Types: Supertypes And Subtypes

The set of built-in and user-defined types in Hack can be thought of as a type hierarchy of supertypes and subtypes in which a variable of some type can hold the values of any of its subtypes. For example, int and float are subtypes of num.

A supertype can have one or more subtypes, and a subtype can have one or more supertypes. A supertype can be a subtype of some other supertype, and a subtype can be a supertype of some other subtype.

The relationship between a supertype and any of its subtypes involves the notion of substitutability. Specifically, if T2 is a subtype of T1, program elements designed to operate on T1 can also operate on T2.

For types in Hack, the following rules apply:

• The root of the type hierarchy is the type mixed; as such, every type is a subtype of that type.
• Any type is a subtype of itself.
• int and float are subtypes of num.
• int and string are subtypes of arraykey.
• For each type T, T is a subtype of the nullable type ?T.
• For each type T, the null type is a subtype of all nullable types ?T.
• string is a subtype of Stringish.
• The predefined types vec, dict, and keyset are subtypes of Container, KeyedContainer, KeyedTraversable, and Traversable.
• If A is an alias for a type T created using type, then A is a subtype of T, and T is a subtype of A.
• If A is an alias for a type T created using newtype, inside the file containing the newtype definition, A is a subtype of T, and T is a subtype of A. Outside that file, A and T have no relationship, except that given newtype A as C = T, outside the file with the newtype definition, A is a subtype of C.
• Any class, interface, or trait, having a public instance method __toString taking no arguments and returning string, is a subtype of Stringish.
• A class type is a subtype of all its direct and indirect base-class types.
• A class type is a subtype of all the interfaces it and its direct and indirect base-class types implement.
• An interface type is a subtype of all its direct and indirect base interfaces.
• A shape type S2 whose field set is a superset of that in shape type S1, is a subtype of S1.
• Although noreturn is not a type, per se, it is regarded as a subtype of all other types, and a supertype of none.