Related papers: Metacat: a categorical framework for formal system…
We introduces a category-theoretic framework for modelling trust as applied to trusted computation systems and remote attestation. By formalizing elements, claims, results, and decisions as objects within a category, and the processes of…
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
Weak $\infty$-categories are known to be more expressive than their strict counterparts, but are more difficult to work with, as constructions in such a category involve the manipulation of explicit coherence data. This motivates the search…
As the usage of theorem prover technology expands, so too does the reliance on correctness of the tools. Metamath Zero is a verification system that aims for simplicity of logic and implementation, without compromising on efficiency of…
The paper gives a detailed presentation of a framework, embedded into the simply typed higher-order logic and aimed at the support of sound and structured reasoning about various properties of models of imperative programs with interleaved…
We define a model of predicate logic in which every term and predicate, open or closed, has an absolute denotation independently of a valuation of the variables. For each variable a, the domain of the model contains an element [[a]] which…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw,…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
In this paper we adapt the definitions and results from Apt and Vermeulen on `First order logic as a constraint programming language' (in: Proceedings of LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important ideas…
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
We introduce the framework of AECats (abstract elementary categories), generalising both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory ("cat", as introduced…