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Using Decision Procedures With a HigherOrder Logic
 In Theorem Proving in Higher Order Logics: 14th International Conference, TPHOLs 2001
, 2001
"... In automated reasoning, there is a perceived tradeo between expressiveness and automation. Higherorder logic is typically viewed as expressive but resistant to automation, in contrast with rstorder logic and its fragments. We argue that higherorder logic and its variants actually achieve a happy ..."
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In automated reasoning, there is a perceived tradeo between expressiveness and automation. Higherorder logic is typically viewed as expressive but resistant to automation, in contrast with rstorder logic and its fragments. We argue that higherorder logic and its variants actually achieve a happy medium between expressiveness and automation, particularly when used as a frontend to a wide range of decision procedures and deductive procedures. We illustrate the discussion with examples from PVS, but some of the observations apply to other variants of higherorder logic as well.
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
A Reference Version of HOL
"... Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, ..."
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Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, to port, to develop, to change, and to informally reason about. The first author has ported gtt to another dialect of ML, and developed the parsing, prettyprinting, and typechecking support needed to take gtt beyond its initial rudimentary conception. The implementation of gtt has already been of use in developing a variant of the HOL logic. As of this writing, there are at least four or five extant implementations of the HOL logic. These have been intensively developed, in some cases over decades, which leads us to an overwhelming question: why another? In particular, why gtt? There are several answers to this, stemming from different desires and needs in the HOL community.
Congruence Classes with Logic Variables
, 2001
"... We are improving equality reasoning in automatic theoremprovers, and congruence classes provide an e#cient storage mechanism for terms, as well as the congruence closure decision procedure. We describe the technical steps involved in integrating logic variables with congruence classes, and present ..."
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We are improving equality reasoning in automatic theoremprovers, and congruence classes provide an e#cient storage mechanism for terms, as well as the congruence closure decision procedure. We describe the technical steps involved in integrating logic variables with congruence classes, and present an algorithm that can be proved to find all matches between classes (modulo certain equalities). An application of this algorithm makes possible a percolation algorithm for undirected rewriting in minimal space; this is described and an implementation in hol98 is examined in some detail. 1 Keywords: Congruence Closure, Equality Reasoning 1
1 Introduction From LCF to HOL: a short history
"... The original LCF system was a proofchecking program developed at Stanford University by Robin Milner in 1972. Descendents of LCF now form a thriving ..."
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The original LCF system was a proofchecking program developed at Stanford University by Robin Milner in 1972. Descendents of LCF now form a thriving