This is an experimental implementation of semantic subtyping for the type system of the Ballerina programming language, implemented in Ballerina.

The algorithm here is based on the work of Giuseppe Castagna and Alain Frisch, implemented in CDuce. I have found the most accessible paper to be:

Covariance and Contravariance: a fresh look at an old issue (a primer in advanced type systems for learning functional programmers), G. Castagna, 2020

Section 4 of the above paper has a description of the algorithms.

There is also a tutorial by Andrew M. Kent, which is great for getting started:

Down and Dirty with Semantic Set-theoretic Types (a tutorial)

The implementation currently handles a subset of Ballerina type system:

• nil, boolean, int, float, decimal, string, handle types
• array and tuple types
• map and record types
  • no optional record fields yet
  • no readonly record fields yet
• function types
• readonly
• union
• intersection
• string, int, boolean singletons
• byte and other built-in int subtypes
• error with detail record subtypes (but not distinct)
• typedesc, xml (without type parameters)
• json (can be derived from the above)
• any, never (can be derived from the above)
• complement and difference (Ballerina has no syntax for this, but deciding whether S is a subtype of T is equivalent to deciding whether the difference of S and T is empty)

Most of the code is in modules:

• core - this implements the subtyping algorithm
• bdd - this implements binary decision diagrams, which is a key data-structure used by the core module
• json - this parses a JSON representation of types, and uses the core module to build an internal representation

The JSON representation of types is Lisp-like, and documented in the file schema.bal.

Running the program checks the type relationships asserted in tests.json. This is a JSON file that contains an array of tests; each test is a triple [R, T1 T2], where R is a string specifying the relationship that holds between T1 and T2, as follows:

• equivalent: T1 is a subtype of T2 and T2 is a subtype of T1
• proper_subtype: T1 is a subtype of T2 and T2 is not a subtype of T1
• incomparable: T1 is not a subtype of T2 and T2 is not a subtype of T1

The program can be built with the Swan Lake Alpha5 version of Ballerina.

There is a list of everything still to be done to handle the whole type system. There are also implementation notes.