Abstract
An algebraic presentation of Martin-Löf’s intuitionistic type theory is given which is based on the notion of a category with families with extra structure. We then present a type-checking algorithm for the normal forms of this theory, and sketch how it gives rise to an initial category with families with extra structure. In this way we obtain a purely algebraic formulation of the correctness of the type-checking algorithm which provides the core of proof assistants for intuitionistic type theory.
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Abel, A., Coquand, T., Dybjer, P. (2008). On the Algebraic Foundation of Proof Assistants for Intuitionistic Type Theory. In: Garrigue, J., Hermenegildo, M.V. (eds) Functional and Logic Programming. FLOPS 2008. Lecture Notes in Computer Science, vol 4989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78969-7_2
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DOI: https://doi.org/10.1007/978-3-540-78969-7_2
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