Related papers: On Complete Categorical Semantics for Effect Handl…
We describe a number of experiments that demonstrate the usefulness of prosodic information for a processing module which parses spoken utterances with a feature-based grammar employing empty categories. We show that by requiring certain…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is a hybrid classical-quantum computational paradigm. The…
The nonstandard approach to program semantics has successfully resolved the completeness problem of Floyd-Hoare logic. The known versions of nonstandard semantics, the Hungary semantics and axiomatic semantics, are so general that they are…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to…
Distributional semantics has had enormous empirical success in Computational Linguistics and Cognitive Science in modeling various semantic phenomena, such as semantic similarity, and distributional models are widely used in…
Transformer-based language models are effective but complex, and understanding their inner workings and reasoning mechanisms is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name…
Traditional category theory is typically based on set-theoretic principles and ideas, which are often non-constructive. An alternative approach to formalizing category theory is to use E-category theory, where hom sets become setoids. Our…
Types-and-effects are type systems, which allow one to express general semantic properties and to statically reason about program's execution. They have been widely exploited to specify static analyses, for example to track computational…
The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…