Results 1 
3 of
3
A Comparative Study of Coq and HOL
 In Gunter and Felty [GF97
, 1997
"... . This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discus ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
. This paper illustrates the differences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to support some of the arguments discussed in this paper. The mechanisms for specifying definitions and for theorem proving are discussed separately, building in parallel two pictures of the different approaches of mechanisation given by these systems. 1 Introduction This paper compares the different theorem proving approaches of the HOL [10] and Coq [5] proof assistants. This comparison is based on a case study involving the mechanisation of parts of the theory of computation in the two systems. This paper does not illustrate these mechanisations but rather discusses the differences between the two systems and backs up certain points by examples taken from the case studies. One motivation of this work is that many users of theo...
A proof of the S m n theorem in Coq
, 1997
"... This report describes the implementation of a mechanisation of the theory of computation in the Coq proof assistant which leads to a proof of the S m n theorem. This mechanisation is based on a model of computation similar to the partial recursive function model and includes the denition of a comput ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This report describes the implementation of a mechanisation of the theory of computation in the Coq proof assistant which leads to a proof of the S m n theorem. This mechanisation is based on a model of computation similar to the partial recursive function model and includes the denition of a computable function, proofs of the computability of a number of functions and the denition of an eective coding from the set of partial recursive functions to natural numbers. This work forms part of a comparative study of the HOL and Coq proof assistants.
Towards a judgmental reconstruction of logical relation proofs
, 2006
"... Abstract. Tait’s method (a.k.a. proof by logical relations) is a powerful proof technique frequently used for showing foundational properties of languages based on typed lambdacalculi. Historically, these proofs have been difficult to formalize in proof assistants with weak metalogics, such as Twe ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Tait’s method (a.k.a. proof by logical relations) is a powerful proof technique frequently used for showing foundational properties of languages based on typed lambdacalculi. Historically, these proofs have been difficult to formalize in proof assistants with weak metalogics, such as Twelf. Logical relations are notoriously difficult to define judgmentally. In this paper, we present and discuss a Twelf proof of weak normalization for System F making use of higherorder encodings. We exhibit a modular technique on how to formalize proofs of this kind, and make explicit all logical principles that one needs to trust in order believe in the proof. 1