Related papers: A Domain-Theoretic Approach to Statistical Program…
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
Value-based static analysis techniques express computed program invariants as logical formula over program variables. Researchers and practitioners use these invariants to aid in software engineering and verification tasks. When selecting…
We give a commutative valuations monad Z on the category DCPO of dcpo's and Scott-continuous functions. Compared to the commutative valuations monads given in [Jia et al., 2021], our new monad Z is larger and it contains all push-forward…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
Gradually typed programming languages, which allow for soundly mixing static and dynamically typed programming styles, present a strong challenge for metatheorists. Even the simplest sound gradually typed languages feature at least…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this paper we present three such monads and a general…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
We introduce continuous $R$-valuations on directed-complete posets (dcpos, for short), as a generalization of continuous valuations in domain theory, by extending values of continuous valuations from reals to so-called Abelian d-rags $R$.…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
Domain theory has a long history of applications in theoretical computer science and mathematics. In this article, we explore the relation of domain theory to probability theory and stochastic processes. The goal is to establish a theory in…
Stochastic memoization is a higher-order construct of probabilistic programming languages that is key in Bayesian nonparametrics, a modular approach that allows us to extend models beyond their parametric limitations and compose them in an…
In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…