A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
LCF Examples in HOL

1994
*
BRICS Report Series
*

*In*this paper a number of

*examples*are used to demonstrate that an extension of

*HOL*with domain theory combines the benefits of both systems. ... The

*examples*illustrate reasoning about infinite values and non-terminating functions and show how mixing domain and set theoretic reasoning eases reasoning about finite

*LCF*types and strict functions. ... I am grateful to Larry Paulson for digging up the

*LCF*proof of correctness of the uni cation algorithm. ...

##
###
Computer Assisted Reasoning

2009
*
Journal of automated reasoning
*

Mike abandoned

doi:10.1007/s10817-009-9144-7
fatcat:rd5iyn6gw5canbyhgz4gfxt2yi
*LCF*LSM*in*favour of higher order logic (*HOL*) following discussions with Ben Moszkowski; the benefits of higher-order functions for hardware are discussed*in*[19] . ... The techniques developed by them were applied to more sophisticated*examples*; for*example*, by Graham Birtwistle and Brian Graham at Calgary [28] . ...##
###
Tactics for mechanized reasoning: a commentary on Milner (1984) 'The use of machines to assist in rigorous proof'

2015
*
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
*

For

doi:10.1098/rsta.2014.0234
pmid:25750147
pmcid:PMC4360087
fatcat:bskjoaarmjc7fofocrwgfqjzsm
*example*,*in*the Flyspeck project, parts of the proof of the Kepler conjecture were checked using*HOL*and other parts checked using Isabelle. ... Besides standard ML, the*LCF*metalanguage also led to OCaml [42] , which is the metalanguage for Coq and one of the*HOL*implementations (*HOL*Light), and is growing*in*popularity*in*industry. ...##
###
HOL Light: An Overview
[chapter]

2009
*
Lecture Notes in Computer Science
*

Theorem provers

doi:10.1007/978-3-642-03359-9_4
fatcat:hmqwv5qmyjajxbz52xatepemo4
*in*this family use a version of ML as both the implementation and interaction language;*in**HOL*Light's case this is Objective CAML (OCaml). ... Thanks to its adherence to the so-called '*LCF*approach', the system can be extended with new inference rules without compromising soundness. ...*LCF*,*HOL*and*HOL*Light Both*HOL*Light and its implementation language OCaml can trace their origins back to Edinburgh*LCF*, developed by Milner and his research assistants*in*the 1970s [6] . ...##
###
From LCF to Isabelle/HOL

2019
*
Formal Aspects of Computing
*

For

doi:10.1007/s00165-019-00492-1
fatcat:rv5zmo22fjedvjxjz4lm22v6de
*example*, simplification by rewriting-coupled with recursive simplification to handle conditional rewrite rules-was already realised*in*both the Boyer/Moore theorem prover [BM79] and Edinburgh*LCF*by ... The resulting type, thm, From*LCF*to Isabelle/*HOL*677 ... distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction*in*...##
###
HOLCF: Higher order logic of computable functions
[chapter]

1995
*
Lecture Notes in Computer Science
*

Therefore techniques from higher order logic and

doi:10.1007/3-540-60275-5_72
fatcat:mlrfpmxhtzh2zfz5jtoicd7mxm
*LCF*can be combined*in*a fruitful manner avoiding drawbacks of both logics. ... With the help of type classes the extension can be formulated*in*a way s u c h t h a t the logic*LCF*constitutes a proper sublanguage of HOLCF. ... The theory Fun1 is an*example*for an extension by a new constant which corresponds to the same notion*in*Gordon's*HOL*. ...##
###
An LCF-Style Interface between HOL and First-Order Logic
[chapter]

2002
*
Lecture Notes in Computer Science
*

*In*addition to MESON

*in*

*HOL*, there have been many other

*examples*of automatic first-order provers being used to prove problems

*in*an interactive theorem prover, including: FAUST

*in*

*HOL*[5] ; Paulson's ... For

*example*, the

*HOL*boolean term m ≤ n can be translated to the first-order formula B(@(@(≤, m), n)). ...

##
###
Fast LCF-Style Proof Reconstruction for Z3
[chapter]

2010
*
Lecture Notes in Computer Science
*

We present independent reconstruction of these proofs

doi:10.1007/978-3-642-14052-5_14
fatcat:yvi5yovfijayhmc6nnkj34mfju
*in*the theorem provers Isabelle/*HOL*and HOL4 with particular focus on efficiency. ... Detailed performance data shows that*LCF*-style proof reconstruction can be faster than proof search*in*Z3. ... Conclusions We have presented*LCF*-style proof reconstruction for Z3*in*the theorem provers Isabelle/*HOL*and HOL4. ...##
###
A HOL Basis for Reasoning about Functional Programs

1994
*
BRICS Report Series
*

<br /> <br />The advantages of combining the best of the domain and set theoretic worlds

doi:10.7146/brics.v1i44.21598
fatcat:5aowedoqnbdlxnjcfplcsygyum
*in*the same system are demonstrated*in*a larger*example*, showing the correctness of a unification algorithm. ... A thorough comparison with*LCF*is provided. ... Note that types of*LCF*correspond to pointed cpos*in**HOL*-CPO. ...##
###
Standalone Tactics Using OpenTheory
[chapter]

2012
*
Lecture Notes in Computer Science
*

This enables, for

doi:10.1007/978-3-642-32347-8_28
fatcat:jas6ssyzhjd6ddqgb6p3zbp5cq
*example*,*LCF*-style proof reconstruction efforts to be shared by users of different interactive theorem provers and removes the need for each user to install the external tool being integrated ... Proof tools*in*interactive theorem provers are usually developed within and tied to a specific system, which leads to a duplication of effort to make the functionality available*in*different systems. ... Introduction There are many*LCF*-style systems for interactively developing machine-checked formal theories, including HOL4 [1] ,*HOL*Light [2] , ProofPower [3] and Isabelle/*HOL*[4] . ...##
###
Michael John Caldwell Gordon. 28 February 1948—22 August 2017

2018
*
Biographical Memoirs of Fellows of the Royal Society
*

His achievements include his work at Edinburgh University helping to create Edinburgh

doi:10.1098/rsbm.2018.0019
fatcat:lionn75yjnddfeupt7dpwmvdcu
*LCF*, the first interactive theorem prover of its kind, and the ML family of functional programming languages. ... Michael Gordon was a pioneer*in*the field of interactive theorem proving and hardware verification. ...*In*the 1980s, he worked with Mike Gordon on further development of the*LCF*proof assistant, which became the foundation of Gordon's*LCF*LSM and*HOL*systems. ...##
###
Integrating a SAT Solver with an LCF-style Theorem Prover

2006
*
Electronical Notes in Theoretical Computer Science
*

This paper describes the integration of a leading SAT solver with Isabelle/

doi:10.1016/j.entcs.2005.12.007
fatcat:52nuhgbxs5efxkfzqwmztuy5qy
*HOL*, a popular interactive theorem prover. ... The*LCF*-approach instead demands that we verify zChaff's claim of unsatisfiability within Isabelle/*HOL*. ... A Simple*Example**In*this section we illustrate the proof reconstruction using a small*example*. Consider the following input formula φ ≡ (¬v1 ∨ v2) ∧ (¬v2 ∨ ¬v3) ∧ (v1 ∨ v2) ∧ (¬v2 ∨ v3). ...##
###
History of Interactive Theorem Proving
[chapter]

2014
*
Handbook of the History of Logic
*

ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience

doi:10.1016/b978-0-444-51624-4.50004-6
fatcat:sngnxnl3ivectj5taj3dgsaa7m
*in*the face of our lengthy delays. ...*HOL*As emphasized by Gordon [1982] , despite the name '*LCF*', nothing*in*the Edinburgh*LCF*methodology is tied to the Logic of Computable Functions. ... A good*example*of such methods at work is the implementation by Slind [1991] of Knuth-Bendix completion*in**HOL*. ...##
###
Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present independent reconstruction of unsatisfiability proofs for bit-vector theories

doi:10.1007/978-3-642-25379-9_15
fatcat:gesxkp2cm5girliosyngzyuwmi
*in*the theorem provers HOL4 and Isabelle/*HOL*. ... We thereby obtain high correctness assurances for Z3's results, and increase the degree of proof automation for bit-vector problems*in*HOL4 and Isabelle/*HOL*. ... The*LCF*-style systems that we consider here, HOL4 and Isabelle/*HOL*, are popular theorem provers for polymorphic higher-order logic (*HOL*) [21] , based on the simply-typed λ-calculus. ...##
###
Possibly infinite sequences in theorem provers: A comparative study
[chapter]

1997
*
Lecture Notes in Computer Science
*

The formalizations have been carried out

doi:10.1007/bfb0028388
fatcat:jkh254z3tvfrhkn72ndcnknq24
*in*di erent proof tools, namely*in*Gordon's*HOL*,*in*Isabelle and*in*PVS. ... We compare four di erent formalizations of possibly*in*nite sequences*in*theorem provers based on higher-order logic. ... For*example*, suppose one wants to lter all symbols a*in*the sequence x = (b a a b a : : : 6*HOL*-*LCF*: Domain Theory*in*Isabelle/*HOL*De nition 12 (Type of Sequences). ...
« Previous

*Showing results 1 — 15 out of 689 results*