Step-Indexed Normalization for a Language with General Recursion

The Trellys project has produced several designs for practical dependently typed languages. These languages are broken into two fragments-a_logical_fragment where every term normalizes and which is consistent when interpreted as a logic, and a_programmatic_fragment with general recursion and other convenient but unsound features. In this paper, we present a small example language in this style. Our design allows the programmer to explicitly mention and pass information between the two fragments. We show that this feature substantially complicates the metatheory and present a new technique, combining the traditional Girard-Tait method with step-indexed logical relations, which we use to show normalization for the logical fragment.Comment: In Proceedings MSFP 2012, arXiv:1202.240

Proving termination of evaluation for System F with control operators

We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of Girard's proof method based on reducibility candidates, where the reducibility predicates are defined on values and on evaluation contexts as prescribed by the reduction semantics format. We address both abortive control operators (callcc) and delimited-control operators (shift and reset) for which we introduce novel polymorphic type systems, and we consider both the call-by-value and call-by-name evaluation strategies.Comment: In Proceedings COS 2013, arXiv:1309.092

Translating Generalized Algebraic Data Types to System F

Generalized algebraic data types (GADTs) extend ordinary algebraic data types by refining the types of constructors with syntactic equality constraints. This is highly useful and allows for novel applications such as strongly-typed evaluators, typed LR parsing etc. To translate GADTs we need to enrich the System F style typed intermediate languages of modern language implementations to capture these equality constraints. We show that GADTs can be translated to a minor extension of System F where type equality proofs are compiled into System F typable proof terms. At run-time proof terms evaluate to the identity. Hence, they can be safely erased before execution of the program. We provide evidence that our approach scales to deal with extensions where equality is not anymore syntactic. The benefit of our method is that type checking of target programs remains as simple as type checking in System F. Thus, we can offer a light-weight approach to integrate GADTs and extensions of it into existing implementations

A formal soundness proof of region-based memory management for object-oriented paradigm.

Region-based memory management has been proposed as a viable alternative to garbage collection for real-time applications and embedded software. In our previous work we have developed a region type inference algorithm that provides an automatic compile-time region-based memory management for object-oriented paradigm. In this work we present a formal soundness proof of the region type system that is the target of our region inference. More precisely, we prove that the object-oriented programs accepted by our region type system achieve region-based memory management in a safe way. That means, the regions follow a stack-of-regions discipline and regions deallocation never create dangling references in the store and on the program stack. Our contribution is to provide a simple syntactic proof that is based on induction and follows the standard steps of a type safety proof. In contrast the previous safety proofs provided for other region type systems employ quite elaborate techniques

A WSDL-Based Type System for WS-BPEL

We tackle the problem of providing rigorous formal foundations to current software engineering technologies for web services. We focus on two of the most used XML-based languages for web services: WSDL and WS-BPEL. To this aim, first we select an expressive subset of WS-BPEL, with special concern for modeling the interactions among web service instances in a network context, and define its operational semantics. We call ws-calculus the resulting formalism. Then, we put forward a rigorous typing discipline that formalizes the relationship existing between ws-calculus terms and the associated WSDL documents and supports verification of their compliance. We prove that the type system and the operational semantics of ws-calculus are ‘sound’ and apply our approach to an example application involving three interacting web services