Related papers: A Recipe for State-and-Effect Triangles
We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…
We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…
Soundness and completeness with respect to equational theories for programming languages are fundamental properties in the study of categorical semantics. However, completeness results have not been established for programming languages…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
In most contemporary approaches to decision making, a decision problem is described by a sets of states and set of outcomes, and a rich set of acts, which are functions from states to outcomes over which the decision maker (DM) has…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the…
Model-checking is one of the most powerful techniques for verifying systems and programs, which since the pioneering results by Knapik et al., Ong, and Kobayashi, is known to be applicable to functional programs with higher-order types…
We investigate the phenomenon that "every monad is a linear state monad". We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value…
G. Plotkin and the author have worked out the equivalence between state transformer semantics and predicate transformer semantics in a domain theoretical setting for programs combining nondeterminism and probability. Works of C. Morgan and…
In the paper we introduce graphical objects (called state diagrams) related to functional programs. It is shown that state diagrams of functional programs can be used to solve problems of verification of functional programs. The proposed…
Monads provide a simple and concise interface to user-defined computational effects in functional programming languages. This enables equational reasoning about effects, abstraction over monadic interfaces and the development of monad…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
In this paper we propose a logic-based, framework inspired by artificial intelligence, but scaled down for practical database and programming applications. Computation in the framework is viewed as the task of generating a sequence of state…
This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…
This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…
Writers generally rely on plans or sketches to write long stories, but most current language models generate word by word from left to right. We explore coarse-to-fine models for creating narrative texts of several hundred words, and…