User defined type is determined by:

• its name;
• underlying type for in-memory representation and binary serialization;
• expressions to convert from/to String;
• default expression;
• constraints on internal representation;
• constraints on input string;
• function overloads;

Details

1. User defined type can map to parametrized type with fixed parameters:

CREATE TYPE Point2D AS Tuple(Float64, Float64)

It can also be parametrized itself. Then parameters can be substituted to the parameters of the underlying type:

CREATE TYPE Point2D(T) AS Tuple(T, T)

CREATE TYPE DecimalPoint2D(N, M) AS Tuple(Decimal(N, M), Decimal(N, M))

It can map to a simple type as well.

2. Expressions to convert from/to String can be composed from SQL functions.
   It's in question how it's better to specify these expressions:

• as expressions with predefined argument name (value, string), e.g. OUTPUT IPv4NumToString(value)
• as lambda functions, e.g. OUTPUT x -> IPv4NumToString(x)

If we choose the first variant, we can write constraints on binary or string representations in uniform way, e.g. CONSTRAINT isValidUTF8(value) (in this example, value is the internal representation).

3. There are multiple possible options to specify which functions will be available:

• we can enable all existing functions that work on underlying type to also work on aliased type; but in some cases it can be undesired;
• we can provide custom overloads for some functions (e.g. length AS lengthUTF8(value)) or define some functions with custom names (e.g. area AS (value.x1 - value.x2) * (value.y1 - value.y2));
• it can be desired for some functions to work automatically by converting some of arguments from String, e.g. equals(T, String)

It is uncrear how to define all these options.

Examples

These examples are probably impractical, just to illustrate the idea:

CREATE TYPE IPv4 AS UInt32
INPUT IPv4StringToNum(string)
OUTPUT IPv4NumToString(value)
DEFAULT IPv4StringToNum('127.0.0.1')

CREATE TYPE UTF8String AS String
CONSTRAINT isValidUTF8(value)
FUNCTION length: value -> lengthUTF8(value)
FUNCTION substring: value, n, m -> substringUTF8(value, n, m)

References

https://www.postgresql.org/docs/9.5/sql-createtype.html

It's not required to do anything similar. But we need to look what is offered by other DBMS.