Domains

What are Domains and Types

A Domain is the discrete and finite set of values that a variable or expression can take. A Type is a more general description about some collection. The simplest domains are Concrete domains: empty, boolean, int(min..max). Abstract domains use some high-level types (such as a Set, Matrix, etc) to instantiate a domain where the objects of the domain contain more objects. These objects are called Literals; a literal is one specific value taken from a domain.

In the original language description, found in the Conjure Docs

Domain := "bool"
        | "int" list(Range, ",", "()")
        | "int" "(" Expression ")"
        | Name list(Range, ",", "()") # the Name refers to an enumerated type
        | Name                        # the Name refers to an unnamed type
        | "tuple" list(Domain, ",", "()")
        | "record" list(NameDomain, ",", "{}")
        | "variant" list(NameDomain, ",", "{}")
        | "matrix indexed by" list(Domain, ",", "[]") "of" Domain
        | "set" list(Attribute, ",", "()") "of" Domain
        | "mset" list(Attribute, ",", "()") "of" Domain
        | "function" list(Attribute, ",", "()") Domain "-->" Domain
        | "sequence" list(Attribute, ",", "()") "of" Domain
        | "relation" list(Attribute, ",", "()") "of" list(Domain, "*", "()")
        | "partition" list(Attribute, ",", "()") "from" Domain

Range := Expression
       | Expression ".."
       | ".." Expression
       | Expression ".." Expression

Attribute := Name
           | Name Expression

NameDomain := Name ":" Domain

Ground and Unresolved

Looking at conjure-cp-core::ast::domains, there is a Domain Enum, with variants Ground and Unresolved.

• An Unresolved domain is a domain whose bounds are tied to an expression that has not been evaluated. For example x: int(1..(2+1)) and x: int(1..n) are both unresolved.
• A Ground domain is a domain entirely composed of literals. For example: int(2..5), set (maxSize 2) of int(1..3).

Attributes

Abstract domains tend to also have attributes defined on them, which often restricts the possible values of the domain.

When defining a Set type, it may have attributes and an inner domain. For example, the domain set (size 2) of int(1..3) could have valid values like {1,2}, {1,3}, {2,3}. The ‘inner’ domain is int(1..3), from which the values that make up the set are pulled.

The most common attribute is cardinality (which restricts the range objects in an object), but they are type-specific and there is a large variety.