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In this paper, we introduce DeLaM, a dependent layered modal type theory which enables meta-programming in Martin-Löf type theory (MLTT) with recursion principles on open code. DeLaM includes three layers: the layer of static syntax objects of MLTT ...

Type soundness, which asserts that “well-typed programs cannot go wrong,” is widely viewed as the canonical theorem one must prove to establish that a type system is doing its job. It is commonly proved using the so-called syntactic approach (also known ...

The Application Binary Interface (ABI) for a language defines the interoperability rules for its target platforms, including data layout and calling conventions, such that compliance with the rules ensures “safe” execution and perhaps certain resource ...

In gradual typing, different languages perform different dynamic type checks for the same program even though the languages have the same static type system. This raises the question of whether, given a gradually typed language, the combination of the ...

Parametricity is a property of the syntax of type theory implying, e.g., that there is only one function having the type of the polymorphic identity function. Parametricity is usually proven externally, and does not hold internally. Internalising it is ...

A program is said to be well-bracketed if every called function must return before its caller can resume execution. This is often the case. Well-bracketedness has been captured semantically as a condition on strategies in fully abstract games models and ...

We present guarded interaction trees — a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Coq, inspired by domain theory and the recently proposed interaction trees. We also present an ...

Interoperability pervades nearly all mainstream language implementations, as most systems leverage subcomponents written in different languages. And yet, such linking can expose a language to foreign behaviors that are internally inexpressible, which ...

To ensure programs do not leak private data, we often want to be able to provide formal guarantees ensuring such data is handled correctly. Often, we cannot keep such data secret entirely; instead programmers specify how private data may be declassified. ...

Optimizing the expected values of probabilistic processes is a central problem in computer science and its applications, arising in fields ranging from artificial intelligence to operations research to statistical computing. Unfortunately, automatic ...

Verifying soundness of symbolic execution-based program verifiers is a significant challenge. This is especially true if the resulting tool needs to be usable outside of the proof assistant, in which case we cannot rely on shallowly embedded assertion ...

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming, and fully ...

Programs are rarely implemented in a single language, and thus questions of type soundness should address not only the semantics of a single language, but how it interacts with others. Even between type-safe languages, disparate features can frustrate ...

Metareasoning can be achieved in probabilistic programming languages (PPLs) using agent models that recursively nest inference queries inside inference queries. However, the semantics of this powerful, reflection-like language feature has defied an ...

In this paper we present a novel simulation relation for proving correctness of program transformations that combines syntactic simulations and logical relations. In particular, we establish a new kind of simulation diagram that uses a small-step or big-...

The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction, computational effects, ...

Compositional compiler verification is a difficult problem that focuses on separate compilation of program components with possibly different verified compilers. Logical relations are widely used in proving correctness of program transformations in ...

Step-indexed logical relations are an extremely useful technique for building operational-semantics-based models and program logics for realistic, richly-typed programming languages. They have proven to be indispensable for modeling features like higher-...

The metatheory of Scala’s core type system—the Dependent Object Types (DOT) calculus—is hard to extend, like the metatheory of other type systems combining subtyping and dependent types. Soundness of important Scala features therefore remains an open ...

Information Flow Control (IFC) is a form of dependence analysis that tracks and prohibits dependence of public outputs on secret inputs. Such a dependence analysis is often carried out using a type system. IFC type systems can track dependence (via ...