An official website of the United States government
We present lambda_sym, a typed λ-calculus forlenient symbolic execution, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further addconcreteness polymorphism, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solver-aided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs.
more »
« less
A Dependent Dependency Calculus
Over twenty years ago, Abadi et al. established the Dependency Core Calculus (DCC) as a general purpose framework for analyzing dependency in typed programming languages. Since then, dependency analysis has shown many practical benefits to language design: its results can help users and compilers enforce security constraints, eliminate dead code, among other applications. In this work, we present a Dependent Dependency Calculus (DDC), which extends this general idea to the setting of a dependently-typed language. We use this calculus to track both run-time and compile-time irrelevance, enabling faster typechecking and program execution.
more »
« less
- PAR ID:
- 10318626
- Date Published:
- Journal Name:
- Lecture notes in computer science
- ISSN:
- 1611-3349
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In dependently-typed functional programming languages that allow general recursion, programs used as proofs must be evaluated to retain type soundness. As a result, programmers must make a trade-off between performance and safety. To address this problem, we propose System DE, an explicitly-typed, moded core calculus that supports termination tracking and equality reflection. Programmers can write inductive proofs about potentially diverging programs in a logical sublanguage and reflect those proofs to the type checker, while knowing that such proofs will be erased by the compiler before execution. A key feature of System DE is its use of modes for both termination and relevance tracking, which not only simplifies the design but also leaves it open for future extension. System DE is suitable for use in the Glasgow Haskell Compiler, but could serve as the basis for any general purpose dependently-typed language.more » « less
-
In the simply-typed lambda-calculus we can recover the full range of expressiveness of the untyped lambda-calculus solely by adding a single recursive type U = U -> U. In contrast, in the session-typed pi-calculus, recursion alone is insufficient to recover the untyped pi-calculus, primarily due to linearity: each channel just has two unique endpoints. In this paper, we show that shared channels with a corresponding sharing semantics (based on the language SILL_S developed in prior work) are enough to embed the untyped asynchronous pi-calculus via a universal shared session type U_S. We show that our encoding of the asynchronous pi-calculus satisfies operational correspondence and preserves observable actions (i.e., processes are weakly bisimilar to their encoding). Moreover, we clarify the expressiveness of SILL_S by developing an operationally correct encoding of SILL_S in the asynchronous pi-calculus.more » « less
-
In type systems with dependency tracking, programmers can assign an ordered set of levels to computations and prevent information flow from high-level computations to the low-level ones. The key notion in such systems isindistinguishability: a definition of program equivalence that takes into account the parts of the program that an observer may depend on. In this paper, we investigate the use of dependency tracking in the context of dependently-typed languages. We present the Dependent Calculus of Indistinguishability (DCOI), a system that adopts indistinguishability as the definition of equality used by the type checker. DCOI also internalizes that relation as an observer-indexed propositional equality type, so that programmers may reason about indistinguishability within the language. Our design generalizes and extends prior systems that combine dependency tracking with dependent types and is the first to support conversion and propositional equality at arbitrary observer levels. We have proven type soundness and noninterference theorems for DCOI and have developed a prototype implementation of its type checker.more » « less
-
Dependency analysis is vital to several applications in computer science. It lies at the essence of secure information flow analysis, binding-time analysis, etc. Various calculi have been proposed in the literature for analysing individual dependencies. Abadi et. al., by extending Moggi’s monadic metalanguage, unified several of these calculi into the Dependency Core Calculus (DCC). DCC has served as a foundational framework for dependency analysis for the last two decades. However, in spite of its success, DCC has its limitations. First, the monadic bind rule of the calculus is nonstandard and relies upon an auxiliary protection judgement. Second, being of a monadic nature, the calculus cannot capture dependency analyses that possess a comonadic nature, for example, the binding-time calculus, λ∘, of Davies. In this paper, we address these limitations by designing an alternative dependency calculus that is inspired by standard ideas from category theory. Our calculus is both monadic and comonadic in nature and subsumes both DCC and λ∘. Our construction explains the nonstandard bind rule and the protection judgement of DCC in terms of standard categorical concepts. It also leads to a novel technique for proving correctness of dependency analysis. We use this technique to present alternative proofs of correctness for DCC and λ∘.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-99336-8_15
