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A verified runtime for a verified theorem prover
"... rely on the correctness of runtime systems for programming languages like ML, OCaml or Common Lisp. These runtime systems are complex and critical to the integrity of the theorem provers. In this paper, we present a new Lisp runtime which has been formally verified and can run the Milawa theorem pro ..."
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rely on the correctness of runtime systems for programming languages like ML, OCaml or Common Lisp. These runtime systems are complex and critical to the integrity of the theorem provers. In this paper, we present a new Lisp runtime which has been formally verified and can run the Milawa theorem prover. Our runtime consists of 7,500 lines of machine code and is able to complete a 4 gigabyte Milawa proof effort. When our runtime is used to carry out Milawa proofs, less unverified code must be trusted than with any other theorem prover. Our runtime includes a justintime compiler, a copying garbage collector, a parser and a printer, all of which are HOL4verified down to the concrete x86 code. We make heavy use of our previously developed tools for machinecode verification. This work demonstrates that our approach to machinecode verification scales to nontrivial applications. 1
Steps Towards Verified Implementations of HOL Light
"... Abstract. This short paper describes our plans and progress towards construction of verified ML implementations of HOL Light: the first formally proved soundness result for an LCFstyle prover. Building on Harrison’s formalisation of the HOL Light logic and our previous work on proofproducing synth ..."
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Abstract. This short paper describes our plans and progress towards construction of verified ML implementations of HOL Light: the first formally proved soundness result for an LCFstyle prover. Building on Harrison’s formalisation of the HOL Light logic and our previous work on proofproducing synthesis of ML, we have produced verified implementations of each of HOL Light’s kernel functions. What remains is extending Harrison’s soundness proof and proving that ML’s module system provides the required abstraction for soundness of the kernel to relate to the entire theorem prover. The proofs described in this paper involve the HOL Light and HOL4 theorem provers and the OpenTheory toolchain. 1
A Condensed Semantics for Qualitative Spatial Reasoning About Oriented Straight Line Segments
"... More than 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new invest ..."
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More than 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations of dipole calculi. This new method, which we call condensed semantics, is based on an abstract symbolic model of a specific fragment of our domain. It is based on the fact that qualitative dipole relations are invariant under orientation preserving affine transformations. The dipole calculi allow for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraintbased reasoning capabilities of dipole calculi. We integrate our results into two reasoning tools which are publicly available. Keywords: Qualitative Spatial Reasoning, Relation Algebra, Affine Geometry
Formalizing a Proof that e is Transcendental
, 2011
"... We describe a HOL Light formalization of Hermite’s proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover. 1 ..."
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We describe a HOL Light formalization of Hermite’s proof that the base of the natural logarithm e is transcendental. This is the first time a proof of this fact has been formalized in a theorem prover. 1
Standalone Tactics using OpenTheory
"... Abstract. Proof tools in interactive theorem provers are usually developed within and tied to a specific system, which leads to a duplication of effort to make the functionality available in different systems. Many verification projects would benefit from access to proof tools developed in other sys ..."
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Abstract. Proof tools in interactive theorem provers are usually developed within and tied to a specific system, which leads to a duplication of effort to make the functionality available in different systems. Many verification projects would benefit from access to proof tools developed in other systems. Using OpenTheory as a language for communicating between systems, we show how to turn a proof tool implemented for one system into a standalone tactic available to many systems via the internet. This enables, for example, LCFstyle proof reconstruction efforts to be shared by users of different interactive theorem provers and removes the need for each user to install the external tool being integrated. 1
Communicating Formal Proofs: The Case of Flyspeck
"... Abstract. We introduce a platform for presenting and crosslinking formal and informal proof developments together. The platform supports writing natural language ‘narratives ’ that include islands of formal text. The formal text contains hyperlinks and gives ondemand state information at every pro ..."
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Abstract. We introduce a platform for presenting and crosslinking formal and informal proof developments together. The platform supports writing natural language ‘narratives ’ that include islands of formal text. The formal text contains hyperlinks and gives ondemand state information at every proof step. We argue that such a system significantly lowers the threshold for understanding formal development and facilitates collaboration on informal and formal parts of large developments. As an example, we show the Flyspeck formal development (in HOL Light) and the Flyspeck informal mathematical text as a narrative linked to the formal development. To make this possible, we use the Agora system, a MathWiki platform developed at Nijmegen which has so far mainly been used with the Coq theorem prover: we show that the system itself is generic and easily adapted to the HOL Light case. 1