## The Implementation of ALF - a Proof Editor based on Martin-Löf's Monomorphic Type Theory with Explicit Substitution (1995)

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### BibTeX

@MISC{Magnusson95theimplementation,

author = {Lena Magnusson},

title = {The Implementation of ALF - a Proof Editor based on Martin-Löf's Monomorphic Type Theory with Explicit Substitution},

year = {1995}

}

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### Abstract

This thesis describes the implementation of ALF, which is an interactive proof editor based on Martin-Löf's type theory with explicit substitutions. ALF is a general purpose proof assistant, in which different logics can be represented. Proof objects are manipulated directly, by the usual editing operations. A partial proof is represented as an incomplete proof object, i.e., a proof object containing placeholders. A modular type/proof checking algorithm for complete proof objects is presented, and it is proved sound and complete assuming some basic meta theory properties of the substitution calculus. The algorithm is extended to handle incomplete objects in such a way that the type checking problem is reduced to a unication problem, i.e., the problem of finding instantiations to the placeholders in the object. Placeholders are represented together with their expected type and local context. We show that checking the correctness of instantiations can be localised, which means that it is e...