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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...
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.