Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class

Towards Strong Normalization for Dependent Object Types (DOT)

The Dependent Object Types (DOT) family of calculi has been proposed as a new theoretic foundation for Scala and similar languages, unifying functional programming, object oriented programming and ML-style module systems. Following the recent type soundness proof for DOT, the present paper aims to establish stronger meta-theoretic properties. The main result is a fully mechanized proof of strong normalization for D_<:, a variant of DOT that excludes recursive functions and recursive types. We further discuss techniques and challenges for adding recursive types while maintaining strong normalization, and demonstrate that certain variants of recursive self types can be integrated successfully

Brand Objects for Nominal Typing

Combinations of structural and nominal object typing in systems such as Scala, Whiteoak, and Unity have focused on extending existing nominal, class-based systems with structural subtyping. The typical rules of nominal typing do not lend themselves to such an extension, resulting in major modifications. Adding object branding to an existing structural system integrates nominal and structural typing without excessively complicating the type system. We have implemented brand objects to explicitly type objects, using existing features of the structurally typed language Grace, along with a static type checker which treats the brands as nominal types. We demonstrate that the brands are useful in an existing implementation of Grace, and provide a formal model of the extension to the language

Safe, Flexible Aliasing with Deferred Borrows

In recent years, programming-language support for static memory safety has developed significantly. In particular, borrowing and ownership systems, such as the one pioneered by the Rust language, require the programmer to abide by certain aliasing restrictions but in return guarantee that no unsafe aliasing can ever occur. This allows parallel code to be written, or existing code to be parallelized, safely and easily, and the aliasing restrictions also statically prevent a whole class of bugs such as iterator invalidation. Borrowing is easy to reason about because it matches the intuitive ownership-passing conventions often used in systems languages. Unfortunately, a borrowing-based system can sometimes be too restrictive. Because borrows enforce aliasing rules for their entire lifetimes, they cannot be used to implement some common patterns that pointers would allow. Programs often use pseudo-pointers, such as indices into an array of nodes or objects, instead, which can be error-prone: the program is still memory-safe by construction, but it is not logically memory-safe, because an object access may reach the wrong object. In this work, we propose deferred borrows, which provide the type-safety benefits of borrows without the constraints on usage patterns that they otherwise impose. Deferred borrows work by encapsulating enough state at creation time to perform the actual borrow later, while statically guaranteeing that the eventual borrow will reach the same object it would have otherwise. The static guarantee is made with a path-dependent type tying the deferred borrow to the container (struct, vector, etc.) of the borrowed object. This combines the type-safety of borrowing with the flexibility of traditional pointers, while retaining logical memory-safety

Type soundness for dependent object types (DOT)

Scala's type system unifies aspects of ML modules, object-oriented, and functional programming. The Dependent Object Types (DOT) family of calculi has been proposed as a new theoretic foundation for Scala and similar expressive languages. Unfortunately, type soundness has only been established for restricted subsets of DOT. In fact, it has been shown that important Scala features such as type refinement or a subtyping relation with lattice structure break at least one key metatheoretic property such as environment narrowing or invertible subtyping transitivity, which are usually required for a type soundness proof. The main contribution of this paper is to demonstrate how, perhaps surprisingly, even though these properties are lost in their full generality, a rich DOT calculus that includes recursive type refinement and a subtyping lattice with intersection types can still be proved sound. The key insight is that subtyping transitivity only needs to be invertible in code paths executed at run time, with contexts consisting entirely of valid runtime objects, whereas inconsistent subtyping contexts can be permitted for code that is never executed