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62
Building formal method tools in the Isabelle/Isar framework
 THEOREM PROVING IN HIGHER ORDER LOGICS (TPHOLS 2007), LNCS
, 2007
"... We present the generic system framework of Isabelle/Isar underlying recent versions of Isabelle. Among other things, Isar provides an infrastructure for Isabelle plugins, comprising extensible state components and extensible syntax that can be bound to tactical ML programs. Thus the Isabelle/Isar ..."
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Cited by 10 (6 self)
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We present the generic system framework of Isabelle/Isar underlying recent versions of Isabelle. Among other things, Isar provides an infrastructure for Isabelle plugins, comprising extensible state components and extensible syntax that can be bound to tactical ML programs. Thus the Isabelle/Isar architecture may be understood as an extension and refinement of the traditional “LCF approach”, with explicit infrastructure for building derivative systems. To demonstrate the technical potential of the framework, we apply it to a concrete formal methods tool: the HOLZ 3.0 environment, which is geared towards the analysis of Z specifications and formal proof of forwardrefinements.
Fast Tacticbased Theorem Proving
 TPHOLs 2000, LNCS 1869
, 2000
"... Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance pe ..."
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Cited by 9 (4 self)
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Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind specialpurpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.
Monotonicity Inference for HigherOrder Formulas
, 2010
"... Formulas are often monotonic in the sense that if the formula is satisfiable for given domains of discourse, it is also satisfiable for all larger domains. Monotonicity is undecidable in general, but we devised two calculi that infer it in many cases for higherorder logic. The stronger calculus has ..."
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Cited by 9 (8 self)
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Formulas are often monotonic in the sense that if the formula is satisfiable for given domains of discourse, it is also satisfiable for all larger domains. Monotonicity is undecidable in general, but we devised two calculi that infer it in many cases for higherorder logic. The stronger calculus has been implemented in Isabelle’s model finder Nitpick, where it is used to prune the search space, leading to dramatic speed improvements for formulas involving many atomic types.
A Framework for Specifying, Prototyping, and Reasoning about Computational Systems
, 2009
"... In this thesis we are interested in a framework for specifying, prototyping, and reasoning about systems that describe computations over formal objects such as formulas, proofs, and programs. The computations of interest include those like evaluation and typing in a programming language, provability ..."
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Cited by 9 (2 self)
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In this thesis we are interested in a framework for specifying, prototyping, and reasoning about systems that describe computations over formal objects such as formulas, proofs, and programs. The computations of interest include those like evaluation and typing in a programming language, provability in a logic, and behavior in a concurrency system. The development of these computational systems is often an iterative
HOL Light Tutorial (for version 2.20
, 2006
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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Cited by 9 (0 self)
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
THF0 – the core of the TPTP language for higherorder logic
 Automated Reasoning, 4th International Joint Conference, IJCAR 2008
"... Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type the ..."
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Cited by 9 (1 self)
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Abstract. One of the keys to the success of the Thousands of Problems for Theorem Provers (TPTP) problem library and related infrastructure is the consistent use of the TPTP language. This paper introduces the core of the TPTP language for higherorder logic – THF0, based on Church’s simple type theory. THF0 is a syntactically conservative extension of the untyped firstorder TPTP language. 1
Formal verification of square root algorithms
 Formal Methods in Systems Design
, 2003
"... Abstract. We discuss the formal verification of some lowlevel mathematical software for the Intel ® Itanium ® architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more ..."
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Abstract. We discuss the formal verification of some lowlevel mathematical software for the Intel ® Itanium ® architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications. 1. Overview The Intel ® Itanium ® architecture is a new 64bit architecture jointly developed by Intel and HewlettPackard, implemented in the Itanium® processor family (IPF). Among the software supplied by Intel to support IPF processors are some optimized mathematical functions to supplement or replace less efficient generic libraries. Naturally, the correctness of the algorithms used in such software is always a major concern. This is particularly so for division, square root and certain transcendental function kernels, which are intimately tied to the basic architecture. First, in IA32 compatibility mode, these algorithms are used by hardware instructions like fptan and fdiv. And while in “native ” mode, division and square root are implemented in software, typical users are likely to see them as part of the basic architecture. The formal verification of some of the division algorithms is described by Harrison (2000b), and a representative verification of a transcendental function by Harrison (2000a). In this paper we complete the picture by considering a square root algorithm. Division, transcendental functions and square roots all have quite distinctive features and their formal verifications differ widely from each other. The present proofs have a number of interesting features, and show how important some theorem prover features — in particular programmability — are. The formal verifications are conducted using the freely available 1 HOL Light prover (Harrison, 1996). HOL Light is a version of HOL (Gordon and Melham, 1993), itself a descendent of Edinburgh LCF
R.: A coinduction rule for entailment of recursively defined properties
 In Stuckey, P.J., ed.: 14th CP. Volume 5202 of LNCS
, 2008
"... Abstract. Recursively defined properties are ubiquitous. We present a proof method for establishing entailment G  = H of such properties G and H over a set of common variables. The main contribution is a particular proof rule based intuitively upon the concept of coinduction. This rule allows the i ..."
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Cited by 8 (7 self)
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Abstract. Recursively defined properties are ubiquitous. We present a proof method for establishing entailment G  = H of such properties G and H over a set of common variables. The main contribution is a particular proof rule based intuitively upon the concept of coinduction. This rule allows the inductive step of assuming that an entailment holds during the proof the entailment. In general, the proof method is based on an unfolding (and no folding) algorithm that reduces recursive definitions to a point where only constraint solving is necessary. The constraintbased proof obligation is then discharged with available solvers. The algorithm executes the proof by a searchbased method which automatically discovers the opportunity of applying induction instead of the user having to specify some induction schema, and which does not require any base case. 1
MetaPRL  A Modular Logical Environment
, 2003
"... MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive ..."
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Cited by 8 (2 self)
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MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCFstyle tacticbased proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an opensource license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.
Foundational, Compositional (Co)datatypes for HigherOrder Logic  Category Theory Applied to Theorem Proving
"... Higherorder logic (HOL) forms the basis of several popular interactive theorem provers. These follow the definitional approach, reducing highlevel specifications to logical primitives. This also applies to the support for datatype definitions. However, the internal datatype construction used in H ..."
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Cited by 8 (4 self)
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Higherorder logic (HOL) forms the basis of several popular interactive theorem provers. These follow the definitional approach, reducing highlevel specifications to logical primitives. This also applies to the support for datatype definitions. However, the internal datatype construction used in HOL4, HOL Light, and Isabelle/HOL is fundamentally noncompositional, limiting its efficiency and flexibility, and it does not cater for codatatypes. We present a fully modular framework for constructing (co)datatypes in HOL, with support for mixed mutual and nested (co)recursion. Mixed (co)recursion enables type definitions involving both datatypes and codatatypes, such as the type of finitely branching trees of possibly infinite depth. Our framework draws heavily from category theory. The key notion is that of a rich type constructor—a functor satisfying specific properties preserved by interesting categorical operations. Our ideas are formalized in Isabelle and implemented as a new definitional package, answering a longstanding user request.