作者: 梯田 時間: 2025-3-21 21:10
Reasoning About Algebraic Structures with Implicit Carriers in Isabelle/HOLctures in addition to reasoning in algebraic structures. We present an approach for this using classes and locales with implicit carriers. This involves using function liftings to implement some aspects of dependent types and using embeddings of algebras to inherit theorems. We also formalise a theory of filters based on partial orders.作者: gene-therapy 時間: 2025-3-22 04:15 作者: 使厭惡 時間: 2025-3-22 07:52
Andrew Kakabadse,Nada KakabadseThis paper describes the design of the normalising tactic . for the Lean prover. This tactic improves on existing tactics by extending commutative rings with a binary exponent operator. An inductive family of types represents the normal form, enforcing various invariants. The design can also be extended with more operators.作者: CYN 時間: 2025-3-22 09:28
https://doi.org/10.1057/978-1-349-94994-6A fundamental theorem states that every field admits an algebraically closed extension. Despite its central importance, this theorem has never before been formalised in a proof assistant. We fill this gap by documenting its formalisation in Isabelle/HOL, describing the difficulties that impeded this development and their solutions.作者: flimsy 時間: 2025-3-22 15:03 作者: Abrupt 時間: 2025-3-22 20:51 作者: 高調(diào) 時間: 2025-3-23 00:09
Algebraically Closed Fields in Isabelle/HOLA fundamental theorem states that every field admits an algebraically closed extension. Despite its central importance, this theorem has never before been formalised in a proof assistant. We fill this gap by documenting its formalisation in Isabelle/HOL, describing the difficulties that impeded this development and their solutions.作者: irreparable 時間: 2025-3-23 01:28
Formalization of Forcing in Isabelle/ZFWe formalize the theory of forcing in the set theory framework of Isabelle/ZF. Under the assumption of the existence of a countable transitive model of ., we construct a proper generic extension and show that the latter also satisfies .. In doing so, we remodularized Paulson’s . library.作者: 玩笑 時間: 2025-3-23 08:15 作者: HEAVY 時間: 2025-3-23 10:17
Control Dynamics of Human Metasystemsre general than any of the automation tactics natively available in Coq. It aims to handle as large a part of the Calculus of Inductive Constructions as practically feasible..For efficiency, our procedure is not complete for the entire Calculus of Inductive Constructions, but we prove completeness f作者: Pcos971 時間: 2025-3-23 15:05
Control Dynamics of Human Metasystemsuctive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and—under certain conditions—subtypes are known to preserve the BNF structure. In this paper, we tackle the preservation question for quoti作者: mercenary 時間: 2025-3-23 22:02 作者: 新字 時間: 2025-3-24 01:35
Global Commons in the Global Brain modify source code in large software projects. Consistent conventions in verification projects based on proof assistants, such as Coq, increase in importance as projects grow in size and scope. While conventions can be documented and enforced manually at high cost, emerging approaches automatically作者: NOMAD 時間: 2025-3-24 06:24
World-Systems Evolution and Global Futureserative programs from nondeterministic functional source code. Our approach does not require committing to a single inflexible compilation strategy and instead makes it straightforward to create domain-specific code translators. In addition to a small set of core definitions, our framework is a larg作者: Melodrama 時間: 2025-3-24 06:45
https://doi.org/10.1007/978-3-8349-4139-8en formalizing mathematics in proof assistants. The packed classes methodology is a generic design pattern to define and combine mathematical structures in a dependent type theory with records. When combined with mechanisms for implicit coercions and unification hints, packed classes enable automate作者: RACE 時間: 2025-3-24 14:09
https://doi.org/10.1007/978-3-8349-4139-8pts of a saturating theorem prover. The system is written in extensively commented Python, explaining data structures, algorithms, and many of the underlying theoretical concepts. The prover implements binary resolution with factoring and optional negative literal selection. Equality is handled by a作者: LEVY 時間: 2025-3-24 18:26
The Cambrian Explosion of Brands,s, but plays a critical role in developing reusable abstractions in libraries. Most ITPs support such extensions in the form of restrictive “syntax sugar” substitutions and other ad hoc mechanisms, which are too rudimentary to support many desirable abstractions. As a result, libraries are littered 作者: 容易懂得 時間: 2025-3-24 20:47
Organizational Structures for Global Brandsolyhedra in the proof assistant .. This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps. Moreover, we design a special mechanism which automatically introduces an appropriate re作者: occult 時間: 2025-3-25 00:21 作者: 昆蟲 時間: 2025-3-25 05:48
Global Britain and Neo-colonialism in Africaentity over the integers that is directly checked by polynomial division. Unlike other proofs, no preliminaries such as intersection numbers, Bézout’s theorem, projective geometry, divisors, or Riemann Roch are required. The proof of the group law has been formalized in the Isabelle/HOL proof assist作者: 偽書 時間: 2025-3-25 08:02
https://doi.org/10.1007/978-3-031-27769-6roblem exist. One is described independently by I.?A.?Farad?ev and R.?C.?Read and has since been applied to catalogue many different combinatorial structures. We present an Isabelle/HOL verification of this abstract scheme. To show its practicality, we instantiate it on two concrete problems: enumer作者: 抱狗不敢前 時間: 2025-3-25 13:56
Automated Reasoning978-3-030-51054-1Series ISSN 0302-9743 Series E-ISSN 1611-3349 作者: SEVER 時間: 2025-3-25 16:22 作者: 文字 時間: 2025-3-25 21:45 作者: 實(shí)施生效 時間: 2025-3-26 04:12
https://doi.org/10.1007/978-3-030-51054-1artificial intelligence; automata theory; automated reasoning; computer programming; formal languages; fo作者: atopic-rhinitis 時間: 2025-3-26 07:22 作者: 可忽略 時間: 2025-3-26 10:38 作者: Legion 時間: 2025-3-26 15:50 作者: MELD 時間: 2025-3-26 16:56
Competing Inheritance Paths in?Dependent Type Theory: A Case Study in Functional AnalysisMathematical Components library, geared towards algebra, with topics in analysis. Issues of a more general nature related to the inheritance of poorer structures from richer ones arise due to this combination. We present and discuss a solution, coined forgetful inheritance, based on packed classes and unification hints.作者: Minikin 時間: 2025-3-26 22:54 作者: 沐浴 時間: 2025-3-27 02:58
https://doi.org/10.1007/978-3-8349-4139-8e with packed classes, and propose algorithms to check these invariants. We implement our algorithms as tools for the . proof assistant, and show that they significantly improve the development process of ., a library for formalized mathematics.作者: TOM 時間: 2025-3-27 07:23 作者: vitreous-humor 時間: 2025-3-27 12:19 作者: 來自于 時間: 2025-3-27 16:35 作者: 摸索 時間: 2025-3-27 19:08
Control Dynamics of Human Metasystemsplugin and evaluated it on a collection of Coq libraries, on CompCert, and on the ILTP library of first-order intuitionistic problems. The results are promising and indicate the viablility of our approach to general automated proof search for the Calculus of Inductive Constructions.作者: 敵意 時間: 2025-3-28 00:38
Control Dynamics of Human Metasystemsre from its underlying type. We extend the Isabelle proof assistant with a command that automates the registration of a quotient type as a BNF by lifting the underlying type’s BNF structure. We demonstrate the command’s usefulness through several case studies.作者: 輪流 時間: 2025-3-28 04:34
World-Systems Evolution and Global Futuresadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.作者: 名次后綴 時間: 2025-3-28 09:37
https://doi.org/10.1007/978-3-8349-4139-8The prover can read TPTP CNF/FOF input files and produces TPTP/TSTP proof objects..Evaluation shows, as expected, mediocre performance compared to modern high-performance systems, with relatively better performance for problems without equality. However, the implementation seems to be sound and complete.作者: 夜晚 時間: 2025-3-28 13:13
Practical Proof Search for Coq by Type Inhabitationplugin and evaluated it on a collection of Coq libraries, on CompCert, and on the ILTP library of first-order intuitionistic problems. The results are promising and indicate the viablility of our approach to general automated proof search for the Calculus of Inductive Constructions.作者: 元音 時間: 2025-3-28 15:25
Quotients of Bounded Natural Functorsre from its underlying type. We extend the Isabelle proof assistant with a command that automates the registration of a quotient type as a BNF by lifting the underlying type’s BNF structure. We demonstrate the command’s usefulness through several case studies.作者: Outwit 時間: 2025-3-28 21:44 作者: 浮夸 時間: 2025-3-29 00:46
Teaching Automated Theorem Proving by Example: PyRes 1.2The prover can read TPTP CNF/FOF input files and produces TPTP/TSTP proof objects..Evaluation shows, as expected, mediocre performance compared to modern high-performance systems, with relatively better performance for problems without equality. However, the implementation seems to be sound and complete.作者: 隱藏 時間: 2025-3-29 06:03 作者: 決定性 時間: 2025-3-29 10:20
https://doi.org/10.1007/978-3-031-27769-6ating digraphs and enumerating union-closed families of sets. In the second example abstract algorithm specification is refined to an implementation that can quite efficiently enumerate all canonical union-closed families over a six element universe (there is more than 100 million such families).作者: aerial 時間: 2025-3-29 11:42
Global Commons in the Global Brainverage syntactic and semantic information from Coq ’s lexer (tokens in lemma statements), parser (syntax tree s), and kernel (elaborated terms) for naming; the key insight is that learning from elaborated terms can substantially boost model performance. We implemented our models in a toolchain, dubb作者: SPECT 時間: 2025-3-29 15:44 作者: Arbitrary 時間: 2025-3-29 20:54
The Cambrian Explosion of Brands,n a single, uniform system offering multiple abstraction levels that range from supporting simplest syntax sugars to elaboration of formerly baked-in syntax. We have implemented our new macro system and integrated it into the upcoming version (v4) of the Lean theorem prover. Despite its expressivity作者: 縮短 時間: 2025-3-30 00:36
Conference proceedings 2020eorem proving/ HOL; formalizations; verification; reasoning systems and tools.*The conference was held virtually due to the COVID-19 pandemic...Chapter ‘A Fast Verified Liveness Analysis in SSA Form’ is available open access under a Creative Commons Attribution 4.0 International License via link.spr作者: VEIL 時間: 2025-3-30 06:09 作者: 全部 時間: 2025-3-30 09:35 作者: hypnotic 時間: 2025-3-30 15:36
Extensible Extraction of Efficient Imperative Programs with Foreign Functions, Manually Managed Memol specifications to assembly code. In our main case study, the original specifications are phrased to resemble SQL-style queries, while the final assembly code does manual memory management, calls out to foreign data structures and functions, and is suitable to deploy on resource-constrained platfor作者: A簡潔的 時間: 2025-3-30 18:22 作者: Seminar 時間: 2025-3-30 23:49
Competing Inheritance Paths in?Dependent Type Theory: A Case Study in Functional Analysis dependent type theory. This hierarchy is the backbone of a new library of formalized classical analysis, for the Coq proof assistant. It extends the Mathematical Components library, geared towards algebra, with topics in analysis. Issues of a more general nature related to the inheritance of poorer作者: 一個攪動不安 時間: 2025-3-31 02:02
Practical Proof Search for Coq by Type Inhabitationre general than any of the automation tactics natively available in Coq. It aims to handle as large a part of the Calculus of Inductive Constructions as practically feasible..For efficiency, our procedure is not complete for the entire Calculus of Inductive Constructions, but we prove completeness f作者: guzzle 時間: 2025-3-31 08:28
Quotients of Bounded Natural Functorsuctive and coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class of well-behaved type constructors. Composition, fixpoints, and—under certain conditions—subtypes are known to preserve the BNF structure. In this paper, we tackle the preservation question for quoti作者: 鍵琴 時間: 2025-3-31 09:48
Trakhtenbrot’s Theorem in Coqand decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot’s theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof 作者: Friction 時間: 2025-3-31 14:22
Deep Generation of Coq Lemma Names Using Elaborated Terms modify source code in large software projects. Consistent conventions in verification projects based on proof assistants, such as Coq, increase in importance as projects grow in size and scope. While conventions can be documented and enforced manually at high cost, emerging approaches automatically作者: 榮幸 時間: 2025-3-31 20:59 作者: infringe 時間: 2025-3-31 23:11 作者: ARY 時間: 2025-4-1 03:17
Teaching Automated Theorem Proving by Example: PyRes 1.2pts of a saturating theorem prover. The system is written in extensively commented Python, explaining data structures, algorithms, and many of the underlying theoretical concepts. The prover implements binary resolution with factoring and optional negative literal selection. Equality is handled by a作者: Chronic 時間: 2025-4-1 08:38 作者: arousal 時間: 2025-4-1 10:44
Formalizing the Face Lattice of Polyhedraolyhedra in the proof assistant .. This builds on the formalization of a library providing the basic constructions and operations over polyhedra, including projections, convex hulls and images under linear maps. Moreover, we design a special mechanism which automatically introduces an appropriate re作者: 最初 時間: 2025-4-1 15:20 作者: gastritis 時間: 2025-4-1 21:35
