Set Expressions

The Set Expressions are domain-specific operations for sets and lists, commonly found in OCL (Object Constraint Language) and specifications. These include literal collections, comprehensions, and set algebra (union, intersect, difference).

Java Compatibility: When the Java Integration (Class2MC) feature is enabled, these expressions are fully compatible with Java List and Set collections.

Defining Collections (Set Enumerations)

Set Enumerations allow you to explicitly define sets or lists of values. You can define collections using individual values, ranges, or a combination of both.

• Sets are defined using curly braces { ... } or explicitly prefixed with Set{ ... }.
• Lists are defined using square brackets [ ... ].

Elements and Ranges

A collection can contain single expressions or value ranges defined with the .. operator.

Syntax Example	Type	Description
{1, 2, 3}	Set	A set containing the values 1, 2, and 3.
Set{a, b}	Set	Explicit set definition.
[1, 2, 3]	List	A list containing the values 1, 2, and 3.
{1..3}	Set	A set of values from 1 to 3.
[x+1..10, 21]	List	A list containing a range from x+1 to 10, plus the value 21.

Set Comprehensions

Set Comprehensions allow you to dynamically build sets or lists by generating elements from an existing collection, filtering them, and mapping them.

Syntax:

• { expression | item1, item2, ... }
• [ expression | item1, item2, ... ]

The left side of the pipe | defines the elements stored in the collection. The right side is a comma-separated list of items that characterize the comprehension.

Comprehension Items

A comprehension item on the right side of the | can be one of three things:

1. Generator: Introduces a new variable and lets it range over an existing set.
2. Format: [Type]? Name in Expression

3. Example: x in S, int y in {3..10}

4. Filter (Expression): A boolean expression that filters which elements are included.

5. Example: x < 10

6. Variable Declaration: Introduces an intermediate local variable.

7. Format: [Type]? Name = Expression
8. Example: int y = x * 2

Examples:

{ x * x | x in S, x < 10 }          // Set of squares of elements in S that are less than 10
[ y | x in {1..5}, int y = 2 * x ]  // List [2, 4, 6, 8, 10]

Set Operations

A variety of infix and prefix operators to interact with and combine sets are available.

Membership Operators

Operator	Example	Description
isin	elem isin setA	Evaluates to true if elem exists within setA.
notin	elem notin setA	Evaluates to true if elem does not exist within setA.

Binary Set Algebra

Operator	Example	Description
union	setA union setB	Combines elements from both sets into a single set.
intersect	setA intersect setB	Returns a set containing only the elements present in both sets.
\	setA \ setB	Set difference; returns elements in setA that are not in setB.

Unary Collection Operations (Flattening)

These operations are applied to a single set containing other sets (sets of sets).

Operator	Example	Description
union	union setOfSets	Flattens the collection by taking the union of all contained sets.
intersect	intersect setOfSets	Returns the intersection of all sets contained within the collection.

Logical Set Operations

These prefix operators apply logical aggregation over a set of boolean values.

Operator	Example	Description
setand	setand setOfBools	Returns true if all elements in the set evaluate to true (logical FORALL).
setor	setor setOfBools	Returns true if at least one element in the set evaluates to true (logical EXISTS).