Related papers: A Monadic Framework for Interactive Realizability
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
The selection monad on a set consists of selection functions. These select an element from the set, based on a loss (dually, reward) function giving the loss resulting from a choice of an element. Abadi and Plotkin used the monad to model a…
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…
The remarkable performance of Multimodal Large Language Models (MLLMs) has unequivocally demonstrated their proficient understanding capabilities in handling a wide array of visual tasks. Nevertheless, the opaque nature of their black-box…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
This paper explores epistemic realizability, a form of realizability in which the property that a piece of data constitutes evidence for a logical proposition is semi-decidable. In this framework, each proposition A is assigned a verifier}…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
We introduce a monotone modal analogue of the intuitionistic (normal) modal logic IK using a translation into a suitable (intuitionistic) first-order logic. We axiomatise the logic and give a semantics by means of intuitionistic…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Modeling sequential and parallel composition of effectful computations has been investigated in a variety of languages for a long time. In particular, the popular do-notation provides a lightweight effect embedding for any instance of a…
This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…
Recently deep reinforcement learning has achieved tremendous success in wide ranges of applications. However, it notoriously lacks data-efficiency and interpretability. Data-efficiency is important as interacting with the environment is…
As practitioners increasingly deploy machine learning models in critical domains such as health care, finance, and policy, it becomes vital to ensure that domain experts function effectively alongside these models. Explainability is one way…
Recently, multimodal prompting, which introduces learnable missing-aware prompts for all missing modality cases, has exhibited impressive performance. However, it encounters two critical issues: 1) The number of prompts grows exponentially…