Extending OCL with Map and Function Types

Abstract

Map and function types are of high utility in software specification and design, for example, maps can be used to represent configurations or caches, whilst function values can be used to enable genericity and reuse in a specification, and to support mechanisms such as callbacks or closures in an implementation. Map and function types have been incorporated into the leading programming languages, including Java, C++, Swift and Python.

The Object Constraint Language (OCL) specification notation lacks such types, and in this paper we make a proposal for a consistent extension of OCL with map and function types, and we identify modifications to OCL semantics to include these types. We also describe how map and function types are implemented using the Eclipse AgileUML toolset.

A Additional Map Type Operators

The following map operators can also be formalised in our proposed extension of OCL.

size() : Integer

This is equal to $self{\rightarrow }keys(){\rightarrow }size()$.

includesValue(object : T) : Boolean True if the object is an element of the map range, false otherwise:

Similarly for ${\rightarrow }includesKey()$, ${\rightarrow }excludesValue()$, ${\rightarrow }excludesKey()$.

count(object : T) : Integer The number of times the object occurs as an element of the map range (a bag):

includesAll(c2 : Map(K,T)) : Boolean True if c2 is a map, and the set of pairs of self contains all those of c2, false otherwise:

Similarly for ${\rightarrow }excludesAll()$.

isEmpty() : Boolean, notEmpty() : Boolean Defined based on $self{\rightarrow }asSet()$.

max() : T, min() : T, sum() : T Defined as the corresponding operations on $self{\rightarrow }values()$.

asSet() : Set(Tuple(key : K, value : T)) The set of pairs of elements in the map. Since duplicate keys are not permitted, this has the same size as $self{\rightarrow }keys()$.

restrict(ks : Set(K)) : Map(K,T) Domain restriction . The map restricted to the keys in ks. Its elements are the pairs of self whose key is in ks:

Range restriction is provided via the ${\rightarrow }select$ operator.

-(m: Map(K,T)) : Map(K,T) Map subtraction: the elements of self that are not in m.

union(m : Map(K,T)) : Map(K,T) Map override, the operation $self \oplus m$ or $self~{{<}{+}}~m$ in mathematical notation. This consists of the pairs of self which do not conflict with pairs of m, together with all pairs of m:

This is the same as putAll in EOL [9]. Unlike set union, it is not commutative.

intersection(m : Map(K,T)) : Map(K,T) The pairs of self which are also in m:

This is associative and commutative.

including(k : K, v : T) : Map(K,T) The pairs of self, with the additional/overriding mapping of k to v:

We also use the abbreviated notation $m[k] = v$ for $m = m{\text{@ }pre}{\rightarrow }including(k,v)$.

excluding(k : K, v : T) : Map(K,T) The pairs of self, with any mapping of k to v removed:

any Defined as

Likewise for forAll, exists, one.

select The map formed by restricting to range elements which satisfy the select condition:

Similarly for reject.