Related papers: A Monadic Framework for Interactive Realizability
We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…
Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a…
As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…
Most type systems that support polymorphic functions are based on a version of System-F. We argue that this limits useful programming paradigms for languages with lazy evaluation. We motivate an extension of System-F alleviating this…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
In functional programming, monads are supposed to encapsulate computations, effectfully producing the final result, but keeping to themselves the means of acquiring it. For various reasons, we sometimes want to reveal the internals of a…
Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
Existing human motion Q\&A methods rely on explicit program execution, where the requirement for manually defined functional modules may limit the scalability and adaptability. To overcome this, we propose an implicit program-guided motion…
The technique of "classical realizability" is an extension of the method of "forcing"; it permits to extend the Curry-Howard correspondence between proofs and programs, to Zermelo-Fraenkel set theory and to build new models of ZF, called…
Interpretability aims to explain the behavior of deep neural networks. Despite rapid growth, there is mounting concern that much of this work has not translated into practical impact, raising questions about its relevance and utility. This…
Existing reasoning evaluation paradigms suffer from different limitations: fixed benchmarks are increasingly saturated and vulnerable to contamination, while preference-based evaluations rely on subjective judgments. We argue that a core…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
Monadic programming presents a significant challenge for many programmers. In light of category theory, we offer a new perspective on the use of monads in functional programming. This perspective is clarified through numerous examples coded…
Monads have become a powerful tool for structuring effectful computations in functional programming, because they make the order of effects explicit. When translating pure code to a monadic version, we need to specify evaluation order…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages,…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
We study the algebraic effects and handlers as a way to support decision-making abstractions in functional programs, whereas a user can ask a learning algorithm to resolve choices without implementing the underlying selection mechanism, and…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…