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LCF Examples in HOL
1994
BRICS Report Series
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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. ...
doi:10.7146/brics.v1i18.21649
fatcat:wchog7xakjbfrk7eavij4txiiu
Computer Assisted Reasoning
2009
Journal of automated reasoning
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Mike abandoned 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] . ...
doi:10.1007/s10817-009-9144-7
fatcat:rd5iyn6gw5canbyhgz4gfxt2yi
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
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For 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. ...
doi:10.1098/rsta.2014.0234
pmid:25750147
pmcid:PMC4360087
fatcat:bskjoaarmjc7fofocrwgfqjzsm
HOL Light: An Overview
[chapter]
2009
Lecture Notes in Computer Science
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Theorem provers 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] . ...
doi:10.1007/978-3-642-03359-9_4
fatcat:hmqwv5qmyjajxbz52xatepemo4
From LCF to Isabelle/HOL
2019
Formal Aspects of Computing
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For 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 ...
doi:10.1007/s00165-019-00492-1
fatcat:rv5zmo22fjedvjxjz4lm22v6de
HOLCF: Higher order logic of computable functions
[chapter]
1995
Lecture Notes in Computer Science
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Therefore techniques from higher order logic and 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. ...
doi:10.1007/3-540-60275-5_72
fatcat:mlrfpmxhtzh2zfz5jtoicd7mxm
An LCF-Style Interface between HOL and First-Order Logic
[chapter]
2002
Lecture Notes in Computer Science
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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)). ...
doi:10.1007/3-540-45620-1_10
fatcat:au5jgjzldnadld7ntuxjvvfkhe
Fast LCF-Style Proof Reconstruction for Z3
[chapter]
2010
Lecture Notes in Computer Science
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We present independent reconstruction of these proofs 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. ...
doi:10.1007/978-3-642-14052-5_14
fatcat:yvi5yovfijayhmc6nnkj34mfju
A HOL Basis for Reasoning about Functional Programs
1994
BRICS Report Series
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<br /> <br />The advantages of combining the best of the domain and set theoretic worlds 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. ...
doi:10.7146/brics.v1i44.21598
fatcat:5aowedoqnbdlxnjcfplcsygyum
Standalone Tactics Using OpenTheory
[chapter]
2012
Lecture Notes in Computer Science
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This enables, for 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] . ...
doi:10.1007/978-3-642-32347-8_28
fatcat:jas6ssyzhjd6ddqgb6p3zbp5cq
Michael John Caldwell Gordon. 28 February 1948—22 August 2017
2018
Biographical Memoirs of Fellows of the Royal Society
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His achievements include his work at Edinburgh University helping to create Edinburgh 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. ...
doi:10.1098/rsbm.2018.0019
fatcat:lionn75yjnddfeupt7dpwmvdcu
Integrating a SAT Solver with an LCF-style Theorem Prover
2006
Electronical Notes in Theoretical Computer Science
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This paper describes the integration of a leading SAT solver with Isabelle/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). ...
doi:10.1016/j.entcs.2005.12.007
fatcat:52nuhgbxs5efxkfzqwmztuy5qy
History of Interactive Theorem Proving
[chapter]
2014
Handbook of the History of Logic
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ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience 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. ...
doi:10.1016/b978-0-444-51624-4.50004-6
fatcat:sngnxnl3ivectj5taj3dgsaa7m
Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL
[chapter]
2011
Lecture Notes in Computer Science
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We present independent reconstruction of unsatisfiability proofs for bit-vector theories 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. ...
doi:10.1007/978-3-642-25379-9_15
fatcat:gesxkp2cm5girliosyngzyuwmi
Possibly infinite sequences in theorem provers: A comparative study
[chapter]
1997
Lecture Notes in Computer Science
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The formalizations have been carried out 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). ...
doi:10.1007/bfb0028388
fatcat:jkh254z3tvfrhkn72ndcnknq24
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