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Experiments with ZF set theory in HOL and Isabelle
[chapter]

1995
*
Lecture Notes in Computer Science
*

This paper compares the representation and use

doi:10.1007/3-540-60275-5_55
fatcat:3ormlf77dvdp7ld77ltd7kulhm
*of*ZF*set**theory*within both*HOL*and Isabelle. The main case study is the construction*of*D∞. ... The advantages and disadvantages*of*higher-order*set**theory*versus firstorder*set**theory*are explored experimentally. ... Francisco Corella, whose PhD thesis [6] contains many insights into mechanizing*set**theory*(including the use*of*simple type*theory*as the underlying logic) has had a significant influence on the second ...##
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Experiments with ZF Set Theory in HOL and Isabelle

1995
*
BRICS Report Series
*

<br /><br />This paper compares the representation and use

doi:10.7146/brics.v2i37.19940
fatcat:4ptzes5o2vbmhh3m3wmwjn6ake
*of*ZF*set**theory*within<br />both*HOL*and Isabelle. The main case study is the construction*of*D_inf. ... <br />The advantages and disadvantages*of*higher-order*set**theory*versus first-order<br />*set**theory*are explored experimentally. ... Francisco Corella, whose PhD thesis [6] contains many insights into mechanizing*set**theory*(including the use*of*simple type*theory*as the underlying logic) has had a significant influence on the second ...##
###
Higher-Order Logic and Theorem Proving for Structured Specifications
[chapter]

2000
*
Lecture Notes in Computer Science
*

Then we show that for maps

doi:10.1007/978-3-540-44616-3_23
fatcat:3dfhrzw3wvgpxjbob3masrh54y
*of*institutions into*HOL*that satisfy certain technical conditions we can reuse the proof*system**of*the higher-order logic*to*reason about structured specifications built over ... We also show some maps*of*institutions underlying the CASL specification formalism (see [CASL 99]) into*HOL*that satisfy conditions needed for reusing proof*systems*. ... A task for the future is*to*extend presented work*to*the CASL language and*to*design a tool for automatic translation*of*the CASL specifications into one*of*the theorem-provers for*HOL*logic together with ...##
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Unique Solutions of Contractions, CCS, and their HOL Formalisation

2018
*
Electronic Proceedings in Theoretical Computer Science
*

The paper presents an overview

doi:10.4204/eptcs.276.10
fatcat:5p4xhummsvd5fh3hamg6pito5e
*of*a rather comprehensive formalisation*of*the core*of*the*theory**of*CCS in the*HOL*theorem prover (HOL4), with a focus towards the*theory**of*unique solutions*of*contractions ... (The formalisation consists*of*about 20,000 lines*of*proof scripts in Standard ML.) Some refinements*of*the*theory*itself are obtained. ... The second half*of*this paper was written in memory*of*Michael J. C. Gordon, the creator*of**HOL*theorem prover. ...##
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Mechanizing coinduction and corecursion in higher-order logic

1997
*
Journal of Logic and Computation
*

A

doi:10.1093/logcom/7.2.175
fatcat:lmmrync4qnhxzbmggldyyvppje
*theory**of*recursive and corecursive definitions has been developed in higher-order logic (*HOL*) and mechanized using Isabelle. ... The*theory*rests on a traditional formalization*of*infinite trees. The*theory*is intended for use in specification and verification. ... Martin Coen helped*to**set*up the environment for coinduction proofs. Andrew Pitts gave much advice, for example on proving that equality is a gfp. ...##
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Page 8785 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

Chapter 6 contrasts computer algebra

*systems*and theorem provers, pointing out the strengths and*weaknesses**of*each. ... Chapter 5 describes an*HOL*implementation*of*a quantifier elimination procedure for the first order*theory**of*reals. ...##
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Formal verification of a partial-order reduction technique for model checking
[chapter]

1996
*
Lecture Notes in Computer Science
*

As a case study, we use the mechanical theorem prover

doi:10.1007/3-540-61042-1_48
fatcat:mzcv3l3bgbbbvpllnzgynp6zg4
*HOL**to*verify the correctness*of*a partial-order reduction technique for cutting down the amount*of*state search performed by model checkers. ... In this paper we explore another possibility: we use mechanical theorem proving*to*formally verify a meta-*theory**of*model checking. ... Acknowledgements We would like*to*thank Elsa Gunter for her penetrating remarks (especially regarding the formalization*of*deterministic transition*systems*), and Rajeev Alur, Gerard Holzmann, Doug Howe ...##
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Isomorphisms — A Link Between the Shallow and the Deep
[chapter]

1999
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/3-540-48256-3_4
fatcat:pzwrcinecrc5xafccf6lj7wemq
*theory**of*isomorphisms between typed*sets*in Isabelle/*HOL*. Those isomorphisms can serve*to*link a shallow embedding with a*theory*that defines certain concepts directly in*HOL*. ... Thus, it becomes possible*to*use the advantage*of*a shallow embedding that it allows for efficient proofs about concrete terms*of*the embedded formalism with the advantage*of*a deeper*theory*that establishes ... Thanks*to*the referees for their constructive comments and for their patience with the first version*of*the paper. ...##
###
Heterogeneous Development Graphs and Heterogeneous Borrowing
[chapter]

2002
*
Lecture Notes in Computer Science
*

Often, different aspects

doi:10.1007/3-540-45931-6_23
fatcat:i6gfn65dfzacrbiuezalt36epu
*of*a software*system*have*to*be specified in different logics, since the construction*of*a huge logic covering all needed features would be too complex*to*be feasible. ... Therefore, we introduce heterogeneous development graphs as a means*to*cope with heterogeneous specifications. We cover both the semantics and the proof*theory**of*heterogeneous development graphs. ... Acknowledgments This work came out*of*both a cooperation with Andrzej Tarlecki on the semantic aspects and with Serge Autexier and Dieter Hutter on the proof theoretic aspects*of*specifications. ...##
###
A Formalization of the Process Algebra CCS in HOL4
[article]

2017
*
arXiv
*
pre-print

We have used HOL4's new co-inductive

arXiv:1705.07313v2
fatcat:atvk2h3jfbghtpqcldme3ahkiy
*relation*support*to*re-define strong and*weak*bisimulation equivalances, and shows that the new definitions are equivalent with old ones. ... The aim is*to*provide an up-*to*-date sound and effective tool*to*support verification and reasoning about CCS, and*to*provide a formal logic basis for further theoretical developments in Concurrency*Theory*... And the use*of*CURRY and UNCURRY is*to*transform the*relation*from types between CCS -> CCS -> bool and CCS × CCS -> bool, since*relations*in*HOL*cannot be treated directly as mathematical*sets*. ...##
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Foundational, Compositional (Co)datatypes for Higher-Order Logic: Category Theory Applied to Theorem Proving

2012
*
2012 27th Annual IEEE Symposium on Logic in Computer Science
*

Our framework draws heavily from category

doi:10.1109/lics.2012.75
dblp:conf/lics/TraytelPB12
fatcat:gxwn5ptan5b6niq3qf4ahwbcua
*theory*. ... Interactive theorem provers based on higher-order logic (*HOL*) traditionally follow the definitional approach, reducing high-level specifications*to*logical primitives. ...*HOL*supports a restrictive, simply typed flavor*of**set**theory*. We write α*set*for the powertype*of*α, consisting*of**sets**of*α elements; it is isomorphic*to*α → bool. ...##
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Traces of I/O-automata in Isabelle/HOLCF
[chapter]

1997
*
Lecture Notes in Computer Science
*

We make use

doi:10.1007/bfb0030627
fatcat:dyxboezwgrf5xgcowqdg543igy
*of*the logic HOLCF, an extension*of**HOL*with domain*theory*and show how*to*move between*HOL*and HOLCF. ... This allows us*to*restrict the use*of*HOLCF*to*metatheoretic arguments while actual re nement proofs between I/O automata are carried out within the simpler logic*HOL*. ... (Unless noted otherwise,*HOL*will refer*to*Isabelle/*HOL*rather than Gordon's*HOL**system*7] .) ...##
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A new interface for HOL — Ideas, issues and implementation
[chapter]

1995
*
Lecture Notes in Computer Science
*

TkHolWorkbench is a new

doi:10.1007/3-540-60275-5_74
fatcat:te7fkrxfcjagnbb7madijixvbq
*set**of*interface tools for*HOL*implemented using the Tk toolkit. It aims*to*be robust, extensible, lightweight and user-friendly. ... The tools are designed*to*augment the existing*HOL*interface. The project applies rapid prototyping and the use*of*an interpreted toolkit*to*the eld*of*theorem proving interfaces. ... It draws from several sources 11, 4 , 9 , 7 ] . { The current i n terface*to**HOL*is very*weak*, particularly in the area*of*visualisation. ...##
###
Further Formalization of the Process Algebra CCS in HOL4
[article]

2017
*
arXiv
*
pre-print

We have added full supports on

arXiv:1707.04894v2
fatcat:wfejjkivvvafrdlmxeqelolkay
*weak*bisimulation equivalence and observation congruence (rooted*weak*equivalence), with*related*definitions, theorems and algebraic laws. ... Some deep lemmas were also formally proved in this project, including Deng Lemma, Hennessy Lemma and several versions*of*the "Coarsest congruence contained in*weak*equivalence". ... It's know that, the typed logic implemented in the various*HOL**systems*(including Isabelle/*HOL*) is not strong enough*to*define a type for all possible ordinal values (a proper class in a*set**theory*like ...##
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A Formalization of Unique Solutions of Equations in Process Algebra
[article]

2017
*
arXiv
*
pre-print

This includes all classical properties

arXiv:1712.09402v1
fatcat:hgzwipj3qfekbioxaus2jzjtzq
*of*strong/*weak*bisimulation equivalences and observation congruence, a*theory**of*congruence for CCS, various versions*of*"bisimulation up*to*" techniques, and several ... This work is further extended*to*support recent developments in Concurrency*Theory*, namely the "contraction"*relation*and the*related*"unique solutions*of*contractions" theorem found by Prof. ... The*HOL*deductive*system*The deductive*system**of*the*HOL*logic is specified by the following eight rules*of*inference. ...
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