An Equational Logical Framework for Type Theories

Robert Harper

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arXiv · 2106.01484

An Equational Logical Framework for Type Theories

Robert Harper

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Abstract

A wide range of intuitionistic type theories may be presented as equational theories within a logical framework. This method was formulated by Per Martin-L\"{o}f in the mid-1980's and further developed by Uemura, who used it to prove an initiality result for a class of models. Herein is presented a logical framework for type theories that includes an extensional equality type so that a type theory may be given by a signature of constants. The framework is illustrated by a number of examples of type-theoretic concepts, including identity and equality types, and a hierarchy of universes.

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BibTeX RIS

Robert Harper. 2021-06-02. An Equational Logical Framework for Type Theories. https://arxiv.org/abs/2106.01484

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