Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 23 for “"Theorem Provers"”.
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Interactive theorem provers: issues faced as a user and tackled as a developer
Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a …
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Compiling Haskell into Lean: A Common Abstract Syntax for Haskell and Interactive Theorem Provers
… and executable Lean code that users can prove theorems about. We conducted a case study using a heap sort algorithm to support our claim that HS-TO-LEAN produces verifiable Lean code. Our approach is inspired by recent advances in formal verification of Haskell programs in Coq, and we currently …
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TEMPLAR : efficient determination of relevant axioms in big formula sets for theorem proving
… selection system for classical first order theorem proving based on the relevance of formulae for the proof of a conjecture. It is based on unifiability of predicates and is also able to use a linguistic approach for the selection. The scope of the technique is the reduction of the set of …
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An analysis and implementation of linear derivation strategies
… the ME -TP, SL-TP, GC-TP, SLM-TP and SLM5-TP theorem provers respectively. In addition to the original features of each derivation strategy, the following search strategies were included in the implementations : the modified consecutively bounded depth-first search unit preference strategy, …
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Language models for verifiable mathematical automation: Interaction, integration, and autoformalization
… those scenarios with assistance from automated theorem provers, and use them to translate mathematical theorems and proofs from LATEX to formal languages. Concretely, (1) We conduct the first interactive evaluation of language models on informal mathematical reasoning. The evaluation reveals …
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Theorem proving with the real numbers
… thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of …
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Theorem-proving distributed algorithms with dynamic analysis
Theorem provers are notoriously hard to use because of the amount of human interaction they require, but they are important tools that can verify infinite state distributed systems. We present a method to make theorem-proving safety properties of distributed algorithms more productive by reducing …
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User interaction widgets for interactive theorem proving
… means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive …
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Magpy: A Python Package for Magmas
… such as interactive and automated theorem provers, finite counter-example generators, and computer algebra systems, most of which have a complicated installation process, unintuitive syntax, a lack of comprehensiveness for mathematical structures, or some combination of these. …
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Prototyping a Scalable Proof Engine
… process of verifying large programs in popular theorem provers such as Coq (now known as Rocq) or Lean is painfully slow. These proof assistants rely on proof engines to construct proofs of correctness for given properties, but to our knowledge, there is no widely available proof engine that …
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An Efficient Data Structure for Implementing Splitter Hyperobjects in Task-Parallel Systems
… expensive applications, such as SAT solvers, theorem provers, and game-playing programs. This thesis also contains theory and implementation work on other topics related to task-parallel programming and work stealing schedulers. Some parts of this thesis represent joint work with William …
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Reasoning about knowledge using extensional logics
… cannot be drawn. Standard first-order theorem provers (like Prolog) can then be used to solve problems which involve reasoning about knowledge
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Modular data structure verification
… approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to …
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Foundational Verification of Running-Time Bounds for Interactive Programs
… via traditional static analysis to powerful theorem provers that can express very precise specifications. It is sometimes desirable to prove properties about programs that make reference to not just semantic behavior but also to other metaproperties of the program’s execution, such as runtime …
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Verification of full functional correctness for imperative linked data structures
… automated reasoning systems-automated theorem provers, decision procedures, and program analyses-that work together to prove the verification conditions that the system automatically generates. Our proof language enables the developer to direct the efforts of these automated reasoning …
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Predicting SMT solver performance for software verification
… with a wide variety of interactive and automatic theorem provers works well: it is designed to overcome limitations on what can be proved by a system which relies on a single tightly-integrated solver. In common with other systems, however, the degree to which proof obligations (or “goals”) are …
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Relational compilation: Functional-to-imperative code generation for performance-critical applications
… functional programs verified using interactive theorem provers typically need to be translated to run: either by extracting them to a similar language (like Coq to OCaml) or by proving them equivalent to deeply embedded implementations (like C programs). Traditionally, the first approach is …
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Towards justifying computer algebra algorithms in Isabelle/HOL
As verification efforts using interactive theorem proving grow, we are in need of certified algorithms in computer algebra to tackle problems over the real numbers. This is important because uncertified procedures can drastically increase the size of the trust base and under- mine the overall …
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Safety cases for the formal verification of automatically generated code
… automatically generated code, based on automated theorem proving, and driven by a set of safety requirements and properties. We also present an approach to systematically derive safety cases that argue along the hierarchical structure of systems in model-based development. This core safety case is …
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Rewriting Prover9
Prover9/Mace4 were the most popular automated theorem provers (ATP) among mathematicians. They had a number of peculiarities that made them especially helpful for research and for teaching. When their author, Bill McCune, died the programs’ destiny was sealed and that was a great loss for many …
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