752 research outputs found
Game Semantics and Subtyping
Game Semantics is a relatively new framework for the description of the semantics of programming languages. By combining the mathematical elegance of Denotational Semantics with explicitly operational concepts, Game Semantics has made possible the direct and intuitive modelling of a large range of programming constructs.
In this thesis, we show how Game Semantics is able to model subtyping. We start by designing an untyped λ-calculus with ground values that explicitly internalises the notion of typing error. We then equip this calculus with a rich typing system that includes quantification (both universal and existential) as well as recursive types.
In a second part, we show how to interpret the untyped calculus; after equipping the domain of the interpretation with an ordering --- the liveness ordering --- loosely inspired from implication on process specifications, we show how our interpretation is both sound and computationally adequate.
In a third part, we introduce a notion of game which we use for interpreting types, and show how the liveness ordering on games is suitable for interpreting subtyping. Finally, we prove that under the (unproved) assumption that recursive types are compatible with quantification, our interpretation is sound with respect to both subtyping and typing
A Type System for First-Class Layers with Inheritance, Subtyping, and Swapping
Context-Oriented Programming (COP) is a programming paradigm to encourage
modularization of context-dependent software. Key features of COP are
layers---modules to describe context-dependent behavioral variations of a
software system---and their dynamic activation, which can modify the behavior
of multiple objects that have already been instantiated. Typechecking programs
written in a COP language is difficult because the activation of a layer can
even change objects' interfaces. Inoue et al. have informally discussed how to
make JCop, an extension of Java for COP by Appeltauer et al., type-safe.
In this article, we formalize a small COP language called ContextFJ
with its operational semantics and type system and show its type soundness. The
language models main features of the type-safe version of JCop, including
dynamically activated first-class layers, inheritance of layer definitions,
layer subtyping, and layer swapping
Dinaturality Meets Genericity: A Game Semantics of Bounded Polymorphism
We study subtyping and parametric polymorphism, with the aim of providing direct and tractable semantic representations of type systems with these expressive features. The liveness order uses the Player-Opponent duality of game semantics to give a simple representation of subtyping: we generalize it to include graphs extracted directly from second-order intuitionistic types, and use the resulting complete lattice to interpret bounded polymorphic types in the style of System F_<:, but with a more tractable subtyping relation.
To extend this to a semantics of terms, we use the type-derived graphs as arenas, on which strategies correspond to dinatural transformations with respect to the canonical coercions ("on the nose" copycats) induced by the liveness ordering. This relationship between the interpretation of generic and subtype polymorphism thus provides the basis of the semantics of our type system
Value Types in Eiffel
Identifies a number of problems with Eiffel's expanded types in modelling value types, and proposes a backward compatible syntactic extension, and a modified semantics. The latter is also shown to be (effectively) backward compatible, in the sense that existing programs would run unaffected if compilers implemented the new semantics. The benefits of the approach are discussed, including an elegant approach to rebuilding data structure libraries
Liquid Intersection Types
We present a new type system combining refinement types and the
expressiveness of intersection type discipline. The use of such features makes
it possible to derive more precise types than in the original refinement
system. We have been able to prove several interesting properties for our
system (including subject reduction) and developed an inference algorithm,
which we proved to be sound.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
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