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By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…
Concurrency theory has received considerable attention, but mostly in the scope of synchronous process algebras such as CCS, CSP, and ACP. As another way of handling concurrency, data-based coordination languages aim to provide a clear…
We establish a close connection between a reversible programming language based on type isomorphisms and a formally presented univalent universe. The correspondence relates combinators witnessing type isomorphisms in the programming…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Natural language processing for programming aims to use NLP techniques to assist programming. It is increasingly prevalent for its effectiveness in improving productivity. Distinct from natural language, a programming language is highly…
There is increasing interest within the research community in the design and use of recursive probability models. Although there still remains concern about computational complexity costs and the fact that computing exact solutions can be…
Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute…
In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…
This work introduces the novel concept of kind refinement, which we develop in the context of an explicitly polymorphic ML-like language with type-level computation. Just as type refinements embed rich specifications by means of…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
We study the problem of automated hypersafety verification of infinite-state recursive programs. We propose an infinite class of product programs, specifically designed with recursion in mind, that reduce the hypersafety verification of a…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
We show how security type systems from the literature of language-based noninterference can be represented more directly as predicates defined by structural recursion on the programs. In this context, we show how our uniform syntactic…
The "correct by construction" paradigm is an important component of modern Formal Methods, and here we use the probabilistic Guarded-Command Language $\mathit{pGCL}$ to illustrate its application to $\mathit{probabilistic}$ programming.…