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OpenTheory: Package Management for Higher Order Logic Theories
"... Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective pack ..."
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Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective package management system for logical theories. The OpenTheory article format allows higher order logic theories to be exported from one theorem prover, compressed by a standalone tool, and imported into a different theorem prover. Articles naturally support theory interpretations, which is the mechanism by which theories can be cleanly transferred from one theorem prover context to another, and which also leads to more efficient developments of standard theories.
Species and functors and types, oh my
 in: Proceedings of the third ACM Haskell symposium on Haskell, Haskell ’10 (2010
"... The theory of combinatorial species, although invented as a purely mathematical formalism to unify much of combinatorics, can also serve as a powerful and expressive language for talking about data types. With potential applications to automatic test generation, generic programming, and language des ..."
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The theory of combinatorial species, although invented as a purely mathematical formalism to unify much of combinatorics, can also serve as a powerful and expressive language for talking about data types. With potential applications to automatic test generation, generic programming, and language design, the theory deserves to be much better known in the functional programming community. This paper aims to teach the basic theory of combinatorial species using motivation and examples from the world of functional programming. It also introduces the species library, available on Hack age, which is used to illustrate the concepts introduced and can serve as a platform for continued study and research.
Composable Packages for Higher Order Logic Theories
"... Interactive theorem proving is tackling ever larger formalization and verification projects, and there is a critical need for theory engineering techniques to support these efforts. One such technique is effective package management, which has the potential to simplify the development of logical the ..."
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Interactive theorem proving is tackling ever larger formalization and verification projects, and there is a critical need for theory engineering techniques to support these efforts. One such technique is effective package management, which has the potential to simplify the development of logical theories by precisely checking dependencies and promoting reuse. This paper introduces a domainspecific language for defining composable packages of higher order logic theories, which is designed to naturally handle the complex dependency structures that often arise in theory development. The package composition language functions as a module system for theories, and the paper presents a welldefined semantics for the supported operations. Preliminary tests of the package language and its toolset have been made by packaging the theories distributed with the HOL Light theorem prover. This experience is described, leading to some initial theory engineering discussion on the ideal properties of a reusable theory. 1