Type Hierarchy

Types in Theta are grouped into a type hierarchy. Each type can have several supertypes. At the top of the hierarchy is type "any", which has no methods and is the supertype of all types.

The type hierarchy is based on the notion of type equality. A type is always a subtype and also a supertype of itself. The subtype (supertype) relation is transitive: if T is a subtype of S and S is a subtype of R, then T is a subtype of R.

"Any" is the only supertype of the built-in types except that a rich hierarchy is defined for routine types. In particular, no subtype relation is provided for "record" and "struct" types, e.g.,

record[a: int, b: int, c: int]

record[a: int, b: int]

Specifications for user-defined types and user-defined parameterized types indicate the immediate supertypes explicitly (9.2). All supertypes must be user-defined types, except that every user-defined type is automatically a subtype of "any". All types generated by instantiating a user-defined parameterized type are similarly subtypes of "any". The Theta compiler guarantees that subtypes have all the methods of their supertypes, with compatible signatures (9.2).

Routine Type Hierarchy

1. The two routine types must either both be procedure types or both be iterator types.

2. Contravariance of arguments: They must have the same number of arguments, and in each argument position, the type of [tex2html_wrap2875]'s argument must be a supertype of the type of [tex2html_wrap2877]'s argument.

3. Covariance of results: If the two routine types are procedure types, they must have the same number of return results, and the types of [tex2html_wrap2879]'s results must be subtypes of the types of the corresponding [tex2html_wrap2881] results.

4. Covariance of yields: If the two routine types are iterator types, they must have the same number of yielded results, and the types of [tex2html_wrap2883]'s yielded results must be subtypes of the types of the corresponding [tex2html_wrap2885] yielded results.

5. [tex2html_wrap2887] must not have any exceptions that are not also exceptions of [tex2html_wrap2889].

6. Covariance of exception results: Corresponding exceptions must have the same numbers of results, and in the corresponding result positions, the type of [tex2html_wrap2891]'s result must be a subtype of the type of [tex2html_wrap2893]'s result.