing all the elements of l.
Indexes yields the set of indexes of l, i.e. the set
{1,...,len l}.
Concatenation
Distributed concatenation
applica-
Sequence
tion
Sequence modification
yields the concatenation of l1 and l2, i.e. the sequence
consisting of the elements of l1 followed by
those of l2, in order.
yields the sequence where the elements (these are sequences
themselves) of ll are concatenated: the first
and the second, and then the third, etc.
the elements of l whose indexes are in the domain of
m are modified to the range value that the index maps
into. dom m must be a subset of inds l
yields the element of index from l. i must be in the
indexes of l.
Examples: Let l1 = [3,1,4,1,5,9,2], l2 = [2,7,1,8],
l3 = [, , , ] then:
len l1 ≡ 7
hd (l1ˆl2) ≡ 3
tl (l1ˆl2) ≡ [1,4,1,5,9,2,2,7,1,8]
l3(len l3) ≡
"England"(2) ≡ ’n’
reverse l1 ≡ [2,9,5,1,4,1,3]
conc [l1,l2] = l1ˆl2 ≡ true
conc [l1,l1,l2] = l1ˆl2 ≡ false
elems l3 ≡ { ,
,
,}
(elems l1) inter (elems l2) ≡ {1,2}
inds l1 ≡ {1,2,3,4,5,6,7}
(inds l1) inter (inds l2) ≡ {1,2,3,4}
l3 ++ {2 |-> ,4 |-> } ≡ [ ,
,
,
]
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