1,549 research outputs found
Really Natural Linear Indexed Type Checking
Recent works have shown the power of linear indexed type systems for
enforcing complex program properties. These systems combine linear types with a
language of type-level indices, allowing more fine-grained analyses. Such
systems have been fruitfully applied in diverse domains, including implicit
complexity and differential privacy. A natural way to enhance the
expressiveness of this approach is by allowing the indices to depend on runtime
information, in the spirit of dependent types. This approach is used in DFuzz,
a language for differential privacy. The DFuzz type system relies on an index
language supporting real and natural number arithmetic over constants and
variables. Moreover, DFuzz uses a subtyping mechanism to make types more
flexible. By themselves, linearity, dependency, and subtyping each require
delicate handling when performing type checking or type inference; their
combination increases this challenge substantially, as the features can
interact in non-trivial ways. In this paper, we study the type-checking problem
for DFuzz. We show how we can reduce type checking for (a simple extension of)
DFuzz to constraint solving over a first-order theory of naturals and real
numbers which, although undecidable, can often be handled in practice by
standard numeric solvers
Applied Type System: An Approach to Practical Programming with Theorem-Proving
The framework Pure Type System (PTS) offers a simple and general approach to
designing and formalizing type systems. However, in the presence of dependent
types, there often exist certain acute problems that make it difficult for PTS
to directly accommodate many common realistic programming features such as
general recursion, recursive types, effects (e.g., exceptions, references,
input/output), etc. In this paper, Applied Type System (ATS) is presented as a
framework for designing and formalizing type systems in support of practical
programming with advanced types (including dependent types). In particular, it
is demonstrated that ATS can readily accommodate a paradigm referred to as
programming with theorem-proving (PwTP) in which programs and proofs are
constructed in a syntactically intertwined manner, yielding a practical
approach to internalizing constraint-solving needed during type-checking. The
key salient feature of ATS lies in a complete separation between statics, where
types are formed and reasoned about, and dynamics, where programs are
constructed and evaluated. With this separation, it is no longer possible for a
program to occur in a type as is otherwise allowed in PTS. The paper contains
not only a formal development of ATS but also some examples taken from
ats-lang.org, a programming language with a type system rooted in ATS, in
support of employing ATS as a framework to formulate advanced type systems for
practical programming
Session Types in a Linearly Typed Multi-Threaded Lambda-Calculus
We present a formalization of session types in a multi-threaded
lambda-calculus (MTLC) equipped with a linear type system, establishing for the
MTLC both type preservation and global progress. The latter (global progress)
implies that the evaluation of a well-typed program in the MTLC can never reach
a deadlock. As this formulated MTLC can be readily embedded into ATS, a
full-fledged language with a functional programming core that supports both
dependent types (of DML-style) and linear types, we obtain a direct
implementation of session types in ATS. In addition, we gain immediate support
for a form of dependent session types based on this embedding into ATS.
Compared to various existing formalizations of session types, we see the one
given in this paper is unique in its closeness to concrete implementation. In
particular, we report such an implementation ready for practical use that
generates Erlang code from well-typed ATS source (making use of session types),
thus taking great advantage of the infrastructural support for distributed
computing in Erlang.Comment: This is the original version of the paper on supporting programming
with dyadic session types in AT
Combining type checking with model checking for system verification
Type checking is widely used in mainstream programming languages to detect programming errors at compile time. Model checking is gaining popularity as an automated technique for systematically analyzing behaviors of systems. My research focuses on combining these two software verification techniques synergically into one platform for the creation of correct models for software designs.
This thesis describes two modeling languages ATS/PML and ATS/Veri that inherit the advanced type system from an existing programming language ATS, in which both dependent types of Dependent ML style and linear types are supported. A detailed discussion is given for the usage of advanced types to detect modeling errors at the stage of model construction. Going further, various modeling primitives with well-designed types are introduced into my modeling languages to facilitate a synergic combination of type checking with model checking.
The semantics of ATS/PML is designed to be directly rooted in a well-known modeling language PROMELA. Rules for translation from ATS/PML to PROMELA are designed and a compiler is developed accordingly so that the SPIN model checker can be readily employed to perform checking on models constructed in ATS/PML. ATS/Veri is designed to be a modeling language, which allows a programmer to construct models for real-world multi-threaded software applications in the same way as writing a functional program with support for synchronization, communication, and scheduling among threads. Semantics of ATS/Veri is formally defined for the development of corresponding model checkers and a compiler is built to translate ATS/Veri into CSP# and exploit the state-of-the-art verification platform PAT for model checking ATS/Veri models. The correctness of such a transformational approach is illustrated based on the semantics of ATS/Veri and CSP#.
In summary, the primary contribution of this thesis lies in the creation of a family of modeling languages with highly expressive types for modeling concurrent software systems as well as the related platform supporting verification via model checking. As such, we can combine type checking and model checking synergically to ensure software correctness with high confidence
Session types in practical programming
Programs are more distributed and concurrent today than ever before, and structural communications are at the core. Constructing and debugging such programs are hard due to the lack of formal specifications and verifications of concurrency. Recent advances in type systems allow us to specify the structures of communications as session types, thus enabling static type checking of the usages of communication channels against protocols. The soundness of session type systems implies communication fidelity and absence of deadlock. This work proposes to formalize multiparty dependent session types as an expressive and practical type discipline for enforcing communication protocols. The type system is formulated in the setting of multi-threaded λ-calculus with inspirations from multirole logic. It is sound, and it provides linearity and coherence guarantees entirely statically. The type system supports recursion and polymorphism. The formulation is particularly suitable for practical implementation, and this work provides such a runtime implementation
Linearly Typed Dyadic Group Sessions for Building Multiparty Sessions
Traditionally, each party in a (dyadic or multiparty) session implements
exactly one role specified in the type of the session. We refer to this kind of
session as an individual session (i-session). As a generalization of i-session,
a group session (g-session) is one in which each party may implement a group of
roles based on one channel. In particular, each of the two parties involved in
a dyadic g-session implements either a group of roles or its complement. In
this paper, we present a formalization of g-sessions in a multi-threaded
lambda-calculus (MTLC) equipped with a linear type system, establishing for the
MTLC both type preservation and global progress. As this formulated MTLC can be
readily embedded into ATS, a full-fledged language with a functional
programming core that supports both dependent types (of DML-style) and linear
types, we obtain a direct implementation of linearly typed g-sessions in ATS.
The primary contribution of the paper lies in both of the identification of
g-sessions as a fundamental building block for multiparty sessions and the
theoretical development in support of this identification.Comment: This paper can be seen as the pre-sequel to classical linear
multirole logic (CLML). arXiv admin note: substantial text overlap with
arXiv:1603.0372
Strong normalization for System F by HOAS on top of FOAS
We present a point of view concerning HOAS (Higher-Order Abstract Syntax) and an extensive exercise in HOAS along this point of view. The point of view is that HOAS can be soundly and fruitfully regarded as a definitional extension on top of FOAS (First-Order Abstract Syntax). As such, HOAS is not only an encoding technique, but also a higher-order view of a first-order reality. A rich collection of concepts and proof principles is developed inside the standard mathematical universe to give technical life to this point of view. The exercise consists of a new proof of Strong Normalization for System F. The concepts and results presented here have been formalized in the theorem prover Isabelle/HOL
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