Gradual typing is a discipline for integrating dynamic checking into a static type system. Since its introduction in functional languages, it has been adapted to a variety of type systems, including objectoriented, security, and substructural. This work studies its application to implicitly typed languages based on type inference. Siek and Vachharajani designed a gradual type inference system and algorithm that infers gradual types but still rejects ill-typed static programs. However, the type system requires local reasoning about type substitutions, an imperative inference algorithm, and a subtle correctness statement.This paper introduces a new approach to gradual type inference, driven by the principle that gradual inference should only produce static types. We present a static implicitly typed language, its gradual counterpart, and a type inference procedure. The gradual system types the same programs as Siek and Vachharajani, but has a modular structure amenable to extension. The language admits letpolymorphism, and its dynamics are defined by translation to the Polymorphic Blame Calculus (Ahmed et al. 2009(Ahmed et al. , 2011.The principal types produced by our initial type system mask the distinction between static parametric polymorphism and polymorphism that can be attributed to gradual typing. To expose this difference, we distinguish static type parameters from gradual type parameters and reinterpret gradual type consistency accordingly. The resulting extension enables programs to be interpreted using either the polymorphic or monomorphic Blame Calculi.

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Many languages are beginning to integrate dynamic and static typing. Siek and Taha offered gradual typing as an approach to this integration that provides a coherent and full-span migration between the two disciplines. However, the literature lacks a general methodology for designing gradually typed languages. Our first contribution is to provide a methodology for deriving the gradual type system and the compilation to the cast calculus. Based on this methodology, we present the Gradualizer, an algorithm that generates a gradual type system from a well-formed type system and also generates a compiler to the cast calculus. Our algorithm handles a large class of type systems and generates systems that are correct with respect to the formal criteria of gradual typing. We also report on an implementation of the Gradualizer that takes a type system expressed in lambda-prolog and outputs its gradually typed version and a compiler to the cast calculus in lambda-prolog.

In this paper we propose an extension of the Rebeca language that can be used to model distributed and asynchronous systems with timing constraints. We provide the formal semantics of the language using Structural Operational Semantics, and show its expressiveness by means of examples. We developed a tool for automated translation from timed Rebeca to the Erlang language, which provides a first implementation of timed Rebeca. We can use the tool to set the parameters of timed Rebeca models, which represent the environment and component variables, and use McErlang to run multiple simulations for different settings. Timed Rebeca restricts the modeller to a pure asynchronous actor-based paradigm, where the structure of the model represents the service oriented architecture, while the computational model matches the network infrastructure. Simulation is shown to be an effective analysis support, specially where model checking faces almost immediate state explosion in an asynchronous setting.

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