相关论文: The Agda Universal Algebra Library, Part 1: Founda…

We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…

In literature, NAND and NOR are two logic gates that display functional completeness, hence regarded as Universal gates. So, the present effort is focused on exploring a library of universal gates in binary that are still unexplored in…

This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these…

Nominal techniques provide a mathematically principled approach to dealing with names and variable binding in programming languages. This paper explores an attempt to make nominal techniques accessible as an Agda library. We aim for a…

The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…

As an example of empirical metamathematics, we present a detailed study of the dependency structure of the 465 theorems in Euclid's Elements, finding empirical signatures of concepts such as the power of a theorem. We apply similar methods…

Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…

The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…

Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…

Logical frameworks can be used to translate proofs from a proof system to another one. For this purpose, we should be able to encode the theory of the proof system in the logical framework. The Lambda Pi calculus modulo theory is one of…

Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a…

For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie algebras. More generally, for n even and any (n+1)-dimensional n-Lie algebra L, we construct a universal associative enveloping…

This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…

We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…

In this work we will study the universal labeling algebra A(Gamma), a related algebra B(Gamma), and their behavior as invariants of layered graphs. We will introduce the notion of an upper vertex-like basis, which allows us to recover…

Nested datatypes have been widely studied in the past 25 years, both theoretically using category theory, and practically in programming languages such as Haskell. They consist in recursive polymorphic datatypes where the type parameter…

Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…