Herby: A Semantic—Tree Theorem Prover

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.

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CSim 2

ACM Transactions on Programming Languages and Systems ◽

10.1145/3436808 ◽

2021 ◽

Vol 43 (1) ◽

pp. 1-46

Author(s):

David Sanan ◽

Yongwang Zhao ◽

Shang-Wei Lin ◽

Liu Yang

Keyword(s):

Programming Languages ◽

Concurrent Systems ◽

Theorem Prover ◽

Compositional Techniques ◽

Machine Code ◽

Top Down ◽

Hol Theorem Prover ◽

High Level ◽

High Degree

To make feasible and scalable the verification of large and complex concurrent systems, it is necessary the use of compositional techniques even at the highest abstraction layers. When focusing on the lowest software abstraction layers, such as the implementation or the machine code, the high level of detail of those layers makes the direct verification of properties very difficult and expensive. It is therefore essential to use techniques allowing to simplify the verification on these layers. One technique to tackle this challenge is top-down verification where by means of simulation properties verified on top layers (representing abstract specifications of a system) are propagated down to the lowest layers (that are an implementation of the top layers). There is no need to say that simulation of concurrent systems implies a greater level of complexity, and having compositional techniques to check simulation between layers is also desirable when seeking for both feasibility and scalability of the refinement verification. In this article, we present CSim 2 a (compositional) rely-guarantee-based framework for the top-down verification of complex concurrent systems in the Isabelle/HOL theorem prover. CSim 2 uses CSimpl, a language with a high degree of expressiveness designed for the specification of concurrent programs. Thanks to its expressibility, CSimpl is able to model many of the features found in real world programming languages like exceptions, assertions, and procedures. CSim 2 provides a framework for the verification of rely-guarantee properties to compositionally reason on CSimpl specifications. Focusing on top-down verification, CSim 2 provides a simulation-based framework for the preservation of CSimpl rely-guarantee properties from specifications to implementations. By using the simulation framework, properties proven on the top layers (abstract specifications) are compositionally propagated down to the lowest layers (source or machine code) in each concurrent component of the system. Finally, we show the usability of CSim 2 by running a case study over two CSimpl specifications of an Arinc-653 communication service. In this case study, we prove a complex property on a specification, and we use CSim 2 to preserve the property on lower abstraction layers.

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Learning about Proof with the Theorem Prover LEAN: the Abundant Numbers Task

International Journal of Research in Undergraduate Mathematics Education ◽

10.1007/s40753-021-00140-1 ◽

2021 ◽

Author(s):

Athina Thoma ◽

Paola Iannone

Keyword(s):

Theorem Prover

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Structural ambiguity in Montague Grammar and categorial grammar

The Linguistic Review ◽

10.1515/tlr-2014-0017 ◽

2015 ◽

Vol 32 (1) ◽

Author(s):

Glyn Morrill

Keyword(s):

Categorial Grammar ◽

Theorem Prover ◽

Montague Grammar ◽

Structural Ambiguity

AbstractWe give a type logical categorial grammar for the syntax and semantics of Montague's seminal fragment, which includes ambiguities of quantification and intensionality and their interactions, and we present the analyses assigned by a parser/theorem prover CatLog to the examples in the first half of Chapter 7 of the classic text

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