HOL Light: A tutorial introduction

Harrison, John

doi:10.1007/bfb0031814

Cited by 269 publications

(204 citation statements)

References 4 publications

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“…One camp, represented by provers such as Agda [7], Coq [6], Matita [5] and Nuprl [10], uses expressive type theories as a foundation. The other camp, represented by the HOL family of provers (including HOL4 [2], HOL Light [14], HOL Zero [3] and Isabelle/HOL [26]), mostly sticks to a form of classic set theory typed using simple types with rank 1 polymorphism. (Other successful provers, such as ACL2 [19] and Mizar [12], could be seen as being closer to the HOL camp, although technically they are not based on HOL.…”

Section: Motivationmentioning

confidence: 99%

From Types to Sets by Local Type Definitions in Higher-Order Logic

Kunčar

Popescu

2016

Interactive Theorem Proving

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Abstract. Types in Higher-Order Logic (HOL) are naturally interpreted as nonempty sets-this intuition is reflected in the type definition rule for the HOL-based systems (including Isabelle/HOL), where a new type can be defined whenever a nonempty set is exhibited. However, in HOL this definition mechanism cannot be applied inside proof contexts. We propose a more expressive type-definition rule that addresses the limitation and we prove its soundness. This higher expressive power opens the opportunity for a HOL tool that relativizes type-based statements to more flexible set-based variants in a principled way. We also address particularities of Isabelle/HOL and show how to perform the relativization in the presence of type classes. MotivationThe proof assistant community is divided in two successful camps. One camp, represented by provers such as Agda [7] According to the HOL school of thought, a main goal is to acquire a sweet spot: keep the logic as simple as possible while obtaining sufficient expressiveness. The notion of sufficient expressiveness is of course debatable, and has been debated. For example, PVS [29] includes dependent types (but excludes polymorphism), HOL-Omega [16] adds first-class type constructors to HOL, and Isabelle/HOL adds ad hoc overloading of polymorphic constants. In this paper, we want to propose a gentler extension of HOL: we do not want to promote new "first-class citizens," but merely to give better credit to an old and venerable HOL citizen: the notion of types emerging from sets.The problem we address in this paper is best illustrated by an example. Let lists : α set → α list set be the constant that takes a set A and returns the set of lists whose elements are in A, and P : α list → bool be another constant (whose definition is not important here). Consider the following statements, where we extend the usual HOL syntax by explicitly quantifying over types at the outermost level:∀α. ∃xs α list . P xs (1) ∀α. ∀A α set . A ̸ = / 0 −→ (∃xs ∈ lists A. P xs)

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Section: Motivationmentioning

confidence: 99%

From Types to Sets by Local Type Definitions in Higher-Order Logic

Kunčar

Popescu

2016

Interactive Theorem Proving

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“…HOL Light [15] and Coq [6] are two interactive theorem provers written in OCaml [18]. Although the ancestries of Coq and HOL Light can both be traced back to LCF, there are important differences, between the logical formalisms as well as in the way they are implemented.…”

Section: Hol Light and Coqmentioning

confidence: 99%

Importing HOL Light into Coq

Keller

Werner

2010

Interactive Theorem Proving

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Abstract. We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and rechecked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In particular, our translation keeps the mathematical statements intelligible. This translation has been implemented and allows the importation of the HOL Light basic library into Coq.

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“…The formal verifications are conducted using the freely available 2 HOL Light prover [7]. HOL Light is a version of HOL [5], itself a descendent of Edinburgh LCF [6] which first defined the 'LCF approach' that these systems take to formal proof.…”

Section: Formal Floating Point Theorymentioning

confidence: 99%

Formal Verification of IA-64 Division Algorithms

Harrison

2000

Lecture Notes in Computer Science

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Abstract. The IA-64 architecture defers floating point and integer division to software. To ensure correctness and maximum efficiency, Intel provides a number of recommended algorithms which can be called as subroutines or inlined by compilers and assembly language programmers. All these algorithms have been subjected to formal verification using the HOL Light theorem prover. As well as improving our level of confidence in the algorithms, the formal verification process has led to a better understanding of the underlying theory, allowing some significant efficiency improvements.

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HOL Light: A tutorial introduction

Cited by 269 publications

References 4 publications

From Types to Sets by Local Type Definitions in Higher-Order Logic

From Types to Sets by Local Type Definitions in Higher-Order Logic

Importing HOL Light into Coq

Formal Verification of IA-64 Division Algorithms

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