HOL, a machine orientated formulation of higher order logic. by M. J. C. Gordon

Cover of: HOL, a machine orientated formulation of higher order logic. | M. J. C. Gordon

Published by University of Cambridge, ComputerLaboratory in Cambridge .

Written in English

Read online

Edition Notes

Book details

SeriesTechnical report -- No.68
ContributionsUniversity of Cambridge. Computer Laboratory.
The Physical Object
Pagination52p.
Number of Pages52
ID Numbers
Open LibraryOL13934367M

Download HOL, a machine orientated formulation of higher order logic.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): HOL is a computer system for generating proofs in a version of higher order logic derived from Church's simple theory of types.

This paper is the original description of the logic underlying the HOL system. Since it was written the system has changed enormously, but the logic has been. Technical Report Number 68 Computer Laboratory UCAM-CL-TR ISSN HOL A machine oriented formulation of higher order logic Mike Gordon July Cited by: HOL - A Machine Oriented Formulation of Higher Order Logic.

By Mike Gordon. Abstract. HOL is a computer system for generating proofs in a version of higher order logic derived from Church's simple theory of types.

This paper is the original description of the logic underlying the HOL system. Since it was written the system has changed Author: Mike Gordon. Abstract. HOL is a version of Robin Milner’s LCF theorem proving system for higher-order logic. It is currently being used to investigate (1) how various levels of hardware behaviour can be rigorously modelled and (2) how the resulting behavioral representations can be the basis for verification by mechanized formal by: The HOL system is a higher order logic theorem proving system implemented at Edinburgh University, Cambridge University and INRIA.

Its many applications, from the verification of hardware designs at all levels to the verification of programs and communication protocols are considered in depth in this volume. In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same.

Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory.

Part III is devoted to recursive by: 71 A Sequent Formulation of a Logic of Predicates in HOL Ching-Tsun C h o u 1 () C o m p u t e r Science Department, University of California at Los Angeles, Los Angeles, CAU.S.A.

Abstract By a predicate we mean a t e r m in t h e HOL logic of type * -> bool, where * can be any by: 4. ually guided heuristics applied to intermediate goals.

So far, machine learning has generally not been used to filter or generate these steps. In this paper, we introduce a new dataset based on Higher-Order Logic (HOL) proofs, for the purpose of de-veloping new machine learning-based theorem-proving strategies.

We make this. HOL A machine oriented formulation of higher order logic. Mike Gordon. July52 pages Abstract. In this paper we describe a formal language intended as a basis for hardware specification and verification.

The language is not new; the only originality in what follows lies in the presentation of the by:   M. Gordon, ‘HOL: A Machine Oriented Formulation of Higher Order Logic', Technical Rep Computer Laboratory, University of Cambridge, revised version (July ).Cited by:   HOL: A Machine Oriented Formulation of Higher-Order Logic.

Technical Rep University of Cambridge Computer Laboratory, Technical Rep University of Cambridge Computer Laboratory, Cited by: 8. Abstract. This paper describes a mechanisation of computability theory in HOL using the Unlimited Register Machine (URM) model of computation. The URM model is first specified as a rudimentary machine language and then the notion of Cited by: 5.

HOL: A machine oriented formulation of higher order logic. Technical Rep University of Cambridge Computer Laboratory, [50] A. Pitts.

The HOL logic. In M. Gordon and T. Melham, editors, Introduction to HOL: A Theorem Proving Environment for Higher Order Logic, pages Cambridge University Press, The logic that HOL supports and how this logic is embedded in ML are then described in detail.

This is followed by an explanation of the theorem-proving infrastructure provided by HOL. Finally two appendices contain a subset of the reference manual, and an overview of the HOL library, including an example of an actual library : Hardcover.

“The book is highly recommended for learning and teaching theorem proving and semantics, picking up a lot of useful knowledge on higher-order logic along the way.

The book is well-structured and written to support learning about the two main by: comes from using higher-order terms and higher-order rules, thus avoiding the overhead of issues like name binding and scoping which typically plague implementations. This book builds up the ideas behind Lambda Prolog progressively starting with traditional Prolog (presented as a logic) and then adding in more powerful by: The HOL interactive theorem prover is a proof assistant for higher-order logic: a programming environment in which theorems can be proved and proof tools implemented.

Built-in decision procedures and theorem provers can automatically establish many simple theorems (users may have to prove the hard theorems themselves!).

We devise a shallow semantical embedding of Åqvist's dyadic deontic logic E in classical higher-order logic. This embedding is shown to be faithful, viz. sound and complete. The B-book: assigning programs to meanings.

HOL: A Machine Oriented Formulation of Higher Order Logic. HOL: A Machine Oriented Formulation of Higher Order Logic, Isabelle Logics: ().Author: Michael Butler and Issam Maamria. It is argued that techniques for proving the correctness of hardware designs must use abstraction mechanisms for relating formal descriptions at different levels of detail.

Four such abstraction mechanisms and their formalisation in higher order logic are discussed. Gordon, M.J.C., ‘HOL: A Machine Oriented Formulation of Higher Order Cited by: In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger -order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic.

The term "higher-order logic", abbreviated as HOL. A gentle introduction to HOL: A Machine-Oriented Formulation of Higher-Order Logic by Gordon Proof assistants: HOL4, HOL Light and Isabelle/HOL (Paulson's MPhil course on Isabelle/HOL) Plotkin: A Structural Approach to Operational Semantics.

This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics.

In these applica­ tions, higher-order logic provides the necessary level of abstraction for con­ cise and natural by: (). HOL a machine oriented formulation of higher order logic. Interpretation fonctionelle et elimination des coupures dans l'arithetique d'ordre superieur.

Introduction to HOL: a theorem proving environment for higher order logic. Intuitionistic Type : Vincent Zammit. The HOL System. The HOL System is an environment for interactive theorem proving in a higher-order most outstanding feature is its high degree of programmability through the meta-language ML.

The system has a wide variety of uses from formalizing pure mathematics to verification of industrial hardware. S.V.P a toolbox for Specification and Verification of Processors. A Machine Oriented Formulation of Higher-order Logic.

Speci cation and veri cation using higher-order logic: a. HOL-OCL is an interactive proof environment for the Object Constraint Language (OCL).It is implemented as a shallow embedding of OCL into the Higher-order Logic (HOL) instance of the interactive theorem prover -OCL is developed by Achim D.

Brucker and Burkhart Wolff. HOL-OCL allows one to reason over OCL specifications, refine OCL specifications, and. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higher-order logic.

AMS Subject Classification:68T15, 03B35, 03B15, 03B Key words: higher-order logic, type theory, mating, connection, expansion proof, natural deduction. Welcome to the home page for the book Programming with Higher-Order Logic by Dale Miller and Gopalan book was published by Cambridge University Press in June Use the menu above to explore this site.

Implementing HOL in an Higher Order Logic Programming Language Cvetan Dunchev, Claudio Sacerdoti Coen, Enrico Tassi To cite this version: Cvetan Dunchev, Claudio Sacerdoti Coen, Enrico Tassi.

Implementing HOL in an Higher Order Logic Programming Language. Logical Frameworks and Meta Languages: Theory and Practice, Jun The context Γ Σ here consists of A: Type, R: (A→A→Prop).

Now one may wonder if the type system λHOL is really faithful to higher order predicate logic differently, one can ask the question of completeness: given a proposition of HOL such that Γ φ ⊢ M: ([φ]) in λHOL, is φ derivable in HOL.

It turns out that this is the case. State of the art — yes, so far as I know all algorithms more or less take the same shape as Huet's (I follow theory of logic programming, although my expertise is tangential) provided you need full higher-order matching: subproblems such as higher-order matching (unification where one term is closed), and Dale Miller's pattern calculus, are decidable.

HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems in this family follow the LCF approach as they are implemented as a library in some programming language.

This library implements an abstract data type of proven theorems so that new objects of this type can only Designed by: Michael J C Gordon. Gordon has written: 'HOL, a machine orientated formulation of higher order logic' Asked in Business Plans, Angel and Venture Capital, Business Networking Explain why problem formulation.

The version of higher-order logic implemented in the HOL system is then described. This is followed by an introduction to goal-directed proof with tactics and tacticals.

Find out information about HOL. Higher Order Logic. A proof-generating system for higher order logic based on LCF. Implementations include HOL and HOL Explanation of HOL. A Machine Oriented Formulation of Higher Order Logic", M.J.C.

Gordon, Rep Comp Lab U Cambridge ()]. As a complementary approach, we propose to use the higher-order logic theorem prover HOL to conduct RBD-based analysis.

For this purpose, we present a higher-order logic formalization of commonly used RBD configurations, such as series, parallel, parallel-series and series-parallel, and the formal verification of their equivalent mathematical Cited by: A. Pitts. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic, Chapter The HOL Logic, – In Gordon and Melham [ Gordon and Melham ].

Google Scholar; Andrei Popescu and Elsa L. Gunter. Recursion principles for syntax with bindings and substitution. In ICFP. – Google Scholar Digital LibraryAuthor: KunčarOndřej, PopescuAndrei. HOL is a computer system for generating proofs in a version of higher order logic derived from Church's simple theory of types.

This paper is the original description of the logic Author: Patricia Johann. Looking for definition of Hol? Hol explanation. Define Hol by Webster's Dictionary, WordNet Lexical Database, Dictionary of Computing, Legal .Programming with Higher-Order Logic.

Book reviews. Some book reviews. December Andrew Gacek. Review on Amazon. March Frank Pfenning. Review for Theory and Practice of Logic Programming. March James Cheney. Review on his blog. June Mechanizing Security In HOL. September for an event-based model of computer systems in the HOL (higher order logic) system to prove the .

92499 views Tuesday, November 24, 2020