Type inference with recursive types: Syntax and semantics

Type Inference with Recursive Types: Syntax and Semantics

In this paper we study type inference systems for I-calculus with a recursion operator over types. The main syntactical properties, notably the existence of principal type schemes, are proved to hold when recursive types are viewed as finite notations for infinite (regular) type expressions representing their infinite unfoldings. Exploiting the approximation structure of a model for the untyped...

Type Inference for Guarded Recursive Data Types

We consider type inference for guarded recursive data types (GRDTs) – a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference. Inference is incomplete because the set of type constraints allowed to appear in the type system is only a subset of those type constraints generated by type infere...

Type inference in systems of recursive types with subtyping

We present general methods for performing type inference and deciding subtyping in languages with recursive types. Our type inference algorithm generalizes a common idea of previous work: type inference is reduced to a constraint satisfaction problem, whose satisfiability can be decided by a process of closure and consistency checking. We prove a general correctness theorem for this style of ty...

Syntax and Semantics of Linear Dependent Types

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are developed, the latter in terms of (strict) indexed symmetric monoidal categories with comprehension. Various optional type formers are treated in a modular way. In ...

Syntax and Semantics of Dependent Types