Related papers: Type Universes as Allocation Effects
In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the…
We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
A heap is a structure with a ternary operation which is intuitively a group with forgotten unit element. Quantum heaps are associative algebras with a ternary cooperation which are to the Hopf algebras what heaps are to groups, and, in…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the {\em universal memory architecture}…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
Multi-hop reasoning over real-life knowledge graphs (KGs) is a highly challenging problem as traditional subgraph matching methods are not capable to deal with noise and missing information. To address this problem, it has been recently…
We study how large language models (LLMs) reason about memorized knowledge through simple binary relations such as equality ($=$), inequality ($<$), and inclusion ($\subset$). Unlike in-context reasoning, the axioms (e.g., $a < b, b < c$)…
This paper introduces a type system for resource management in the context of nested virtualization. With nested virtualization, virtual machines compete with other processes for the resources of their host environment in order to provision…
We present a formal analysis of Douglas Hofstadter's concept of \emph{superrationality}. We start by defining superrationally justifiable actions, and study them in symmetric games. We then model the beliefs of the players, in a way that…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We extend resource-bounded type theory to Martin-Lof type theory (MLTT) with dependent types, enabling size-indexed cost bounds for programs over inductive families. We introduce a resource-indexed universe hierarchy U_r where r is an…
We take a utility-based approach to categorization. We construct generalizations about events and actions by considering losses associated with failing to distinguish among detailed distinctions in a decision model. The utility-based…
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…
Many of the essential features of the evolution of scientific research are imprinted in the structure of citation networks. Connections in these networks imply information about the transfer of knowledge among papers, or in other words,…
Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
The specifics of data layout can be important for the efficiency of functional programs and interaction with external libraries. In this paper, we develop a type-theoretic approach to data layout that could be used as a typed intermediate…
We present $\lambda_B$, a quantum-control $\lambda$-calculus that refines previous basis-sensitive systems by allowing abstractions to be expressed with respect to arbitrary -- possibly entangled -- bases. Each abstraction and let construct…