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Firstorder proof tactics in higherorder logic theorem provers
 Design and Application of Strategies/Tactics in Higher Order Logics, number NASA/CP2003212448 in NASA Technical Reports
, 2003
"... Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology: an ‘ ..."
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Cited by 49 (4 self)
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Abstract. In this paper we evaluate the effectiveness of firstorder proof procedures when used as tactics for proving subgoals in a higherorder logic interactive theorem prover. We first motivate why such firstorder proof tactics are useful, and then describe the core integrating technology: an ‘LCFstyle’ logical kernel for clausal firstorder logic. This allows the choice of different logical mappings between higherorder logic and firstorder logic to be used depending on the subgoal, and also enables several different firstorder proof procedures to cooperate on constructing the proof. This work was carried out using the HOL4 theorem prover; we comment on the ease of transferring the technology to other higherorder logic theorem provers. 1
Integrating Gandalf and HOL
 Theorem Proving in Higher Order Logics: TPHOLs ’99, LNCS 1690
, 1999
"... Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a ..."
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Cited by 42 (2 self)
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Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a Gandalf server may be set up servicing multiple HOL clients. In addition, the translation of the Gandalf proof into HOL fits in with the LCF model and guarantees logical consistency.
A thread of HOL development
 Computer Journal
"... The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evoluti ..."
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Cited by 11 (7 self)
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The HOL system is a mechanized proof assistant for higher order logic that has been under continuous development since the mid1980s, by an everchanging group of developers and external contributors. We give a brief overview of various implementations of the HOL logic before focusing on the evolution of certain important features available in a recent implementation. We also illustrate how the module system of Standard ML provided security and modularity in the construction of the HOL kernel, as well as serving in a separate capacity as a useful representation medium for persistent, hierarchical logical theories.
SETHEO and ESETHEO  The CADE13 Systems
 Journal of Automated Reasoning
, 1997
"... . The model elimination theorem prover SETHEO (version V3.3) and its equational extension ESETHEO are presented. SETHEO employs sophisticated mechanisms of subgoal selection, elaborate iterative deepening techniques, and local failure caching methods. Its equational counterpart ESETHEO transforms ..."
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Cited by 10 (0 self)
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. The model elimination theorem prover SETHEO (version V3.3) and its equational extension ESETHEO are presented. SETHEO employs sophisticated mechanisms of subgoal selection, elaborate iterative deepening techniques, and local failure caching methods. Its equational counterpart ESETHEO transforms formulae containing equality (using a variant of Brand's modification method) and processes the output with the standard SETHEO system. The paper gives an overview of the theoretical background, the system architecture, and the performance of both systems. Key words: Automated theorem proving, competition, SETHEO, ESETHEO, firstorder logic, model elimination, equality. 1. Introduction In this paper we describe the theorem provers SETHEO and ESETHEO. SETHEO is based on the model elimination calculus [13] and performs proof search using iterative deepening. The proof procedure is implemented as an extension of the Warren Abstract Machine. The system is being continuously extended and enh...
The HOL Light manual (1.1)
, 2000
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 6 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...
Predicate subtyping with predicate sets
 14th International Conference on Theorem Proving in Higher Order Logics: TPHOLs 2001
, 2001
"... Abstract. We show how PVSstyle predicate subtyping can be simulated in HOL using predicate sets, and explain how to perform subtype checking using this model. We illustrate some applications of this to specification and verification in HOL, and also demonstrate some limits of the approach. Finally ..."
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Cited by 5 (1 self)
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Abstract. We show how PVSstyle predicate subtyping can be simulated in HOL using predicate sets, and explain how to perform subtype checking using this model. We illustrate some applications of this to specification and verification in HOL, and also demonstrate some limits of the approach. Finally we report on the effectiveness of a subtype checker used as a condition prover in a contextual rewriter. 1
Tool Building Requirements for an API to FirstOrder Solvers
"... Abstract. Effective formal verification tools require that robust implementations of automatic procedures for firstorder logic and satisfiability modulo theories be integrated into expressive interactive frameworks for logical deduction, such as higherorder logic ..."
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Cited by 3 (0 self)
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Abstract. Effective formal verification tools require that robust implementations of automatic procedures for firstorder logic and satisfiability modulo theories be integrated into expressive interactive frameworks for logical deduction, such as higherorder logic
The HOL Light manual (1.0)
, 1998
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 1 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. "x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with firstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordinary...
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
www.elsevier.com/locate/entcs Tool Building Requirements for an API to FirstOrder Solvers
"... Effective formal verification tools require that robust implementations of automatic procedures for firstorder logic and satisfiability modulo theories be integrated into expressive interactive frameworks for logical deduction, such as higherorder logic theorem provers. This paper states some prag ..."
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Effective formal verification tools require that robust implementations of automatic procedures for firstorder logic and satisfiability modulo theories be integrated into expressive interactive frameworks for logical deduction, such as higherorder logic theorem provers. This paper states some pragmatic requirements for implementations of decision procedures that make them wellsuited to integration into such frameworks. The aim is to open a dialogue with the designers of decision procedure software that will lead to greater and easier uptake of their implementations by verification users.