VDM-10 Language Manual

Chapter 3. Data Type Definitions
Operator Name Type
dom m Domain (map A to B) → set of A
rng m Range (map A to B) → set of B
m1 munion m2 Merge (map A to B) * (map A to B) → map A to B
m1 ++ m2 Override (map A to B) * (map A to B) → map A to B
merge ms Distributed merge set of (map A to B) → map A to B
s s Range restrict by (map A to B) * (set of B) → map A to B
m(d) Map apply (map A to B) * A → B
m1 comp m2 Map composition (map B to C) * (map A to B) → map A to C
m ** n Map iteration (map A to A) * nat → map A to A
m1 = m2 Equality (map A to B) * (map A to B) → bool
m1 m2 Inequality (map A to B) * (map A to B) → bool
inverse m Map inverse inmap A to B → inmap B to A
Semantics of Operators: Two maps m1 and m2 are compatible if any common element of dom
m1 and dom m2 is mapped to the same value by both maps.
Operator Name Semantics Description
Domain yields the domain (the set of keys) of m.
Range yields the range (the set of information values) of m.
Merge
yields a map combined by m1 and m2 such that the
resulting map maps the elements of dom m1 as does
m1, and the elements of dom m2 as does m2. The
two maps must be compatible.
Override
overrides and merges m1 with m2, i.e. it is like a
merge except that m1 and m2 need not be compatible;
any common elements are mapped as by m2 (so
m2 overrides m1).
Distributed merge yields the map that is constructed by merging all the
maps in ms. The maps in ms must be compatible.
Domain restricted to creates the map consisting of the elements in m whose
key is in s. s need not be a subset of dom m.
Domain restricted creates the map consisting of the elements in m whose
by
key is not in s. s need not be a subset of dom m.
Range restricted to creates the map consisting of the elements in m whose
information value is in s. s need not be a subset of
rng m.
19