Recursive data type

Abstract: Programming computers is a notoriously error-prone process. It is the job of the programming language designer to make this process more reliable. One approach to this is to impose some sort of typing discipline on the programs. In doing this, the programming language designer is immediately faced with a tradeoff: if the type system is too simple, it cannot accurately express important properties of the program; if it is too expressive, then mechanically checking or inferring the types becomes impractical. This thesis describes a type system called refinement types, which is an example of a new way to make this tradeoff, as well as a potentially useful system in itself. Refinement type inference requires programs to have types in two type systems: an expressive type inference system (intersection types with subtyping) and a relatively simple type system (basic polymorphic type inference). Refinement type inference inherits some properties from each of these: as in intersection types with subtyping, we can use the type system to do abstract interpretation; as in basic polymorphic type inference, refinement type inference is decidable (preliminary experiments suggest refinement type inference may be practical as well). We have implemented refinement type inference for a subset of Standard ML to test these ideas. We have added new syntax, called rectype declarations, to allow the programmer to specify relevant domains for the abstract interpretation. A prototype implementation of refinement type inference can do some interesting case analysis for Standard ML programs; for example, if the programmer uses a rectype declaration to declare interest in whether a boolean expression is in conjunctive normal form (CNF), refinement type inference can efficiently prove that a function for converting boolean expressions to CNF does indeed always return a boolean expression in CNF. Rectype declarations and refinement type inference seem flexible and efficient enough to practically enforce many other useful program properties as well.