Related papers: Homotopy Type Theory in Isabelle
We introduce Open Horn Type Theory (OHTT), an extension of dependent type theory with two primitive judgment forms: coherence and gap, subject to a mutual exclusion law. Unlike classical or intuitionistic negation, gap is not defined via…
Some advantages of Cubical Type Theory, as implemented by Cubical Agda, over intensional Martin-L\"of Type Theory include Quotient Inductive Types (QITs), which exist as instances of Higher Inductive Types, and functional extensionality,…
When working in Homotopy Type Theory and Univalent Foundations, the traditional role of the category of sets, Set, is replaced by the category hSet of homotopy sets (h-sets); types with h-propositional identity types. Many of the properties…
This is an introduction to Homotopy Type Theory and Univalent Foundations for philosophers, written as a chapter for the book "Categories for the Working Philosopher" (ed. Elaine Landry)
Formal programming language semantics are imperative when trying to verify properties of programs in an automated manner. Using a new approach, Din et al. strengthen the ability of reasoning about concurrent programs by proposing a modular…
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…
Multi-hop reasoning requires aggregating multiple documents to answer a complex question. Existing methods usually decompose the multi-hop question into simpler single-hop questions to solve the problem for illustrating the explainable…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution…
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
We present a new way to control the unfolding of definitions in dependent type theory. Traditionally, proof assistants require users to fix whether each definition will or will not be unfolded in the remainder of a development; unfolding…
This is the first installment of a series of papers whose aim is to lay a foundation for homotopy probability theory by establishing its basic principles and practices. The notion of a homotopy probability space is an enrichment of the…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
In systems verification we are often concerned with multiple, inter-dependent properties that a program must satisfy. To prove that a program satisfies a given property, the correctness of intermediate states of the program must be…
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…