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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 ..."
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. 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 ..."
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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.
System Fi A HigherOrder Polymorphic λCalculus with Erasable TermIndices
"... Abstract. We introduce a foundational lambda calculus, System Fi, for studying programming languages with termindexed datatypes – higherkinded datatypes whose indices range over data such as natural numbers or lists. System Fi is an extension of System Fω that introduces the minimal features needed ..."
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Abstract. We introduce a foundational lambda calculus, System Fi, for studying programming languages with termindexed datatypes – higherkinded datatypes whose indices range over data such as natural numbers or lists. System Fi is an extension of System Fω that introduces the minimal features needed to support termindexing. We show that System Fi provides a theory for analysing programs with termindexed types and also argue that it constitutes a basis for the design of logicallysound lightweight dependent programming languages. We establish erasure properties of Fitypes that capture the idea that termindices are discardable in that they are irrelevant for computation. Index erasure projects typing in System Fi to typing in System Fω. So,SystemFi inherits strong normalization and logical consistency from System Fω.
Modules as classes in Logical Frameworks with explicit substitution
, 1998
"... Using machine assisted proof systems to reason about mathematics and various aspects of programs and computer systems has gained a lot of attention by mathematicians and theoretical computer scientists during the last fifteen years. The work going on under the name Logical Frameworks [HuP91] is impl ..."
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Using machine assisted proof systems to reason about mathematics and various aspects of programs and computer systems has gained a lot of attention by mathematicians and theoretical computer scientists during the last fifteen years. The work going on under the name Logical Frameworks [HuP91] is implementations of general frameworks in which the user can define a logic or formal system and by doing so get a proof assistant or proof environment for this specific system. The various projects in Logical Frameworks use type theory as the framework language and there are several different (though related) implementations in work. This paper gives a suggestion to add classes to the framework language in order to enable modularization and reuse of denitions and proofs in different settings. It is based on the framework ALF [Mag95] with MartinLöf's explicit substitutions for type theory [Mar84, NPS90, Tas93] and uses many of the ideas of Simula [DMN70] with respect to the class concept. H...
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"... Issues paper commissioned by the Department of Education, Training and Youth Affairs to contribute to addressing the school student assessment and reporting aspects of the ..."
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Issues paper commissioned by the Department of Education, Training and Youth Affairs to contribute to addressing the school student assessment and reporting aspects of the