Related papers: ProofCloud: A Proof Retrieval Engine for Verified …
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Proof-of-Work (PoW) is a popular blockchain consensus algorithm that is used in cryptocurrencies like Bitcoin in which hashing operations are repeated until the resulting hash has certain properties. This approach uses lots of computational…
This paper is a tutorial introducing the underlying technology and the use of the tool Liquid Haskell, a type-checker for the functional language Haskell that can help programmers to verify non-trivial properties of their programs with a…
We present DocPuzzle, a rigorously constructed benchmark for evaluating long-context reasoning capabilities in large language models (LLMs). This benchmark comprises 100 expert-level QA problems requiring multi-step reasoning over long…
Tabled evaluation is an implementation technique that solves some problems of traditional Prolog systems in dealing with recursion and redundant computations. Most tabling engines determine if a tabled subgoal will produce or consume…
We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
This paper explores the idea of using defunctionalization as a proof technique for higher-order programs. Defunctionalization builds on substituting functional values by a first-order representation. Thus, its interest is that one can use…
With the wide application of cloud storage, cloud security has become a crucial concern. Related works have addressed security issues such as data confidentiality and integrity, which ensure that the remotely stored data are well maintained…
Contemporary AI systems achieve extraordinary performance yet remain opaque and non-verifiable, creating a crisis of trust for safety-critical deployment. We introduce MathLedger, a substrate for verifiable machine cognition that integrates…
AI systems, in particular with deep learning techniques, have demonstrated superior performance for various real-world applications. Given the need for tailored optimization in specific scenarios, as well as the concerns related to the…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…
Recent advances in the cryptographic field of "Zero-Knowledge Proofs" have sparked a new wave of research, giving birth to many exciting theoretical approaches in the last few years. Such research has often overlapped with the need for…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit…
Recent developments in deep neural networks (DNNs) have led to their adoption in safety-critical systems, which in turn has heightened the need for guaranteeing their safety. These safety properties of DNNs can be proven using tools…
Search engines for equations now exist, which return results matching the query's mathematical meaning or structural presentation. Operating over scientific papers, online encyclopedias, and math discussion forums, their content includes…