Proofs and types

Types for Proofs and Programs

Proofs for “Integrating Dependent and Linear Types”

The basic approach of this paper is to build a realizability model of dependent LNL in the style of Harper [4]. Essentially, we give an untyped operational semantics for the language, and then construct a PER for the syntactic types, and a function mapping each semantic type to a PER giving the equality relation for that type. For linear types, we give a map from semantic types to a map from mo...

Gradual Refinement Types Extended Version with Proofs

Refinement types are an effective language-based verification technique. However, as any expressive typing discipline, its strength is its weakness, imposing sometimes undesired rigidity. Guided by abstract interpretation, we extend the gradual typing agenda and develop the notion of gradual refinement types, allowing smooth evolution and interoperability between simple types and logicallyrefin...

Modular Type-Safety Proofs using Dependant Types

While methods of code abstraction and reuse are widespread and well researched, methods of proof abstraction and reuse are still emerging. We consider the use of dependent types for this purpose, introducing a completely mechanical approach to proof composition. We show that common techniques for abstracting algorithms over data structures naturally translate to abstractions over proofs. We fir...

: examining l2 teachers’ corrective feedback types in relation to learners’ uptake, proficiency levels, and context types

abstract this study investigates the teachers’ correction of students’ spoken errors of linguistic forms in efl classes, aiming at (a) examining the relationship between the learners’ proficiency level and the provision of corrective feedback types, (b) exploring the extent to which teachers’ use of different corrective feedback types is related to the immediate types of context in which err...