Vincent Zammit. A comparative study of Coq and HOL. In Elsa L. Gunter and Amy Felty, editors, Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, TPHOLs'97, Murray Hill, NJ, USA, volume 1275 of Lecture Notes in Computer Science, pages 323--337. Springer-Verlag, August 1997.  Home/Search Document Details and Download
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A Prototype Proof Translator from HOL to Coq - Denney (2000) (3 citations) (Correct)
....a form of higher order logic over a version of the lambda calculus, there are significant differences in the details of the logic and in the pragmatics of proof development, so that it can be surprisingly difficult for users of one system to understand the mind set of those of the other. Zammit [Zam97] compares Coq and HOL, and we add some more details from the perspective of translation. We first compare the practicalities of proof construction, and then the details of the logics. 2.1 Proof Development Proof Metalanguage HOL is an LCF style theorem prover, meaning that the user uses the ....
....a special case of variables because to assume P is to assume a proof H : P . We can add an assumption using the command, Variable n:nat, for example. In HOL, however, the context is a list of assumptions which can be open. Free term and type variables are not explicit. 4 As pointed out in [Zam97] though, this is often more a measure of the low level at which HOL proofs would otherwise be carried out. 2.2 Proof Language Propositions In HOL, there is no distinction between booleans and propositions. Propositions are manipulated just like any other terms. A direct consequence of this is ....
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Vincent Zammit. A comparative study of Coq and HOL. In Elsa L. Gunter and Amy Felty, editors, Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, TPHOLs'97, Murray Hill, NJ, USA, volume 1275 of Lecture Notes in Computer Science, pages 323--337. Springer-Verlag, August 1997.
Theorem Provers of LCF - Larson (1997) (Correct)
....in COQ. One advantage frequently touted by COQ users is its ability to generate an executable program from the proof of a formal specification. This helps a programmer or verifier check that the program they specified actually does what they intended. In a recent paper comparing HOL to COQ [Zam97] Zammet makes a detailed comparison of HOL and COQ. Zammet says that HOL s meta language is more powerful, allowing for more powerful proof tactics, although he argues this makes the system more difficult to learn, and the code harder to interpret. Also, large scale proofs are better handled in ....
....more powerful proof tactics, although he argues this makes the system more difficult to learn, and the code harder to interpret. Also, large scale proofs are better handled in HOL because COQ proof terms may become very large, and fiffi convertability my become infeasible for large objects. Zam97] COQ s strengths include a single language for terms and types, which is expressive enough to include dependant types and quantification over types. Zammet al..so claims that the logic used by COQ gives a more natural formalisation of mathematical concepts. 5 4.3 NUPRL NUPRL is based on a ....
Vincent Zammet. A comparative study of coq and hol. In Elsa Gunter, editor, Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, New Jersey, August 1997. Springer Verlag. 9
A Comparison of PVS and Isabelle/HOL - Griffioen, Huisman (1998) (3 citations) (Correct)
....language of PVS is described as too complex and sometimes confusing, while the second comparison is more enthusiastic about it. Gordon describes PVS from a HOL perspective [Gor95] Other comparisons have been made between HOL and Isabelle ZF (in the field of set theory) AG95] HOL and Coq [Zam97] and Nuprl and NQTHM [BK91] Three proof tool interfaces (including PVS) are compared from a human computer interaction perspective in [MH96] To the best of our knowledge, we are the first to compare PVS and Isabelle HOL. Our comparison is not based on a particular example, but treats ....
Vincent Zammit. A comparative study of Coq and HOL. In Gunter and Felty [GF97].
A Proof of the - Theorem In Coq (1997) Self-citation (Zammit) (Correct)
....of computation has also been implemented in HOL. This mechanisation is based on the URM model of computation and includes a proof that partial recursive functions are URM computable. This mechanisation is illustrated separately in [13] The results of the comparative study will be published in [14]. 2 Partial Recursive Functions The set of partial recursive functions is defined in the literature (see for instance [3, 10] as the smallest set of n ary partial functions on natural numbers which contains the three basic types of functions: ffl the zero functions: 8n; x 0 ; xn Gamma1 ....
....as the underlying logic of Coq. In fact, during the implementation described in this report, no need was felt for implementing new tactics which would somehow facilitate the mechanisation considerably. The results of the comparative study of Coqand HOL will be published in more detail in [14]. ....
Vincent Zammit. A comparative study of Coq and HOL. In Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, Lecture Notes in Computer Science, Bell Labs, New Jersey, US, August 1997. Springer-Verlag. 15
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